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Electric and magnetic fields associated with sea tides in the English Channel
1970, Phys. Earth Planet. Interiors 4, 65—77. North-Holland Publishing Company, Amsterdam
ELECTRIC AND MAGNETIC FIELDS ASSOCIATED WITH SEA TIDES IN THE ENGLISH CHANNEL
C. OS000D*, W. G. V. ROSSER and N. I. W. WEBBER** Department of Physics, Exeter University, Exeter, England
Received 2 April 1970
The electric field 1 km from the coast at Sidmouth due to sea tides in the English Channel is 5 x 10~V ni’ (peak to peak) at 1 (peak to peak) at the x 10 ~gradiometer Vm the time time of ofspring neap tides tides. and A 2.5 magnetic was used to record the difference between the total magnetic fields at Sidmouth and at Exeter, which is 20 km from the coast. The dif-
1. Introduction
Aberystwyth and at several inland stations in the vicinity of Cardigan Bay, Wales. In view of this comprehensive work, only a brief review of our electric field measurements in the vicinity of the English Channel will be given. It has been known for some time that there are vanations in the Earth’s magnetic field of periods of 24 h, 12 h and 12.42 h. The quiet day magnetic field variation which varies with solar period is known as the Sq magnetic variation, and the variation with semi-diurnal lunar period (12.42 h) is known as the L 2 magnetic variation. Around midday, the Sq decrease in the total magnetic field at Sidmouth (geographic coordinates 50°40’ N, 3°15’ W, geomagnetic coordinates 540 20’ N, 9 80°6’ 30 to to 50 y, where (1970), 1 ~ = i0the tesla =E) 10is generally ~ gauss. about According WEEKES total L 2 magnetic variation in the total magnetic field observed at Sidmouth is about 6 y peak to peak during solar day. These magnetic field variations arise in two main ways. The gravitational attractions of the Sun and the Moon, and probably heating effects due to the Sun, give rise to mass motions in the ionosphere, and these can give rise to electric current systems in the ionosphere due to a dynamo action. These electric current systems give rise to magnetic field variations. These electric current systems in the ionosphere are of global dimensions, but since the conductivity of the
The prediction that emf’s would be induced in a sea moving across the Earth’s magnetic field under the influence of a tidal force was made as early as 1832 by Faraday who conducted an experiment at Waterloo Bridge, London. Faraday suspended electrodes in the River Thames, but he failed to observe a detectable tidal variation in the potential difference between the electrodes. The first recordings of tellunic potential differences varying with lunar period were made by Wollaston in 1851. A comprehensive review of early work on the potential differences due to sea tides was given by LONGUET-HIGGINS (1949), who also reported on work carriedthat outthe bypotential the British Admiralty. These results showed differences observed in the sea were proportional to the speed of the sea water in the tides, being greater at spring tides than at neap tides. Longuet-Higgins reported a few measurements on land a few kilometres from the coast. Longuet-Higgins gave a comprehensive theory for the electric field produced by sea water flowing with uniform velocity along an infinitely long channel of elliptic cross section. More recently, extensive measurements have been carried out by BROWN et a!. (1969) at *
Now with C.E.G.B., Berkeley Nuclear Laboratories, Berkeley,
**NOWWit1IB.P.
ference is separated into a solar component and a lunar compo nent of period 12.42 h. The latter variation is interpreted quantitatively in terms of a tidally induced electric current system in the English Channel. The magnitudes of other magnetic variations of 12.42 h period are discussed.
ionosphere is much greater on the day side of the Earth than on the night side, the electric current sys-
(Alaska) Inc., North Slope Oil Well, Alaska,
U.S.A.
65
66
C. OSGOOD, W. G. V. ROSSER AND N. J. W. WEBB ER
tems in the ionosphere are confined mainly to the day side. The gravitational attractions of the Sun and the Moon also give rise to the tidal motions of the waters in the seas and oceans. The motion of conducting sea water across the Earth’s magnetic field gives rise to motional emf’s in the sea, which in turn give rise to electric current systems in the sea, with some electric current flow in the land near the sea and in the rocks beneath the sea. References: HILL and MASON (1962), MALIN (1969, 1970), CHAPMAN and KENDALL (1970), KENDALL and CHAPMAN (1970). 2. Electric field measurements The theory of the production of emf’s induced by tidal motions in the sea is illustrated in figs. 1(a) and 1(b) for the special idealized case of an infinitely long channel of elliptic cross section with its axis along the z axis. Let the major axis of an elliptic cross section be
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Fig. 1. (a). A channel ofelliptic cross section. (b). The electric fields induced inside the channel by the moving conducting water.
of length 2a and be parallel to the x axis, and let the minor axis be of length 2b and be parallel to the y axis as shown in fig. 1(a). It will be assumed that the sea water in the channel is moving with uniform velocity u. It will be assumed, at present, that the rocks surrounding the channel are non-conducting. Consider a charge of magnitude q moving with the water. For the present, only the effect of the vertical component B~of the Earth’s magnetic field will be considered. Since it is moving in the Earth’s magnetic field, there is a magnetic force q u x B~acting on the charge q, which is moving with the water. Since the ions in sea water are relatively free to move, electric current will flow in the sea water until charge distributions are built up on the surfaces of the channel, which give rise to an electric field E0 inside the channel, which is equal and opposite to u xB~,as shown in fig. 1(b). When the steady state is reached, if no return electric current flows in the rocks or in the sea, the electric force qE0 is equal and opposite to the magnetic force qu x By on a charge of magnitude q moving with the sea water, and there is then no resultant force acting on the charge q. The charge distributions on the surface of the channel also give rise to electric fields outside the channel, as shown in fig. 1(b). The direction of the electric field along the x axis changes at the boundary of the channel as shown in fig. 1(b). The problem of calculating these surface charge distributions and the electric fields associated with them is similar to the electrostatic problem of a stationary conducting elliptic cross section cylinder in a uniform external electric field E0 numerically equal to uBy applied in a direction parallel to the major axis of the ellipse. In this case, charge distributions will be built up on the surface of the conducting cylinder, such that the external applied electric field E0 is compensated inside the conductor, giving zero electric field inside the conductor. The charge distribution and extra electric field due to these charge distributions should be the same as those built up when sea water flows with uniform velocity in the elliptic channel in the Earth’s magnetic field in fig. 1(a). [One could transform to a reference frame moving with velocity u relative to the laboratory, and in which the sea water is at rest. In this reference frame, there is 2/c2)4 associated an electric field equal to uBv/(l u with the Earth’s magnetic field. In this case the problem is the same as the electrostatic one.] —
67
ELECTRIC AND MAGNETIC FIELDS ASSOCIATED WITH SEA TIDES IN THE ENGLISH CHANNEL
Introduce elliptic cylindrical coordinates defined by x
=
c cosh
y
=
c sinh ~ sin
i~
cos
MAGNETIC GRADIOMETER
~ FE~JARY ~69
~,
ER i~,
where
c2 = a2—b2. Along the major axis, ~ = 0 and cos ~ = 1. The solution for the electric field outside the channel on the major axis for a>> b is then E E
—
0 e~sinh~
______________________________
(1)
The value of E depends on c which depends on b and a. Just outside the coast line E = (a/b)E0. The smaller b is, compared with a, the larger E becomes at the boundary. (This is consistent the fact thatalong E tends to infinity at a point). Ifb .ci~a,with for field points the x axis, the effect of the finite depth of the sea is only important for distances of the order of b from the coast. For a channel of elliptic cross section, the variation of E with distance from the coast would depend primarily on the width of the channel. In the theoretical discussion so far, the horizontal component BH of the Earth’s magnetic field has been neglected. The contribution ux BH to the motional emf gives rise to charge distributions on the top and bottom surfaces of the channel, which in turn give electric fields which only extend inland from the coast for distances of the order of the depth of the channel (~ 50 m in the case of the English Channel). The electric fields in the geomagnetic north—south and east—west directions have been measured at the Norman Lockyer Observatory, at Sidmouth, which is at a distance of 1 km from the coast of the English Channel, using probes in the ground 100 m apart. The electric field variation in the north—south direction for a typical day at the time of spring tides (16 February 1969) is shown in fig. 2(b). The variation of the electric field in the east—west direction (which is approximately parallel to the coast) at Sidmouth, was significantly smaller than the electric field in the north—south direction. Thus the resultant electric field at Sidmouth is approximately perpendicular to the coastline of the English Channel. The peak to peak amplitude of the electric potential difference variation in the north—south direction in fig. 2(b) at the time of spring tides, when the solar and lunar components of the sea tides are in
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Fig. 2. Theresults, results (b) for the a typical showing (a) the magnetic gradiometer Earth day, current records, (c) the water velocity up the English Channel at a distance ~ 10 km from Sidmouth.
phase, is about 5 mY between the two probes 100 m apart, so that the electric field variation is 5 x i0~ V m1 peak to peak. At the time of neap tides when the solar and lunar tidal effects are oppositely directed, the peak to peak variation in the electric field was generally about 2.5 x iO~V m 1, or about half the variation at the time of spring tides. This change in amplitude with a repetition period of approximately fourteen days suggests that sea tides produce the observed electric fields. The results presented in fig. 3 are for the north—south component of the electric field for the period 29 Janu-
68
C. OSGOOD, W. G. V. ROSSER AND N. J. W. WEBBER
EARTH CL~RENTS NGRTH-SOJTH 1969
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cient between the earth current variations for 16 February 1969 shown in fig. 2(b) and the water velocity up the English Channel shown in fig. 2(c) is 0.89 for zero time shift, and increases to 0.93 if the earth current results are shifted by half an hour. It can be seen from figs. 2(b) and 2(c) that the direction of the electric field at the Norman Lockyer Observatory is in the north direction when the sea water is moving up the English Channel. This is consistent with the directions shown in fig. 1(b) for the electric field outside the channel. At the time of spring tides, according to the Admiralty Pocket Tidal Stream Atlas (English and Bristol Channels), the maximum value of u, the speed of the water up the English Channel, is 0.85 knots, or 0.45 ms1, at a point ~ 10 km from the coast at Sidmouth. Since B~= 4.2 x 10 ~ tesla, at this position uB~= 2 x iO—~V nf’, so that the electric field E 0 inside the sea should be 2 x iO-~V m 1, if there were no return electric currents in the English Channel and in the sea bed. If it were assumed that, for the model of the channel shown in fig. 1(a), the velocity of water right
G.M.T. (b)
Fig. 3. Separation of the earth current records at Sidmouth for the period 29 January to 26 February 1969 into lunar and solar components. The lunar times quoted in fig. 3(a) are the number of lunar hours after the lower transit of the mean moon at Greenwich.
ary to 26 February 1969. If the data for this period are averaged in lunar time (24.84 h/d), then over a period as long as 28 d the component with solar period (24 h) and its harmonics should average out to zero. The resuits of this analysis are shown in fig. 3(a). The data were also averaged in solar time. Over a 28 d period, the lunar components should then average out. The results of this analysis are shown in fig. 3(b). It can be seen that, at Sidmouth, the electric field variation in the north—south direction, with semi-diurnal lunar period (12.42 h), is about double the electric field variation with semi-diurnal solar period (12 h). This ratio is roughly the same as the ratio of the tide producing forces due to the gravitational attractions of the Moon and of the Sun on the Earth respectively, The velocity of water up the English Channel at a point approximately 10 km from the coast at Sidmouth at the time of spring tides, taken from the Admiralty Pocket Tidal Stream Atlas (English and Bristol Channels) is shown in fig. 2(c). The correlation coeffi-
up to the coast were u = 0.45 m s~’,then from eq. (1), if the width of the elliptic cross section channel were 2a = 150 km, the expected electric intensity 1 km from the coast, corresponding to the position of the Norman Lockyer Observatory, would be E = 5.5E0 = 5.5uB~ whereas for 2a = 75 km, E should be equal to 2.8uBv, where, for u = 0.45 m 5~’, uB~= 2 X 10~ V m The observed value of E in fig. 2(b), at the time of spring tides, is 2.5 x 1O~V m’, that is half the peak to peak value. The experimental value is only 1.25 times the value of uB~,corresponding to u = 0.45 ms’. This is several times less than the value predicted using the value of the water velocity ~ 10 km from the coast. In practice, the tidal velocity of the sea water up the English Channel generally decreases significantly as one approaches the coast of the English Channel, and could be substantially less than 0.45 m s’ near the coast. The electric field on land 1 km from the coast depends primarily on the velocity of sea water within a few km of the coast. Since this may be several times less than the value ~ 10 km out, the value of E0 = uB~, and hence the predicted electric field near the coast may be several times less than the value calculated using u = 0.45 m s Such a reduction would give reasonable agreement between theory and experiment. Furthermore, the sea bed may not be as steep near the ‘.
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69
ELECTRIC AND MAGNETIC FIELDS ASSOCIATED WITH SEA TIDES IN THE ENGLISH CHANNEL
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70
C. OSGOOD, W. G. V. ROSSER AND N. J. W. WEBBER
coast at Sidmouth, that is, the depth of the sea water may not increase as rapidly as one goes towards the centre of the English Channel, as the elliptic cross section chosen would predict. This effect could also reduce the calculated electric field 1 km from the coast. Thus, with a reasonable choice of parameters it is possible to account semi-quantitatively for the magnitude, direction and phase of the electric fields observed at Sidmouth in terms of tidally induced emf’s in the English Channel. So far in this paper, electric current flow in the English Channel and in the rocks beneath the English Channel has been neglected. LONGUET-HIGGINS (1949) considered only an infinitely long channel. In that case, if the water velocity were the same everywhere along the channel, there would be no return electric currents in the channel itself. However, the flow of water up and down the English Channel is not uniform. The distribution of water flow in the English Channel for a time just after the time of high tide at Sidmouth, when the water velocity up the Channel is also a maximum, is shown in fig. 4. If B~is the vertical component of the Earth’s magnetic field, the local contribution to the motional emf in the Channel is proportional to u xB~.It is perpendicular to the arrows in fig. 4 and depends on u, the speed of the water up the Channel. For the time shown in fig. 4 the emf is more localised and is stronger between the Isle of Wight and the Cherbourg Peninsula than in the vicinity of Sidmouth. Such a distrubution of em.f’s could give an electric current system in the Channel of the type (number 1) shown in fig. 4, with the return current flowing in the regions of nearly slack water, for example in the Plymouth region or possibly even further out in the Atlantic Ocean for the case shown in fig. 4. (The distribution of localised emf’s perpendicular to the arrows in fig. 4 is somewhat reminiscent of the suggested distribution of emf’s in the ionosphere responsible for 5q’ where it is believed they produce electric current systems in the ionosphere). The effect of a return electric current flow in the English Channel would be to reduce the potential difference across the Channel and the electric fields on the land. There are also return electric currents in the rocks beneath the sea (type 2 in fig. 4). These electric currents would also reduce the electric fields on land. However, the calculations to be outlined in section 5 show that the combined effect of these two types of electric
current flow would be to reduce the potential difference across the English Channel by about 20 %. 3. Theory of the magnetic gradiometer The two observatories used in the present analysis were the Norman Lockyer Observatory at Sidmouth, which is 1 km from the coast of the English Channel, and the Sports field of the University of Exeter, which is ~ 20km from Sidmouth and the coast of the English Channel. Since the electric current systems due to tidal motions in the ionosphere are of global dimensions, the magnetic variations associated with these large scale ionospheric currents should have almost the same values at two observatories separated by 20 km, apart from any effects associated with coastal effects and local geological differences. It will be shown in section 4 that these latter effects are less than 2 % of the total magnetic field variations. Magnetic effects associated with tidally induced electric current systems in the English Channel should be more localised, since the dimensions of the electric current systems are smaller than the ionospheric electric current systems. Hence magnetic field variations associated with tidally induced electric current systems in the English Channel should differ significantly at Sidmouth and Exeter. Thus the residual magnetic field variation obtained by subtracting the total magnetic fields at Sidmouth and at Exeter should be due mainly to magnetic effects associated with tidally induced electric current systems in the English Channel. Two Varian rubidium vapour sensors were used, one at Sidmouth and one at Exeter. These sensors measure the total ambient magnetic field. The frequencies of the signals from the sensors, which were proportional to the total magnetic field, were both approximately 220 kHz. The 220 kHz signals at Sidmouth and Exeter were mixed with 219 kHz crystal oscillators to give A.F. signals of about 1 kHz each. A telephone link was used to transmit the A.F. signal from Sidmouth to Exeter. The two A.F. signals were demodulated separately to provide the variations in the total magnetic field at Sidmouth and Exeter respectively. The two A.F. signals were also mixed to give the difference between the total magnetic fields at Sidmouth and Exeter, Fuller details of the gradiometer circuits are given by OsGooD (1970). A typical section of the records is shown in fig. 5. The 5q variation can be seen on the total magnetic
ELECTRIC AND MAGNETIC FIELDS ASSOCIATED WITH SEA TIDES IN THE ENGLISH CHANNEL 800 GMT
1200 GMT
1~
.1~
28 APRIL 1969
71
noo GsrT
GRADIOMETER
~EW(atSI~H) Fig. 5.
A tracing of a typical record taken with the magnetic gradiometer, showing the variation in the total magnetic field at Sidmouth and the difference between the total magnetic fields at Exeter and Sidmouth (the gradiometer results).
field variations at around midday. The Sq variation is normally in the range 30—507. The Sq variation is not present to any large extent on the gradiometer (or difference) record, where a semi-diurnal magnetic variation of amplitude about 2.5 y peak to peak can be seen. This difference in the magnetic fields at Sidmouth and at Exeter will be attributed mainly to magnetic fields due to electric currents induced by tidal motions in the English Channel.
4. Magnetic gradiometer results The magnetic gradiometer results for a typical day at the time of spring tides (16 February 1969) showing the difference between the magnetic induction at Sidmouth and at Exeter are shown in fig. 2(a). The north— south electric field (perpendicular to the coastline) at a distance of 1 km from the coast at Sidmouth for the same day is shown in fig. 2(b). The velocity of water up the English Channel, at a distance ~ 10 km from the coast at Sidmouth at the time of spring tides (taken from the Admiralty Pocket Tidal Stream Atlas, English and Bristol Channels) is shown in fig. 2(c). The correlation coefficient between the gradiometer and water velocity is 0.71 for zero time shift. This increases to 0.93 if the gradiometer results are shifted by 1 h. (The
correlation coefficient between the earth current results and water velocity is 0.89 for zero time shift and increases to 0.93, if the earth current results are shifted by half an hour.) The correlation coefficient between the magnetic gradiometer and earth currents is 0.86 for zero time shift, increasing to 0.92, if the magnetic gradiometer results are shifted by half an hour. When the electric field at Sidmouth (1 km from the coast) is in the north direction, the magnetic gradiometer results show that the magnetic field at Sidmouth is generally greater than the magnetic field at Exeter. This could be due to an extra magnetic field in either the north or the vertical downwards direction or both at Sidmouth. The Idistribution of water flow up the English Channel at the time of high tide at Sidmouth (when the water velocity near Sidmouth is also at maximum) was shown in fig. 4. It was suggested in section 2 that the motional emf’s induced could give an electric current system in the English Channel of the type (number 1) shown in fig. 4. It follows from the righthand corkscrew rule that such a current system would give a magnetic field verticallydownwards at Sidmouth, increasing the total magnetic field at Sidmouth, at a time when the water near Sidmouth is moving up the Channel giving rise to an electric field in the north
72
C. OSGOOD, W. G. V. ROSSER AND N. J. W. WEBBER
direction at the Norman Lockyer Observatory. It will be shown in section 5 that such a model also accounts semi-quantitatively for the gradiometer results. The analysis of the results of 28 d continuous recordings with the magnetic gradiometer is shown in fig. 6. The results are for the same period, 29 January to 26 February 1969, as was used for the electric field results shown in fig. 3. (Similar results were obtained for other monthly periods.) The gradiometer data were smoothed to remove the effects of magnetic bays and storms and digitised every half hour. If these data are averaged in lunar time over a 28 d period, the solar component of the magnetic variations should average out to zero. The results of averaging in lunar time are shown in fig. 6(a). The variation shows predominantly an L2 semi-diurnal variation of period 12.42 h and amplitude 0.8 (or 1.6 ‘~‘peak to peak), the maximum (when the magnetic field at Sidmouth is greater than at Exeter) being approximately 1 h after lunar transit. The variation in fig. 6(a) represents the difference between ‘~‘
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the L2 magnetic variations of period 12.42 h at Sidmouth and Exeter. There may be a residual contribution to the total magnetic field at Exeter, associated with a tidally induced electric current system in the English Channel, so that the value of 1.67 peak to peak is probably a lower limit to the total tidally induced magnetic variation of period 12.42 h at Sidmouth. There are other magnetic variations of a period of 12.42 h, but these are likely to have almost the same values at Sidmouth and at Exeter, and will therefore not appear on the gradiometer. For example, there are magnetic effects associated with ionospheric currents and magnetic variations due to electric currents due to sea tides in the Atlantic Ocean (see CHAPMAN and KENDALL, 1970). The results of WEEKES (1970) have shown that the total L2 magnetic variation of period 12.42 h in the total magnetic field at Sidmouth is 6 y peak to peak during solar day and 4y to peak during solar night. If the data are averaged in solar time over the same 28 d period, the 12.42 h lunar component and its harmonics should average out to zero. The results of this analysis are shown in fig. 6(b). The magnetic variation, when averaged in solar time is bigger during solar day when Sq is present than during solar night. It is possible that this difference may be due, partly least, to local 5q atgiving slightly geological and coastal effects on different 5q variations at Sidmouth and Exeter. However, there may be another contributory factor. The two rubidium vapour magnetometers effectively measure the components of the magnetic variations in the direction of the Earth’s resultant magnetic field at Sidmouth and at Exeter, respectively. In order to obtain frequency differences such that the A.F. mixer worked satisfactorily, small compensating magnets were used with the sensors. Consequently, the directions of the resultant total magnetic fields at Sidmouth and at Exeter might differ by about 1°or so. If the magnetic variations at Sidmouth and at Exeter were the same in magnitude and direction, but the directions of the total fields differed by 1°,then the gradiometer would show a difference between Sidmouth and Exeter of
G.MI (b)
Fig. 6. Separation of the magnetic gradiometer results for the period 29 January to 26 February 1969 into lunar and solar cornponents. The lunar times quoted in (a) are the number of lunar hours after the lower transit of the mean moon at Greenwich. The peak in the afternoon in (b) is probably associated with Sq.
about 2 °/~ of the total variation in the magnetic field. Since Sq may be of the order of 507, a difference of 1° in the directions of the total fields at Sidmouth and at Exeter would give a 1 ~ variation in the gradiometer, which would be present during solar day only, when Sq
ELECTRIC AND MAGNETIC FIELDS ASSOCIATED WITH SEA TIDES IN THE ENGLISH CHANNEL
is present. This could account for most of the difference between solar day and solar night in fig. 6(b), though there may also be a contribution due to coastal effects. This makes it difficult to make any firm deductions about the amplitude of the magnetic variation of 12 h period due to sea tides, particularly during solar day when Sq is present. The result does show that the cornbined effects of coastal and geological differences between Sidmouth and Exeter, and effects due to a difference in the directions of the resultant total magnetic fields at Sidmouth and at Exeter amount to less than 2 °/~ of the total variations in the Earth’s magnetic field. The difference between the values at 21.00 h and 01.00 h, corresponding to the night time values in fig. 6(b) is 0.9 y. This compares with a peak to peak value of 1.67 for the lunar component in fig. 6(a). This is approximately the same as the ratio of the tide producing forces due to the Sun and the Moon, respectively, and is consistent with a sea tide origin for most of the variation of solar period (12 h) during solar night in fig. 6(b). Due to the uncertainties in the evaluation of the cornponent of the magnetic variations of solar period due to sea tides, due to the presence of the much larger 5q magnetic variation of ionospheric origin, the theories developed in section 5 will be applied to interpret the L 2 component of period 12.42 h in fig. 6(a).
73
(3). Magnetic fields due to electric current systems due to tides in the Atlantic Ocean. These effects will be considered separately. 5.1. Electric current systems in the English Channel There are so many variations in the parameters, such as the width, depth, speed of tidal waters, etc., in the English Channel that it has not proved possible to give a precise theory for this effect. A simplified model will be chosen, and it will be shown that with a reasonable choice of parameters, this model can account for the gradiometer results presented in fig. 6(a). A modification of the model given by KENDALL and CHAPMAN (1970) will be used. The model of the channel and the coordinate system used are shown in fig. 7. It was assumed that the channel was infinitely long, that the breadth was 2b = 150 km and the depth d = 50 m for a distance of 65 km on either side of the middle, and that the depth of the channel over the remaining distances s = 10 km on both sides decreased parabolically according to the relations depth = d 1~i1 for y> b—s, s i
depth
=
d 1~±~1 2 for y
<
—
(b
—
~sJ
5. Interpretation of the gradiometer results It was shown in section 4 that the contribution to the gradiometer results due to coastal effects, geological differences between Sidmouth and Exeter and differences in the directions of the total magnetic fields at Sidmouth and at Exeter amounted to less than 2 % of the total magnetic field variations at either station. WEEKES (1970) has shown that at Sidmouth the total magnetic variation of period 12.42 h during solar day is 67. Even if it were assumed that all of this variation were of ionospheric origin, it would only give a variation of 0.127 on the gradiometer. Hence the variation other possible sources suggest themselves: in fig. 6(a) is primarily not of ionospheric origin. Three (1). Tidally induced electric current systems, which are entirely in the sea of the English Channel (type 1 in fig. 4). (2). Tidally induced electric current systems across the English Channel with return currents in the rocks beneath the English Channel (type 2 in fig. 4).
respectively (see fig. 7). It was further assumed that the velocity of the water in the channel was zero in the outer regions (65 km < I y I < 75 km), and that in the central region (I y I < 65 km) there was a standing wave variation tidal velocity, such that the water type velocity up the of channel was v
=
v0 cos px cos wt.
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(2)
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~
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Fig. 7.
Model of the channel used to calculate tidally induced magnetic fields.
74
C. OSGOOD, W. G. V. ROSSER AND N. I. W. WEBB ER
The origin of the coordinate system was placed between the Isle of Wight and the Cherbourg Peninsula. The wavelength of the standing wave oscillation was given by 2 = 21t/p = 800km, so that the water velocity was zero at points ~ 200 km from the Isle of Wight. A value of x = + 100 km was chosen for Sidmouth. From the Admiralty Pocket Tidal Stream Atlas (English and Bristol Channels), the maximum water velocity up the English Channel between the Isle of Wight and the Cherbourg Peninsula is ~ 4 knots at the time of spring tides and ~ 2 knots at the time of neap tides. This suggests adopting a value of 3 knots for the component of the tidal velocity having a period of 12.42 h. According to LONGUET HIGGINS (1949), the average value of the tidal velocity of water in the English Channel is about 0.83 of the surface value. Hence the value chosen for v0 in eq. (2) was v0 = 1.4 m S’. The magnitude of the vertical component of the Earth’s magnetic field was taken to be 5 tesla (or 0.42 gauss). B~= 4.2 x i0 The value adopted for the conductivity of the sea was =
5 ~r~m’.
and CHAPMAN (1970) showed that electric current systems in the land were only important at large distances from the coastline. Since we are only interested in variations less than 20 km from the coastline, it will be sufficiently accurate in our case to assume in this calculation that the conductivity of the land is KENDALL
zero. Using a theory similar to that of
I
~ adv
sinhpy
0B~~cosh p(b J~,,~ o’dvoBvll
—
1
KENDALL
~
—
b) cosh p(y b) sinh p(y cothp(b—s) —
—
—
b)} (6)
~
Such a current system is in the same direction as type 1 in fig. 4 and would give a magnetic field vertically downwards at Sidmouth when the water flows up the English Channel, in agreement with the results presented in figs. 2(a) and (c). The vertical magnetic field at x = + 100 km was calculated by computer using the Biot—Savart law. The results obtained using the numerical values quoted for the parameters are shown in fig. 8. The Norman Lockyer Observatory at Sidmouth is 1 km from the coastline, at y = 76 km from the centre of the channel. Exeter was taken to be 20 km from the coastline at y = 95 km. The predicted difference between the vertical components of the magnetic field at Sidmouth and at Exeter has an amplitude of 0.75 y, or 1.5 y peak to peak. This gives a magnetic variation of 1.5 sin 2 = 1.4 ‘y in the direction of the resultant total magnetic field, where 2 = 67° is the dip angle. The value of 1.47 peak to peak compares with the experimental value of 1.67 peak to peak for the L2 compomodelofchosen can account for field the experimental results nent the resultant magnetic in fig. 6(a). Thus the obtained. The calculations suggest that there may be a residual magnetic variation of ~ 1 y peak to peak at Exeter, and that the total vertical magnetic field variation at Sidmouth due to tidally induced electric current systems in the English Channel may be 2.5 y peak to peak. VERTiCAL MN3NETIC FIELD I]JE 10 ELECTRIC CL~RENTS 14 T~E SH CHAN’~L
and 2~
pX,
(3)
iv
—
1
coshpy cosh p(b
I,
p 2~Z < ~
s) are given by
—
Sm
‘~
3Y
(in our case ps ~it 0.08), integrated current CHAPMAN (1970), can be then shownthethat provided ps ~ 1 densities in the region I y I <(b
adv0B~fp(y
—
s)i cos ix.
For the region b s
+
(4)
EXETER
—
—
—
—
Ic~i0
(5)
Fig. 8.
LIE The calculated tidally induced magnetic field.
10
km
ELECTRIC AND MAGNETIC FIELDS ASSOCIATED WITH SEA TIDES IN THE ENGLISH CHANNEL
5.2. Tidally induced current systems with return currents beneath the sea This is similar to the case considered by LONGUET(1949), except that Longuet-Higgins assumed that the velocity of the sea water was constant, and had the same value all along the Channel, in which case all HIGGINS
the return current would in the rocks beneath theelectric sea, and there flow should be nobemagnetic field at sea level outside the electric current system. This is similar to the case of an infinitely long solenoid carrying a uniform current. However, if the water velocity varied along the channel as given by eq. (2), there should be a magnetic field outside the electric current system. In order to make a rough estimate of this magnetic field and its variation from the coast, a very simplified model was used. It was assumed that for every value of x along the channel in fig. 7, the electric current flow across the channel could be calculated using Longuet-Higgins’ theory. It was then assumed that the return electric current flow was in the form of a semicircle of diameter 140 km, with the current across the channel varying with x as cos px. The magnetic field was then calculated by computer using the Biot—Savart law. The results showed that the magnetic variations (peak to peak) at Sidmouth in the north— south, east—west and vertical directions were 0.26, 0.12 and 0.15 y, respectively, whereas at Exeter the corresponding values were 0.21, 0.10 and 0.08 y, respectively. The magnitude of this magnetic field and its variation from the coast were both far too small to account for the gradiometer results presented in fig. 6(a). Thus this model can be eliminated as the main source of the gradiometer results, The two types of current flow discussed in sections 5.1 and 5.2 must be superimposed. This is like joining two resistors in parallel across a cell which has an internal resistance. The effect is to make the total current less than the sum of the currents obtained by treating two circuits of the cell and one resistor separately. However, the internal resistance across the English Channel is probably less than 20 % of the resistance for return current flow in the rocks. Also since the length of current flow in the current systems in the channel is much longer parallel to the coast than across the channel (b = 75 km whereas 2 = 800 km), the internal resistance is again ~ 20 % of the total resistance.
75
Hence the effect of superimposing the two effects should be to reduce the calculated values in fig. 8 by less than ~ 10 %. 5.3. Sea tides in the Atlantic Ocean The velocity of the sea water in the tides in the Atlantic Ocean are 0.03 to 0.10 m s’ compared with v0 ~ 1 in the English Channel. However, the depth 1.4the m sAtlantic Ocean is much greater than that of the of English Channel (5 km compared with 50 m), so that, though the induced emf’s are smaller, the total currents flowing may be larger in the Atlantic Ocean than in the English Channel. The spatial extent of the current systems should also be much larger in the Atlantic Ocean. HILL and MASON (1962) showed that, at a point 200 km southwest of Land’s End, there was an L 2 variation of ~ 307 peak to peak in the total magnetic field. LARSEN (1968) analysed data from San Miguel in the Azores and found an L2 magnetic variation of ~ 7 y peak to peak in the vertical component of the magnetic field. Thus there is some direct evidence for magnetic variations associated with tides in the Atlantic Ocean. Since the scale of the electric current systems in the Atlantic Ocean is probably 1000 km or more, the variation of the magnetic field away from the Continental Shelf should be fairly slow, and there should be significant contributions to the magnetic field all over the British Isles, due to tidally induced electric currents in the Atlantic Ocean. MALIN (1969, 1970) has investigated the L2 cornponent of the magnetic variations at solar midnight at several U.K. stations. For example, for Hartland Point, which is 100 km northwest of Sidmouth, near the North Devon coast, Maim finds that the peak to peak amplitudes of the L2 magnetic variations in the north—south, east—west and vertical components at solar midnight are 2.0, 5.6 and 3.5 7, respectively. CHAPMAN and KENDALL (1970) accounted quantitatively for the magnitude and phase of the east—west variations determined by Malin in terms of a tidally induced electric current flowing in the north—south direction in the Atlantic Ocean, with an image current system in the opposite direction at a depth of 500 km. The phase of the east—west L2 magnetic variation, determined by MALIN (1970) was almost the same at all the U.K. stations. This is consistent with a common origin for most of the L2 magnetic variations in the
76
C. OSGOOD, W. G. V. ROSSER AND N. J. W. WEBB ER
east—west direction in tidally induced electric current systems in the Atlantic Ocean. The theory of CHAPMAN and KENDALL (1970) confirmed that the changes over the U.K. in the magnitudes of the magnetic variations due to tides in the Atlantic Ocean should not be very large. Hence any effects associated with sea tides in the Atlantic Ocean should be virtually the same at Sidmouth and at Exeter, and give no significant contribution to the gradiometer readings in fig. 6(a), unless there is a significant leakage electric current from the Atlantic Ocean up the English Channel. 6. Discussion The only source of magnetic field variation of period 12.42 h, which gives a sufficient variation of the magnetic field away from the coast of the English Channel to account for the gradiometer results presented in fig. 6(a), is a tidally induced electric current system in the English Channel of the type discussed in section 5.1. The theory given in section 5.1 can account quantitatively for the magnetic gradiometer results in a way which is also consistent with the electric field measurements described in section 2. The present results cornplement those of CHAPMAN and KENDALL (1970), who discussed the effects of tides in the Atlantic Ocean. The gradiometer results illustrate the contribution due to more local effects in the English Channel. WEEKES (1970) has shown that at Sidmouth the L2 variation of period 12.42 h in the total magnetic field at Sidmouth is ~ 6 y peak to peak during solar day and ~ 4 ‘y peak to peak during solar night. The difference ~ 2 ~ between solar day and solar night is probably due to tidally induced ionospheric electric current systems during solar day, when the conductivity of the ionosphere is high. [MALIN (1969) showed that at Hartland Point the L2 variation in the vertical component of the magnetic field was 6.4 y peak to peak during solar day and 3.3 y peak to peak during solar night.] Of the L2 variation of 4 y in the total magnetic field at Sidmouth during solar night, according to the calculations given in section 5.1, about 2.5 sin 2 ~ 2.3 ‘y is probably due to tidally induced electric current systems in the English Channel. The calculations given in seetion 5.2 suggest that there may be an L2 variation of 0.3 y in the total magnetic field due to a solenoidal type of electric current flow, with the return currents beneath the sea, of the type discussed in section 5.2. This
leaves anL2 variation of about 1.47 peak to peak in the total magnetic field, which is probably due mainly to tides in the Atlantic Ocean. Preliminary results with a fluxgate magnetometer at Sidmouth have shown that there is an L2 variation of ~ 1.2 y peak to peak in the north—south component of the magnetic field. Since this variation is not in the vertical direction, it is not due to a current system in the English Channel and is probably mainly due to tides in the Atlantic Ocean. This variation would give a variation of 1.2 cos 2 = 0.5 y in the direction of the total magnetic field. This would leave a remainder of about 0.9y in the total magnetic field (or ~ 1.07 peak to peak in the vertical direction) unaccounted for. (This value could be significantly larger if the phases of the various contributions were very different.) Such a value is quite consistent with the estimates of CHAPMAN and KENDALL (1970) for the expected effects in the vertical direction due to sea tides in the Atlantic Ocean. The above subdivision of the 67 peak to peak L2 variation in the total magnetic field at Sidmouth during solar day is very tentative, and is merely meant to indicate the approximate magnitudes of the various possible contributions. In addition, the preliminary fluxgate results at Sidmouth show that there is an L2 magnetic variation of ~ 6 y peak to peak in the geomagnetic east—west direction at Sidmouth. This variation has no component in the direction of the Earth’s resultant magnetic field and does not contribute to the magnetic variations recorded by the rubidium vapour magnetometers and the gradiometer. This variation is probably mainly due to tides in the Atlantic Ocean. Acknowledgments The work described in this paper was carried out at the Norman Lockyer Observatory, Sidmouth, as part of the research program of the Geophysics Section of the Department of Physics, Exeter University. We are very gratefui to the Council of the Corporation of the Observatory for allowing us to use the Observatory as a field station. We would like to thank Dr. K. Weekes, Dr. D. M. Schlapp, Dr. M. Sewter, Mr. G. M. Brown, Professor P. C. Kendall, Mr. S. R. C. Malin and Commander Glen, R. N., for valuable discussions. We would like to thank Mr. G. H. Davey, Mr. J. Denner, Mr. R. Duncan and Mr. R. Bee for their help in the run-
ELECTRIC AND MAGNETIC FIELDS ASSOCIATED WITH SEA TIDES IN THE ENGLISH CHANNEL
ning of the apparatus and in the analysis of the data. We would like to thank the Controller H. M. Stationary Office and the Hydrographer of the Navy for their permission to reproduce fig. 4 References BROWN,
G. M. et al. (1969), Private communication. S. and P. C. KENDALL (1970), Planet. Space Sci., in
CHAPMAN,
press.
77
HILL, M. N. and C. S. MASON (1962), Nature 195, 356. KENDALL, P. C. and S. CHAPMAN (1970), Quart. J. Mech. AppI. Math., in press. LARSEN, J. C. (1968), Geophys. J. 16, 47. LONGIJET-HIGGINS, M. S. (1949), Monthly Notices Roy. Astron. Soc. Geophys. Suppi. 5 (8). MALIN, S. R. C. (1969), Planet. Space Sci. 17, 487. MALIN, S. R. C. (1970), Private communication. OSGOOD C. (1970), Rev. Phys. Appl. 5, 113. WEEKEs, K. E. (1970), Private communication.
ELECTRIC AND MAGNETIC FIELDS ASSOCIATED WITH SEA TIDES IN THE ENGLISH CHANNEL
C. OS000D*, W. G. V. ROSSER and N. I. W. WEBBER** Department of Physics, Exeter University, Exeter, England
Received 2 April 1970
The electric field 1 km from the coast at Sidmouth due to sea tides in the English Channel is 5 x 10~V ni’ (peak to peak) at 1 (peak to peak) at the x 10 ~gradiometer Vm the time time of ofspring neap tides tides. and A 2.5 magnetic was used to record the difference between the total magnetic fields at Sidmouth and at Exeter, which is 20 km from the coast. The dif-
1. Introduction
Aberystwyth and at several inland stations in the vicinity of Cardigan Bay, Wales. In view of this comprehensive work, only a brief review of our electric field measurements in the vicinity of the English Channel will be given. It has been known for some time that there are vanations in the Earth’s magnetic field of periods of 24 h, 12 h and 12.42 h. The quiet day magnetic field variation which varies with solar period is known as the Sq magnetic variation, and the variation with semi-diurnal lunar period (12.42 h) is known as the L 2 magnetic variation. Around midday, the Sq decrease in the total magnetic field at Sidmouth (geographic coordinates 50°40’ N, 3°15’ W, geomagnetic coordinates 540 20’ N, 9 80°6’ 30 to to 50 y, where (1970), 1 ~ = i0the tesla =E) 10is generally ~ gauss. about According WEEKES total L 2 magnetic variation in the total magnetic field observed at Sidmouth is about 6 y peak to peak during solar day. These magnetic field variations arise in two main ways. The gravitational attractions of the Sun and the Moon, and probably heating effects due to the Sun, give rise to mass motions in the ionosphere, and these can give rise to electric current systems in the ionosphere due to a dynamo action. These electric current systems give rise to magnetic field variations. These electric current systems in the ionosphere are of global dimensions, but since the conductivity of the
The prediction that emf’s would be induced in a sea moving across the Earth’s magnetic field under the influence of a tidal force was made as early as 1832 by Faraday who conducted an experiment at Waterloo Bridge, London. Faraday suspended electrodes in the River Thames, but he failed to observe a detectable tidal variation in the potential difference between the electrodes. The first recordings of tellunic potential differences varying with lunar period were made by Wollaston in 1851. A comprehensive review of early work on the potential differences due to sea tides was given by LONGUET-HIGGINS (1949), who also reported on work carriedthat outthe bypotential the British Admiralty. These results showed differences observed in the sea were proportional to the speed of the sea water in the tides, being greater at spring tides than at neap tides. Longuet-Higgins reported a few measurements on land a few kilometres from the coast. Longuet-Higgins gave a comprehensive theory for the electric field produced by sea water flowing with uniform velocity along an infinitely long channel of elliptic cross section. More recently, extensive measurements have been carried out by BROWN et a!. (1969) at *
Now with C.E.G.B., Berkeley Nuclear Laboratories, Berkeley,
**NOWWit1IB.P.
ference is separated into a solar component and a lunar compo nent of period 12.42 h. The latter variation is interpreted quantitatively in terms of a tidally induced electric current system in the English Channel. The magnitudes of other magnetic variations of 12.42 h period are discussed.
ionosphere is much greater on the day side of the Earth than on the night side, the electric current sys-
(Alaska) Inc., North Slope Oil Well, Alaska,
U.S.A.
65
66
C. OSGOOD, W. G. V. ROSSER AND N. J. W. WEBB ER
tems in the ionosphere are confined mainly to the day side. The gravitational attractions of the Sun and the Moon also give rise to the tidal motions of the waters in the seas and oceans. The motion of conducting sea water across the Earth’s magnetic field gives rise to motional emf’s in the sea, which in turn give rise to electric current systems in the sea, with some electric current flow in the land near the sea and in the rocks beneath the sea. References: HILL and MASON (1962), MALIN (1969, 1970), CHAPMAN and KENDALL (1970), KENDALL and CHAPMAN (1970). 2. Electric field measurements The theory of the production of emf’s induced by tidal motions in the sea is illustrated in figs. 1(a) and 1(b) for the special idealized case of an infinitely long channel of elliptic cross section with its axis along the z axis. Let the major axis of an elliptic cross section be
/ /
~,
\~t~ Flaw
________
~
quB~ ~ _______
S
T2b
//
/
~,
(a)
~ _______
E
(
___________
~
E
________
_________
ib)
Fig. 1. (a). A channel ofelliptic cross section. (b). The electric fields induced inside the channel by the moving conducting water.
of length 2a and be parallel to the x axis, and let the minor axis be of length 2b and be parallel to the y axis as shown in fig. 1(a). It will be assumed that the sea water in the channel is moving with uniform velocity u. It will be assumed, at present, that the rocks surrounding the channel are non-conducting. Consider a charge of magnitude q moving with the water. For the present, only the effect of the vertical component B~of the Earth’s magnetic field will be considered. Since it is moving in the Earth’s magnetic field, there is a magnetic force q u x B~acting on the charge q, which is moving with the water. Since the ions in sea water are relatively free to move, electric current will flow in the sea water until charge distributions are built up on the surfaces of the channel, which give rise to an electric field E0 inside the channel, which is equal and opposite to u xB~,as shown in fig. 1(b). When the steady state is reached, if no return electric current flows in the rocks or in the sea, the electric force qE0 is equal and opposite to the magnetic force qu x By on a charge of magnitude q moving with the sea water, and there is then no resultant force acting on the charge q. The charge distributions on the surface of the channel also give rise to electric fields outside the channel, as shown in fig. 1(b). The direction of the electric field along the x axis changes at the boundary of the channel as shown in fig. 1(b). The problem of calculating these surface charge distributions and the electric fields associated with them is similar to the electrostatic problem of a stationary conducting elliptic cross section cylinder in a uniform external electric field E0 numerically equal to uBy applied in a direction parallel to the major axis of the ellipse. In this case, charge distributions will be built up on the surface of the conducting cylinder, such that the external applied electric field E0 is compensated inside the conductor, giving zero electric field inside the conductor. The charge distribution and extra electric field due to these charge distributions should be the same as those built up when sea water flows with uniform velocity in the elliptic channel in the Earth’s magnetic field in fig. 1(a). [One could transform to a reference frame moving with velocity u relative to the laboratory, and in which the sea water is at rest. In this reference frame, there is 2/c2)4 associated an electric field equal to uBv/(l u with the Earth’s magnetic field. In this case the problem is the same as the electrostatic one.] —
67
ELECTRIC AND MAGNETIC FIELDS ASSOCIATED WITH SEA TIDES IN THE ENGLISH CHANNEL
Introduce elliptic cylindrical coordinates defined by x
=
c cosh
y
=
c sinh ~ sin
i~
cos
MAGNETIC GRADIOMETER
~ FE~JARY ~69
~,
ER i~,
where
c2 = a2—b2. Along the major axis, ~ = 0 and cos ~ = 1. The solution for the electric field outside the channel on the major axis for a>> b is then E E
—
0 e~sinh~
______________________________
(1)
The value of E depends on c which depends on b and a. Just outside the coast line E = (a/b)E0. The smaller b is, compared with a, the larger E becomes at the boundary. (This is consistent the fact thatalong E tends to infinity at a point). Ifb .ci~a,with for field points the x axis, the effect of the finite depth of the sea is only important for distances of the order of b from the coast. For a channel of elliptic cross section, the variation of E with distance from the coast would depend primarily on the width of the channel. In the theoretical discussion so far, the horizontal component BH of the Earth’s magnetic field has been neglected. The contribution ux BH to the motional emf gives rise to charge distributions on the top and bottom surfaces of the channel, which in turn give electric fields which only extend inland from the coast for distances of the order of the depth of the channel (~ 50 m in the case of the English Channel). The electric fields in the geomagnetic north—south and east—west directions have been measured at the Norman Lockyer Observatory, at Sidmouth, which is at a distance of 1 km from the coast of the English Channel, using probes in the ground 100 m apart. The electric field variation in the north—south direction for a typical day at the time of spring tides (16 February 1969) is shown in fig. 2(b). The variation of the electric field in the east—west direction (which is approximately parallel to the coast) at Sidmouth, was significantly smaller than the electric field in the north—south direction. Thus the resultant electric field at Sidmouth is approximately perpendicular to the coastline of the English Channel. The peak to peak amplitude of the electric potential difference variation in the north—south direction in fig. 2(b) at the time of spring tides, when the solar and lunar components of the sea tides are in
EARTH
I
I
I
—
TH~~H) ~JENIS(~
I
I
I
I
WATER VELOCITY UP TFE ENGLISH CHANNEL FEAR ~DMCUTH
~TS
I-SGH iiz AT SD1V~JTH
05. 0
Cc)
0
2
4 GM.T.
Fig. 2. Theresults, results (b) for the a typical showing (a) the magnetic gradiometer Earth day, current records, (c) the water velocity up the English Channel at a distance ~ 10 km from Sidmouth.
phase, is about 5 mY between the two probes 100 m apart, so that the electric field variation is 5 x i0~ V m1 peak to peak. At the time of neap tides when the solar and lunar tidal effects are oppositely directed, the peak to peak variation in the electric field was generally about 2.5 x iO~V m 1, or about half the variation at the time of spring tides. This change in amplitude with a repetition period of approximately fourteen days suggests that sea tides produce the observed electric fields. The results presented in fig. 3 are for the north—south component of the electric field for the period 29 Janu-
68
C. OSGOOD, W. G. V. ROSSER AND N. J. W. WEBBER
EARTH CL~RENTS NGRTH-SOJTH 1969
0
I
I
2
4
6
8
P3
12
LUNAR
14
16
TIME
I
I
I
18
20
22
24
(a)
~LAR
I
2
4
I
I
I
•
6
8
10
12
liME
I
14
16
18
20
22
24
cient between the earth current variations for 16 February 1969 shown in fig. 2(b) and the water velocity up the English Channel shown in fig. 2(c) is 0.89 for zero time shift, and increases to 0.93 if the earth current results are shifted by half an hour. It can be seen from figs. 2(b) and 2(c) that the direction of the electric field at the Norman Lockyer Observatory is in the north direction when the sea water is moving up the English Channel. This is consistent with the directions shown in fig. 1(b) for the electric field outside the channel. At the time of spring tides, according to the Admiralty Pocket Tidal Stream Atlas (English and Bristol Channels), the maximum value of u, the speed of the water up the English Channel, is 0.85 knots, or 0.45 ms1, at a point ~ 10 km from the coast at Sidmouth. Since B~= 4.2 x 10 ~ tesla, at this position uB~= 2 x iO—~V nf’, so that the electric field E 0 inside the sea should be 2 x iO-~V m 1, if there were no return electric currents in the English Channel and in the sea bed. If it were assumed that, for the model of the channel shown in fig. 1(a), the velocity of water right
G.M.T. (b)
Fig. 3. Separation of the earth current records at Sidmouth for the period 29 January to 26 February 1969 into lunar and solar components. The lunar times quoted in fig. 3(a) are the number of lunar hours after the lower transit of the mean moon at Greenwich.
ary to 26 February 1969. If the data for this period are averaged in lunar time (24.84 h/d), then over a period as long as 28 d the component with solar period (24 h) and its harmonics should average out to zero. The resuits of this analysis are shown in fig. 3(a). The data were also averaged in solar time. Over a 28 d period, the lunar components should then average out. The results of this analysis are shown in fig. 3(b). It can be seen that, at Sidmouth, the electric field variation in the north—south direction, with semi-diurnal lunar period (12.42 h), is about double the electric field variation with semi-diurnal solar period (12 h). This ratio is roughly the same as the ratio of the tide producing forces due to the gravitational attractions of the Moon and of the Sun on the Earth respectively, The velocity of water up the English Channel at a point approximately 10 km from the coast at Sidmouth at the time of spring tides, taken from the Admiralty Pocket Tidal Stream Atlas (English and Bristol Channels) is shown in fig. 2(c). The correlation coeffi-
up to the coast were u = 0.45 m s~’,then from eq. (1), if the width of the elliptic cross section channel were 2a = 150 km, the expected electric intensity 1 km from the coast, corresponding to the position of the Norman Lockyer Observatory, would be E = 5.5E0 = 5.5uB~ whereas for 2a = 75 km, E should be equal to 2.8uBv, where, for u = 0.45 m 5~’, uB~= 2 X 10~ V m The observed value of E in fig. 2(b), at the time of spring tides, is 2.5 x 1O~V m’, that is half the peak to peak value. The experimental value is only 1.25 times the value of uB~,corresponding to u = 0.45 ms’. This is several times less than the value predicted using the value of the water velocity ~ 10 km from the coast. In practice, the tidal velocity of the sea water up the English Channel generally decreases significantly as one approaches the coast of the English Channel, and could be substantially less than 0.45 m s’ near the coast. The electric field on land 1 km from the coast depends primarily on the velocity of sea water within a few km of the coast. Since this may be several times less than the value ~ 10 km out, the value of E0 = uB~, and hence the predicted electric field near the coast may be several times less than the value calculated using u = 0.45 m s Such a reduction would give reasonable agreement between theory and experiment. Furthermore, the sea bed may not be as steep near the ‘.
— ~.
69
ELECTRIC AND MAGNETIC FIELDS ASSOCIATED WITH SEA TIDES IN THE ENGLISH CHANNEL
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70
C. OSGOOD, W. G. V. ROSSER AND N. J. W. WEBBER
coast at Sidmouth, that is, the depth of the sea water may not increase as rapidly as one goes towards the centre of the English Channel, as the elliptic cross section chosen would predict. This effect could also reduce the calculated electric field 1 km from the coast. Thus, with a reasonable choice of parameters it is possible to account semi-quantitatively for the magnitude, direction and phase of the electric fields observed at Sidmouth in terms of tidally induced emf’s in the English Channel. So far in this paper, electric current flow in the English Channel and in the rocks beneath the English Channel has been neglected. LONGUET-HIGGINS (1949) considered only an infinitely long channel. In that case, if the water velocity were the same everywhere along the channel, there would be no return electric currents in the channel itself. However, the flow of water up and down the English Channel is not uniform. The distribution of water flow in the English Channel for a time just after the time of high tide at Sidmouth, when the water velocity up the Channel is also a maximum, is shown in fig. 4. If B~is the vertical component of the Earth’s magnetic field, the local contribution to the motional emf in the Channel is proportional to u xB~.It is perpendicular to the arrows in fig. 4 and depends on u, the speed of the water up the Channel. For the time shown in fig. 4 the emf is more localised and is stronger between the Isle of Wight and the Cherbourg Peninsula than in the vicinity of Sidmouth. Such a distrubution of em.f’s could give an electric current system in the Channel of the type (number 1) shown in fig. 4, with the return current flowing in the regions of nearly slack water, for example in the Plymouth region or possibly even further out in the Atlantic Ocean for the case shown in fig. 4. (The distribution of localised emf’s perpendicular to the arrows in fig. 4 is somewhat reminiscent of the suggested distribution of emf’s in the ionosphere responsible for 5q’ where it is believed they produce electric current systems in the ionosphere). The effect of a return electric current flow in the English Channel would be to reduce the potential difference across the Channel and the electric fields on the land. There are also return electric currents in the rocks beneath the sea (type 2 in fig. 4). These electric currents would also reduce the electric fields on land. However, the calculations to be outlined in section 5 show that the combined effect of these two types of electric
current flow would be to reduce the potential difference across the English Channel by about 20 %. 3. Theory of the magnetic gradiometer The two observatories used in the present analysis were the Norman Lockyer Observatory at Sidmouth, which is 1 km from the coast of the English Channel, and the Sports field of the University of Exeter, which is ~ 20km from Sidmouth and the coast of the English Channel. Since the electric current systems due to tidal motions in the ionosphere are of global dimensions, the magnetic variations associated with these large scale ionospheric currents should have almost the same values at two observatories separated by 20 km, apart from any effects associated with coastal effects and local geological differences. It will be shown in section 4 that these latter effects are less than 2 % of the total magnetic field variations. Magnetic effects associated with tidally induced electric current systems in the English Channel should be more localised, since the dimensions of the electric current systems are smaller than the ionospheric electric current systems. Hence magnetic field variations associated with tidally induced electric current systems in the English Channel should differ significantly at Sidmouth and Exeter. Thus the residual magnetic field variation obtained by subtracting the total magnetic fields at Sidmouth and at Exeter should be due mainly to magnetic effects associated with tidally induced electric current systems in the English Channel. Two Varian rubidium vapour sensors were used, one at Sidmouth and one at Exeter. These sensors measure the total ambient magnetic field. The frequencies of the signals from the sensors, which were proportional to the total magnetic field, were both approximately 220 kHz. The 220 kHz signals at Sidmouth and Exeter were mixed with 219 kHz crystal oscillators to give A.F. signals of about 1 kHz each. A telephone link was used to transmit the A.F. signal from Sidmouth to Exeter. The two A.F. signals were demodulated separately to provide the variations in the total magnetic field at Sidmouth and Exeter respectively. The two A.F. signals were also mixed to give the difference between the total magnetic fields at Sidmouth and Exeter, Fuller details of the gradiometer circuits are given by OsGooD (1970). A typical section of the records is shown in fig. 5. The 5q variation can be seen on the total magnetic
ELECTRIC AND MAGNETIC FIELDS ASSOCIATED WITH SEA TIDES IN THE ENGLISH CHANNEL 800 GMT
1200 GMT
1~
.1~
28 APRIL 1969
71
noo GsrT
GRADIOMETER
~EW(atSI~H) Fig. 5.
A tracing of a typical record taken with the magnetic gradiometer, showing the variation in the total magnetic field at Sidmouth and the difference between the total magnetic fields at Exeter and Sidmouth (the gradiometer results).
field variations at around midday. The Sq variation is normally in the range 30—507. The Sq variation is not present to any large extent on the gradiometer (or difference) record, where a semi-diurnal magnetic variation of amplitude about 2.5 y peak to peak can be seen. This difference in the magnetic fields at Sidmouth and at Exeter will be attributed mainly to magnetic fields due to electric currents induced by tidal motions in the English Channel.
4. Magnetic gradiometer results The magnetic gradiometer results for a typical day at the time of spring tides (16 February 1969) showing the difference between the magnetic induction at Sidmouth and at Exeter are shown in fig. 2(a). The north— south electric field (perpendicular to the coastline) at a distance of 1 km from the coast at Sidmouth for the same day is shown in fig. 2(b). The velocity of water up the English Channel, at a distance ~ 10 km from the coast at Sidmouth at the time of spring tides (taken from the Admiralty Pocket Tidal Stream Atlas, English and Bristol Channels) is shown in fig. 2(c). The correlation coefficient between the gradiometer and water velocity is 0.71 for zero time shift. This increases to 0.93 if the gradiometer results are shifted by 1 h. (The
correlation coefficient between the earth current results and water velocity is 0.89 for zero time shift and increases to 0.93, if the earth current results are shifted by half an hour.) The correlation coefficient between the magnetic gradiometer and earth currents is 0.86 for zero time shift, increasing to 0.92, if the magnetic gradiometer results are shifted by half an hour. When the electric field at Sidmouth (1 km from the coast) is in the north direction, the magnetic gradiometer results show that the magnetic field at Sidmouth is generally greater than the magnetic field at Exeter. This could be due to an extra magnetic field in either the north or the vertical downwards direction or both at Sidmouth. The Idistribution of water flow up the English Channel at the time of high tide at Sidmouth (when the water velocity near Sidmouth is also at maximum) was shown in fig. 4. It was suggested in section 2 that the motional emf’s induced could give an electric current system in the English Channel of the type (number 1) shown in fig. 4. It follows from the righthand corkscrew rule that such a current system would give a magnetic field verticallydownwards at Sidmouth, increasing the total magnetic field at Sidmouth, at a time when the water near Sidmouth is moving up the Channel giving rise to an electric field in the north
72
C. OSGOOD, W. G. V. ROSSER AND N. J. W. WEBBER
direction at the Norman Lockyer Observatory. It will be shown in section 5 that such a model also accounts semi-quantitatively for the gradiometer results. The analysis of the results of 28 d continuous recordings with the magnetic gradiometer is shown in fig. 6. The results are for the same period, 29 January to 26 February 1969, as was used for the electric field results shown in fig. 3. (Similar results were obtained for other monthly periods.) The gradiometer data were smoothed to remove the effects of magnetic bays and storms and digitised every half hour. If these data are averaged in lunar time over a 28 d period, the solar component of the magnetic variations should average out to zero. The results of averaging in lunar time are shown in fig. 6(a). The variation shows predominantly an L2 semi-diurnal variation of period 12.42 h and amplitude 0.8 (or 1.6 ‘~‘peak to peak), the maximum (when the magnetic field at Sidmouth is greater than at Exeter) being approximately 1 h after lunar transit. The variation in fig. 6(a) represents the difference between ‘~‘
GNADI~tvETER
0
2
4
6
8
LUNAR TIME
~
12
~
2~ 24
SOLAR TIME
__________________________________________ 0
2
4
6
10
1~
14
4)
18
20
2~ 24
the L2 magnetic variations of period 12.42 h at Sidmouth and Exeter. There may be a residual contribution to the total magnetic field at Exeter, associated with a tidally induced electric current system in the English Channel, so that the value of 1.67 peak to peak is probably a lower limit to the total tidally induced magnetic variation of period 12.42 h at Sidmouth. There are other magnetic variations of a period of 12.42 h, but these are likely to have almost the same values at Sidmouth and at Exeter, and will therefore not appear on the gradiometer. For example, there are magnetic effects associated with ionospheric currents and magnetic variations due to electric currents due to sea tides in the Atlantic Ocean (see CHAPMAN and KENDALL, 1970). The results of WEEKES (1970) have shown that the total L2 magnetic variation of period 12.42 h in the total magnetic field at Sidmouth is 6 y peak to peak during solar day and 4y to peak during solar night. If the data are averaged in solar time over the same 28 d period, the 12.42 h lunar component and its harmonics should average out to zero. The results of this analysis are shown in fig. 6(b). The magnetic variation, when averaged in solar time is bigger during solar day when Sq is present than during solar night. It is possible that this difference may be due, partly least, to local 5q atgiving slightly geological and coastal effects on different 5q variations at Sidmouth and Exeter. However, there may be another contributory factor. The two rubidium vapour magnetometers effectively measure the components of the magnetic variations in the direction of the Earth’s resultant magnetic field at Sidmouth and at Exeter, respectively. In order to obtain frequency differences such that the A.F. mixer worked satisfactorily, small compensating magnets were used with the sensors. Consequently, the directions of the resultant total magnetic fields at Sidmouth and at Exeter might differ by about 1°or so. If the magnetic variations at Sidmouth and at Exeter were the same in magnitude and direction, but the directions of the total fields differed by 1°,then the gradiometer would show a difference between Sidmouth and Exeter of
G.MI (b)
Fig. 6. Separation of the magnetic gradiometer results for the period 29 January to 26 February 1969 into lunar and solar cornponents. The lunar times quoted in (a) are the number of lunar hours after the lower transit of the mean moon at Greenwich. The peak in the afternoon in (b) is probably associated with Sq.
about 2 °/~ of the total variation in the magnetic field. Since Sq may be of the order of 507, a difference of 1° in the directions of the total fields at Sidmouth and at Exeter would give a 1 ~ variation in the gradiometer, which would be present during solar day only, when Sq
ELECTRIC AND MAGNETIC FIELDS ASSOCIATED WITH SEA TIDES IN THE ENGLISH CHANNEL
is present. This could account for most of the difference between solar day and solar night in fig. 6(b), though there may also be a contribution due to coastal effects. This makes it difficult to make any firm deductions about the amplitude of the magnetic variation of 12 h period due to sea tides, particularly during solar day when Sq is present. The result does show that the cornbined effects of coastal and geological differences between Sidmouth and Exeter, and effects due to a difference in the directions of the resultant total magnetic fields at Sidmouth and at Exeter amount to less than 2 °/~ of the total variations in the Earth’s magnetic field. The difference between the values at 21.00 h and 01.00 h, corresponding to the night time values in fig. 6(b) is 0.9 y. This compares with a peak to peak value of 1.67 for the lunar component in fig. 6(a). This is approximately the same as the ratio of the tide producing forces due to the Sun and the Moon, respectively, and is consistent with a sea tide origin for most of the variation of solar period (12 h) during solar night in fig. 6(b). Due to the uncertainties in the evaluation of the cornponent of the magnetic variations of solar period due to sea tides, due to the presence of the much larger 5q magnetic variation of ionospheric origin, the theories developed in section 5 will be applied to interpret the L 2 component of period 12.42 h in fig. 6(a).
73
(3). Magnetic fields due to electric current systems due to tides in the Atlantic Ocean. These effects will be considered separately. 5.1. Electric current systems in the English Channel There are so many variations in the parameters, such as the width, depth, speed of tidal waters, etc., in the English Channel that it has not proved possible to give a precise theory for this effect. A simplified model will be chosen, and it will be shown that with a reasonable choice of parameters, this model can account for the gradiometer results presented in fig. 6(a). A modification of the model given by KENDALL and CHAPMAN (1970) will be used. The model of the channel and the coordinate system used are shown in fig. 7. It was assumed that the channel was infinitely long, that the breadth was 2b = 150 km and the depth d = 50 m for a distance of 65 km on either side of the middle, and that the depth of the channel over the remaining distances s = 10 km on both sides decreased parabolically according to the relations depth = d 1~i1 for y> b—s, s i
depth
=
d 1~±~1 2 for y
<
—
(b
—
~sJ
5. Interpretation of the gradiometer results It was shown in section 4 that the contribution to the gradiometer results due to coastal effects, geological differences between Sidmouth and Exeter and differences in the directions of the total magnetic fields at Sidmouth and at Exeter amounted to less than 2 % of the total magnetic field variations at either station. WEEKES (1970) has shown that at Sidmouth the total magnetic variation of period 12.42 h during solar day is 67. Even if it were assumed that all of this variation were of ionospheric origin, it would only give a variation of 0.127 on the gradiometer. Hence the variation other possible sources suggest themselves: in fig. 6(a) is primarily not of ionospheric origin. Three (1). Tidally induced electric current systems, which are entirely in the sea of the English Channel (type 1 in fig. 4). (2). Tidally induced electric current systems across the English Channel with return currents in the rocks beneath the English Channel (type 2 in fig. 4).
respectively (see fig. 7). It was further assumed that the velocity of the water in the channel was zero in the outer regions (65 km < I y I < 75 km), and that in the central region (I y I < 65 km) there was a standing wave variation tidal velocity, such that the water type velocity up the of channel was v
=
v0 cos px cos wt.
I
WF~H VELOCITY
(2)
‘~
~
~
/
Fig. 7.
Model of the channel used to calculate tidally induced magnetic fields.
74
C. OSGOOD, W. G. V. ROSSER AND N. I. W. WEBB ER
The origin of the coordinate system was placed between the Isle of Wight and the Cherbourg Peninsula. The wavelength of the standing wave oscillation was given by 2 = 21t/p = 800km, so that the water velocity was zero at points ~ 200 km from the Isle of Wight. A value of x = + 100 km was chosen for Sidmouth. From the Admiralty Pocket Tidal Stream Atlas (English and Bristol Channels), the maximum water velocity up the English Channel between the Isle of Wight and the Cherbourg Peninsula is ~ 4 knots at the time of spring tides and ~ 2 knots at the time of neap tides. This suggests adopting a value of 3 knots for the component of the tidal velocity having a period of 12.42 h. According to LONGUET HIGGINS (1949), the average value of the tidal velocity of water in the English Channel is about 0.83 of the surface value. Hence the value chosen for v0 in eq. (2) was v0 = 1.4 m S’. The magnitude of the vertical component of the Earth’s magnetic field was taken to be 5 tesla (or 0.42 gauss). B~= 4.2 x i0 The value adopted for the conductivity of the sea was =
5 ~r~m’.
and CHAPMAN (1970) showed that electric current systems in the land were only important at large distances from the coastline. Since we are only interested in variations less than 20 km from the coastline, it will be sufficiently accurate in our case to assume in this calculation that the conductivity of the land is KENDALL
zero. Using a theory similar to that of
I
~ adv
sinhpy
0B~~cosh p(b J~,,~ o’dvoBvll
—
1
KENDALL
~
—
b) cosh p(y b) sinh p(y cothp(b—s) —
—
—
b)} (6)
~
Such a current system is in the same direction as type 1 in fig. 4 and would give a magnetic field vertically downwards at Sidmouth when the water flows up the English Channel, in agreement with the results presented in figs. 2(a) and (c). The vertical magnetic field at x = + 100 km was calculated by computer using the Biot—Savart law. The results obtained using the numerical values quoted for the parameters are shown in fig. 8. The Norman Lockyer Observatory at Sidmouth is 1 km from the coastline, at y = 76 km from the centre of the channel. Exeter was taken to be 20 km from the coastline at y = 95 km. The predicted difference between the vertical components of the magnetic field at Sidmouth and at Exeter has an amplitude of 0.75 y, or 1.5 y peak to peak. This gives a magnetic variation of 1.5 sin 2 = 1.4 ‘y in the direction of the resultant total magnetic field, where 2 = 67° is the dip angle. The value of 1.47 peak to peak compares with the experimental value of 1.67 peak to peak for the L2 compomodelofchosen can account for field the experimental results nent the resultant magnetic in fig. 6(a). Thus the obtained. The calculations suggest that there may be a residual magnetic variation of ~ 1 y peak to peak at Exeter, and that the total vertical magnetic field variation at Sidmouth due to tidally induced electric current systems in the English Channel may be 2.5 y peak to peak. VERTiCAL MN3NETIC FIELD I]JE 10 ELECTRIC CL~RENTS 14 T~E SH CHAN’~L
and 2~
pX,
(3)
iv
—
1
coshpy cosh p(b
I,
p 2~Z < ~
s) are given by
—
Sm
‘~
3Y
(in our case ps ~it 0.08), integrated current CHAPMAN (1970), can be then shownthethat provided ps ~ 1 densities in the region I y I <(b
adv0B~fp(y
—
s)i cos ix.
For the region b s
+
(4)
EXETER
—
—
—
—
Ic~i0
(5)
Fig. 8.
LIE The calculated tidally induced magnetic field.
10
km
ELECTRIC AND MAGNETIC FIELDS ASSOCIATED WITH SEA TIDES IN THE ENGLISH CHANNEL
5.2. Tidally induced current systems with return currents beneath the sea This is similar to the case considered by LONGUET(1949), except that Longuet-Higgins assumed that the velocity of the sea water was constant, and had the same value all along the Channel, in which case all HIGGINS
the return current would in the rocks beneath theelectric sea, and there flow should be nobemagnetic field at sea level outside the electric current system. This is similar to the case of an infinitely long solenoid carrying a uniform current. However, if the water velocity varied along the channel as given by eq. (2), there should be a magnetic field outside the electric current system. In order to make a rough estimate of this magnetic field and its variation from the coast, a very simplified model was used. It was assumed that for every value of x along the channel in fig. 7, the electric current flow across the channel could be calculated using Longuet-Higgins’ theory. It was then assumed that the return electric current flow was in the form of a semicircle of diameter 140 km, with the current across the channel varying with x as cos px. The magnetic field was then calculated by computer using the Biot—Savart law. The results showed that the magnetic variations (peak to peak) at Sidmouth in the north— south, east—west and vertical directions were 0.26, 0.12 and 0.15 y, respectively, whereas at Exeter the corresponding values were 0.21, 0.10 and 0.08 y, respectively. The magnitude of this magnetic field and its variation from the coast were both far too small to account for the gradiometer results presented in fig. 6(a). Thus this model can be eliminated as the main source of the gradiometer results, The two types of current flow discussed in sections 5.1 and 5.2 must be superimposed. This is like joining two resistors in parallel across a cell which has an internal resistance. The effect is to make the total current less than the sum of the currents obtained by treating two circuits of the cell and one resistor separately. However, the internal resistance across the English Channel is probably less than 20 % of the resistance for return current flow in the rocks. Also since the length of current flow in the current systems in the channel is much longer parallel to the coast than across the channel (b = 75 km whereas 2 = 800 km), the internal resistance is again ~ 20 % of the total resistance.
75
Hence the effect of superimposing the two effects should be to reduce the calculated values in fig. 8 by less than ~ 10 %. 5.3. Sea tides in the Atlantic Ocean The velocity of the sea water in the tides in the Atlantic Ocean are 0.03 to 0.10 m s’ compared with v0 ~ 1 in the English Channel. However, the depth 1.4the m sAtlantic Ocean is much greater than that of the of English Channel (5 km compared with 50 m), so that, though the induced emf’s are smaller, the total currents flowing may be larger in the Atlantic Ocean than in the English Channel. The spatial extent of the current systems should also be much larger in the Atlantic Ocean. HILL and MASON (1962) showed that, at a point 200 km southwest of Land’s End, there was an L 2 variation of ~ 307 peak to peak in the total magnetic field. LARSEN (1968) analysed data from San Miguel in the Azores and found an L2 magnetic variation of ~ 7 y peak to peak in the vertical component of the magnetic field. Thus there is some direct evidence for magnetic variations associated with tides in the Atlantic Ocean. Since the scale of the electric current systems in the Atlantic Ocean is probably 1000 km or more, the variation of the magnetic field away from the Continental Shelf should be fairly slow, and there should be significant contributions to the magnetic field all over the British Isles, due to tidally induced electric currents in the Atlantic Ocean. MALIN (1969, 1970) has investigated the L2 cornponent of the magnetic variations at solar midnight at several U.K. stations. For example, for Hartland Point, which is 100 km northwest of Sidmouth, near the North Devon coast, Maim finds that the peak to peak amplitudes of the L2 magnetic variations in the north—south, east—west and vertical components at solar midnight are 2.0, 5.6 and 3.5 7, respectively. CHAPMAN and KENDALL (1970) accounted quantitatively for the magnitude and phase of the east—west variations determined by Malin in terms of a tidally induced electric current flowing in the north—south direction in the Atlantic Ocean, with an image current system in the opposite direction at a depth of 500 km. The phase of the east—west L2 magnetic variation, determined by MALIN (1970) was almost the same at all the U.K. stations. This is consistent with a common origin for most of the L2 magnetic variations in the
76
C. OSGOOD, W. G. V. ROSSER AND N. J. W. WEBB ER
east—west direction in tidally induced electric current systems in the Atlantic Ocean. The theory of CHAPMAN and KENDALL (1970) confirmed that the changes over the U.K. in the magnitudes of the magnetic variations due to tides in the Atlantic Ocean should not be very large. Hence any effects associated with sea tides in the Atlantic Ocean should be virtually the same at Sidmouth and at Exeter, and give no significant contribution to the gradiometer readings in fig. 6(a), unless there is a significant leakage electric current from the Atlantic Ocean up the English Channel. 6. Discussion The only source of magnetic field variation of period 12.42 h, which gives a sufficient variation of the magnetic field away from the coast of the English Channel to account for the gradiometer results presented in fig. 6(a), is a tidally induced electric current system in the English Channel of the type discussed in section 5.1. The theory given in section 5.1 can account quantitatively for the magnetic gradiometer results in a way which is also consistent with the electric field measurements described in section 2. The present results cornplement those of CHAPMAN and KENDALL (1970), who discussed the effects of tides in the Atlantic Ocean. The gradiometer results illustrate the contribution due to more local effects in the English Channel. WEEKES (1970) has shown that at Sidmouth the L2 variation of period 12.42 h in the total magnetic field at Sidmouth is ~ 6 y peak to peak during solar day and ~ 4 ‘y peak to peak during solar night. The difference ~ 2 ~ between solar day and solar night is probably due to tidally induced ionospheric electric current systems during solar day, when the conductivity of the ionosphere is high. [MALIN (1969) showed that at Hartland Point the L2 variation in the vertical component of the magnetic field was 6.4 y peak to peak during solar day and 3.3 y peak to peak during solar night.] Of the L2 variation of 4 y in the total magnetic field at Sidmouth during solar night, according to the calculations given in section 5.1, about 2.5 sin 2 ~ 2.3 ‘y is probably due to tidally induced electric current systems in the English Channel. The calculations given in seetion 5.2 suggest that there may be an L2 variation of 0.3 y in the total magnetic field due to a solenoidal type of electric current flow, with the return currents beneath the sea, of the type discussed in section 5.2. This
leaves anL2 variation of about 1.47 peak to peak in the total magnetic field, which is probably due mainly to tides in the Atlantic Ocean. Preliminary results with a fluxgate magnetometer at Sidmouth have shown that there is an L2 variation of ~ 1.2 y peak to peak in the north—south component of the magnetic field. Since this variation is not in the vertical direction, it is not due to a current system in the English Channel and is probably mainly due to tides in the Atlantic Ocean. This variation would give a variation of 1.2 cos 2 = 0.5 y in the direction of the total magnetic field. This would leave a remainder of about 0.9y in the total magnetic field (or ~ 1.07 peak to peak in the vertical direction) unaccounted for. (This value could be significantly larger if the phases of the various contributions were very different.) Such a value is quite consistent with the estimates of CHAPMAN and KENDALL (1970) for the expected effects in the vertical direction due to sea tides in the Atlantic Ocean. The above subdivision of the 67 peak to peak L2 variation in the total magnetic field at Sidmouth during solar day is very tentative, and is merely meant to indicate the approximate magnitudes of the various possible contributions. In addition, the preliminary fluxgate results at Sidmouth show that there is an L2 magnetic variation of ~ 6 y peak to peak in the geomagnetic east—west direction at Sidmouth. This variation has no component in the direction of the Earth’s resultant magnetic field and does not contribute to the magnetic variations recorded by the rubidium vapour magnetometers and the gradiometer. This variation is probably mainly due to tides in the Atlantic Ocean. Acknowledgments The work described in this paper was carried out at the Norman Lockyer Observatory, Sidmouth, as part of the research program of the Geophysics Section of the Department of Physics, Exeter University. We are very gratefui to the Council of the Corporation of the Observatory for allowing us to use the Observatory as a field station. We would like to thank Dr. K. Weekes, Dr. D. M. Schlapp, Dr. M. Sewter, Mr. G. M. Brown, Professor P. C. Kendall, Mr. S. R. C. Malin and Commander Glen, R. N., for valuable discussions. We would like to thank Mr. G. H. Davey, Mr. J. Denner, Mr. R. Duncan and Mr. R. Bee for their help in the run-
ELECTRIC AND MAGNETIC FIELDS ASSOCIATED WITH SEA TIDES IN THE ENGLISH CHANNEL
ning of the apparatus and in the analysis of the data. We would like to thank the Controller H. M. Stationary Office and the Hydrographer of the Navy for their permission to reproduce fig. 4 References BROWN,
G. M. et al. (1969), Private communication. S. and P. C. KENDALL (1970), Planet. Space Sci., in
CHAPMAN,
press.
77
HILL, M. N. and C. S. MASON (1962), Nature 195, 356. KENDALL, P. C. and S. CHAPMAN (1970), Quart. J. Mech. AppI. Math., in press. LARSEN, J. C. (1968), Geophys. J. 16, 47. LONGIJET-HIGGINS, M. S. (1949), Monthly Notices Roy. Astron. Soc. Geophys. Suppi. 5 (8). MALIN, S. R. C. (1969), Planet. Space Sci. 17, 487. MALIN, S. R. C. (1970), Private communication. OSGOOD C. (1970), Rev. Phys. Appl. 5, 113. WEEKEs, K. E. (1970), Private communication.