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Acoustic observations of high-frequency, near-surface internal wave groups in the deep ocean during GATE
Deep-Sin Research1978,Vol 25, pp 2991o307 PergamonPress Pnntedm Great Britain
Acoustic observations of high-frequency, near-surface internal wave groups in the deep ocean during GATE* J. R.
PRONIt,
F
OSTAPOFFt
and R. L SELLERSt
(Received 14 February 1977, zn rewsedform 18 August 1977, accepted 31 August 1977) Abstract--High-frequency, near-surface mternal wave groups m the deep ocean were observed during G A T E '~The wave groups have several structural features m c o m m o n with internal wave groups observed on continental shelves It is suggested that the wave groups are (a) &stlngulshable because of their structural features from the generally present h~gh-frequency internal wave background and (b) that these same features are to be expected on a theoretical basis from the work of T B BENJAMIN(Journal ol Fluid Mechanics, 29, 559-592, 1967) Some evidence supporting the acoustic data is derived from simultaneously observed temperature and sahmty data and from some imaging radar gathered m the same overall area_
INTRODUCTION
PART OF the oceanographic subprogram of the GARP (Global Atmospheric Research Program) Atlantic Tropical Experimant (GATE) addresses the problem of couphng between the motions in the mixed layer and in the interior ocean. Internal gravity waves in the main thermochne may locally enhance the shear flow, thus providing a mechanism for turbulence and mixing. During the third phase of GATE (August 30 to September 21, 1974) a high resolution experiment that included an internal wave program was carried out. The main components of this program were a two-legged mooring instrumented with current meters and temperature sensors with a horizontal spatial separation resolution of 500 m (University of Klel) and the acoustic probmg that will be discussed in this paper. Acoustic data on the detailed spatial structure of some internal wave groups near the ocean's surface but in deep ocean water will be presented. The observed wave groups have certain structures that &stmgmsh them from the generally present high-frequency internal waves. Observations of high-frequency mternal wave groups along the United States and on other continental shelves have been made m the last several years (LAFOND, 1961, GARGETT and H U G H E S , 1 9 7 2 ; ZIEGENBEIN, 1 9 6 9 ; H A L P E R N , 1971), and internal surges in lakes (a closely related phenomenon) have been reported (THORPE, 1968, HUNKINS and FLIEGEL, 1973, THORPE, 1974). Recent measurements of continental shelf wave packets have been made by satelhte (APEL, BYRNE, PRONI and CHARNELL,1975) and acoustically (PgONI and APEL, 1975). The theory governing the propagation of these wave groups or wave packets for the continental shelf was developed by LEE and BEARDSLEY(1974) and * A GATE Contnbutlon t Atlantic Ooeanographtc and Meteorological Laboratories, Sea-Air Interaction Laboratory, 15 Rlckenbacker Causeway, Mlama, FL 33149, U S A ~_G A T E is the acronym for the G A R P (Global Atmospheric Research Program) Atlantic Tropical Experiment
299
300
J R. PRONI, F OSTAPOFFand R L. SELLERS
for lakes (Loch Ness in particular) by THORPE (1974). A feature shared by shelf and lake theories is that they apply to shallow water (more precisely, the ratm of depth to wavelength of the internal waves is small) The existence of wave packets or groups having hmited spatial extent has been described particularly in recent Soviet literature (SAmNIN, 1971, MIROPOL'SKIV, 1973; BREKHOVSKIKH,KONJAEV,SABININand SERIKOV,1975). The inferences on the existence of internal wave groups are based on the assumption that (i) certain characteristics of internal waves have non-Gausslan probability distributions, (li) certain time series of internal waves are non-stationary, and (ili) the high-frequency Internal wave field is dlrectionally anisotroplc. Relatively little attention was paid to the detailed structure of the internal wave packets. METHOD
Deep-occan internal waves were observed acoustically. The acoustic device, which was towed behind the R.V. Columbus Iselin during the third phase of GATE, utilized 1-ms-long pulses with a carrier frequency of 20kHz. The beamwldth was 12 by 18 °. Normally the acoustic transducer (1.e. the actual sound emlttmg element) is towed in a hydrodynamically streamlined towbody The tow depth is normally a few meters below the surface. For the acoustic device to be able to detect subsurface water movements, some acoustic scatterers must be present It is presently known on theoretical and experimental grounds that at least three classes of acoustic scatterers exist. These include (1) biological scatterers and suspended material both organic and inorgamc, (il) turbulence, and (111) small-scale temperature and density microstructure. Acoustic scatterers often have a clear vertical stratification The scatterers ahgn themselves in layers separated vertically by regions of much lower acoustic reflectivlty. Examples of such layering have been published by PRONI and APEL (1975) (see the Appendix of this paper for an example of layering). Upon passage of internal waves, these layers are caused to oscillate and thus outline the internal wave structure Internal wave amplitude can then be obtained directly from the acoustic records. Acoustically derived layer depth variations and simultaneous temperature variations from the scattering layer have shown good agreement (OSTAPOFF,PRONI and SELLERS,1975). OBSERVATIONS
The R.V. Columbus lselin track for September 16, 1974, is shown in Fig. 1, as are the areas (hatched) in which synthetic aperture radar data were gathered by the Natlonal Aeronautics and Space Administration dev:ce CV990 on September 16, 1974. Fig. 2(a) shows a portion of the acoustic record from 1130 to 1215 U.T. on September 16, 1974. Time runs from left to nght with a total record length of about 4.4 km (ship's speed = 1 6 m s-1). There is evidence that an internal wave packet is portrayed between the pomts marked 'front' and 'end' of a wave packet in Fig. 2(a). The packet seems to be proceeding toward the right in Fig. 2(a); (see the discussion on page 303). Figure 2(b) delineates graphically the acoustic scattering layer to faohtate the &scusslon. The wave group begins with a sharp downgoing oscillation. A range of wavelengths is visible m the wave packets ranging from a few hundred meters to about 600 m. Because the direction of the propagation of the wave packet IS not known exactly (see, however, the discussion in the analysis section), the distances of a few hundred meters to 600 m must be regarded as upper hmzts on the distance between downgoing oscillations. The packet
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J R PRONI,F OSTAPOFF and R L SELLERS
length (again an upper limit) is estimated to be roughly 3.2 km. At a depth of 30 m, the horizontal resolution of the acoustic system is roughly 7 m Any oscillation of this order or larger should be detected (assuming of course, that an acoustic scatterer IS present). The maximum amplitude in the packet is approximately 10 m. The acoustic scatterer before the onset of the wave packet is at a fixed depth (i.e. no oscdlatlons at or near the 350-m-wavelength range*); the scattering layer after the passage of the packet is shghtly lower ( ,-, 4 m) than before the passage of the packet A second observation of a possible internal wave packet was made between 0240 and 0320 U.T. on September 16, 1974 (Fig. 3). There was an area of high acoustic return ranging from a depth of about 25 m to a depth of about 70 m This area of high acoustic return is a manifestation of the deep scattering layer, which is known to be biological in origin. A second area of acoustic return ranges from a depth of about 220 to 230 m. Time runs from left to right in the figure. The ship was underway at a speed of approximately 2.0 m s- ' A sequence of four expendable bathythermograph (XBT) observations was made during and after the ship's passage through the lnterr~al wave group. The launching times of the four XBTs are indicated m Fig 3, and the XBT records are shown in Fig 4 TEMP ('C) 5
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X B T records obtained during the traversal o f the wave g r o u p shown m Fig 3
The wave packet begins with a downgoing oscillation (the packet is thought to be propagating from left to right in Fig. 3; see page 303 for a discussion of this choice of propagation direction) as did the packet shown in Fig. 2 Note also the depression of 2 to 3 m in the mean depth of the uppermost portion of the deep scattering layer, which results upon passage of the internal wave packet Consider now the XBT taken at 0320 U T. (Fig 4) This observation was before the wave group had arrived at its location (Lat. 08°55.4'N, Long. 22°46 3'W) The mixed layer extended to a depth of about 32m. A second layer of uniform temperature is visible in the depth range 162 to 200 m. Consider now the XBT observation at 0310 U.T., the upper mixed layer had Increased its depth to about 25 m. This XBT appears to have * There may be present~ of course, oscillations of the scattering layer m other lower frequency bands, such as the seml-dmrnal tide, for example
SURFACE
SURFACE
150
150 1215 U.T
(a)
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(b) Fig 2 (a) Acoustic record of an Internal wave group observed from September 16. 1974 The record length IS roughly 44km (b) SchematIc packet record III (a)
1130 to 123OUl on portrayal of the wave
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(b) Fig 5 (a) Example of typlcal Internal wave actlvlty observed m the GATE area (no clearly defined wave packets dre \lslble) (b) Temperature. sahmty. and (computed) density profiles for September 16 1914
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OBSERVATION
OF AN INTERNAL
IN THE AREA OF 8.37’NORTH record
LAT
WAVE GROUP MADE ON 22’30’
obtamed from about 1210 to 1245U T These Immediately after the data shown m Fig 2
WEST data
LONG. were
obtamed
17km
WEST lM&lNG RADAR DATA GATHERED ON SEPT. I6 1974 BY ELACHI ET AL. (a) LIO Krn-hJTH IMAGING RADAR DATA GATHERED BY ELKHI ET. AL ON SEPT 5,19?4 (b) Fig 7 (a) Imagmg radar data west to east (b) Imagmg radar
from September 16. 1974 by ELACHI et a/ (1977), whde flying data gathered by ELACHI et al. on Sepkmber 5. 1974 while flying on a north-south course
U
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1000
2000 3000 4000 DISTANCE (ml
I I I
5000
APPENDIX Fig Al
The figure 1s a reproduction of Fig 2 In PRONI and APEL (1975) The leadlng edge of the wave packet 1s on the nght The water depth 1s about IlOm (New York Contmental Shelf) ~icrng
p 3061
Acoustic observations in the deep ocean during G A T E
303
been taken between a trough and a crest of the internal wave packet. The remaining two XBT records (0300 and 0250 U.T.) were made during the passage of the vessel over a trough. The latter three XBTs clearly show the depression (the depth extension of the mixed layer) generated by the passage of the internal wave group. Another interesting comparison can be made between acoustic and XBT information by examining the acoustic scattering layer in the 220- to 230-m range. In the data from the XBT taken at 0320 U.T. (Fig. 4) a deep mixed layer (i.e. a layer of uniform temperature) is evident between 158 and 200m. In the XBT at 0310U.T., this deep mixed layer occupies the range 156 to 190m. At 0300U.T., the deep mixed layer was in the depth range 180 to 212 m. The general trend of the vertical movement of the mixed layer depth is in agreement with the trend observable in the acoustic data in Fig. 4. For example, at 0320U.T., the acoustic scattering layer was several meters deeper than at 0310U.T. Also the shorter internal waves visible within the packet at a depth of about 25 m are absent from the deeper oscillations. Such short wavelength oscillations would have been detected if they were present, because the horizontal resolution of the acoustic system at 200 m is approximately 50 m. ANALYSIS
An attempt is made to interpret the acoustic data using an open ocean internal wave surge as a model. The original interpretation of the GATE data as an internal surge was inspired by the similarity of the structural form of the GATE wave packet to the form of continental shelf wave packets.* A typical continental shelf internal wave packet is shown in Fig. 2 of the paper by PRONI and AVEL(1975).;" This wave packet shows several features in common with wave packets observed in the GATE area. These features are as follows: (i) the wave packets begin with a downgoing oscillation; (ii) the largest oscillations are at the leading edge of the packet; (iii) the mean scatterer depth before the onset of the wave packet is less than the mean scatterer depth after the onset of the wave packet. (This effect is more marked in the continental shelf wave packet than in the GATE data.) Similarity in form alone is not enough to have confidence in a surge interpretation. The next step in establishing a surge interpretation is to determine what are the expected governing equations and then to determine whether these governing equations admit surges as solutions. The propagation of the continental shelf wave packet (LEEand BEARDSLEY,1974) is known to be described by the non-linear Korteweg~teVries-Burger equation. The downward initial oscillation of the continental surge follows as a natural consequence of energy dissipation. The initial oscillations are thought to be so-called solitons. The causative mechanism for shelf packets is thought to be the interaction of tides with bottom topographic features. BENJAMIN (1967) appears to have pioneered the study of non-linear internal waves in fluids of great depth. He has shown that: (i) the non-linear governing equations of a two-fluid system, one of finite thickness, h, and the other of infinite depth, admit solitary waves as solutions; (ii) these same non-linear equations admit the existence of internal bores or surges. The above conclusions are derived using (and are valid only to the limit of) a first * This does not mean to imply that the mechanism of generating the deep ocean internal wave group under consideration need be the same as that of continental shelf internal wave groups. t T h i s figure is reproduced in the Appendix of this paper.
304
J.R. PRONI,F. OSTAPOFF and R. L. SELLERS
approximation to the effects of finite wave amplitude. The necessary condition for nonlinear effects to manifest themselves and for the applicability of Benjamin's theory is: a'2 h2 ~ 0(1),
(1)
where a is the internal wave amplitude, 2 is the internal wave length, and hi is the depth o f the mixed layer. A typical density profile from the GATE area is shown in Fig. 5. From that figure, we have hi ~ 35m. From Fig. 2, we have a ~ 10m, 2 ~ 400m, hence: a.)~ h~- ~ 4.
(2)
Therefore, we assume the applicability of Benjamin's theory and its consequences (i) and (ii) listed earlier. According to BENJAMIN (1967), the speed of propagation, CNL, for a deep ocean solitary wave is: 3p2 a'x
C2L = C 2 1 + T r o T - J , °tpl nl ]
(3)
where Pl is the mixed layer density, P2 is the density of the lower layer (Benjamin has a two-layer model), and CL is the speed of propagation of a linear internal wave and is given by
. C~= ~{P2--Pl"~ ~ - ) gn,,
(4)
where g is gravitational acceleration. It is of interest to try to estimate the place of origin of the internal wave packet. This can be done if it is assumed that the leading edge of the packet travels CNL and the tail of the packet travels at CL. It is also necessary to know the true length of the packet, Lp. From Fig. 2 the observed length, L, of the packet is roughly 3,5 km. From Fig. 5 one obtains P2 = 1.0265 and Pl = 1.0234. Then, using equation (4), it is estimated that CL = 87 cm s- 1 NOW,
Lp = (CNL-- CL) (tobs -- torigin),
(5)
where tobs is the time of observation of the wave packet and torigin is the time of origin of the wave packet• If r is the distance from the point of observation of the wave packet and L the observed packet length, then
Lp r = CNL(tobs--torigin ) = CNL •(CNL--CL) ~ CNL (c~LL_cL) •
(6)
Thus the maximum value for r is roughly 30 km. Benjamin also gives an estimate for the width of a soliton A: A
4(Pl~z(~) = 3\p-~EJ
~ 83 m.
(7)
Acousticobservationsin the deep ocean during GATE
305
Note that the condition [equation (2)] for the appearance of non-linearity is relatively weakly dependent on 2, so that even if A replaced 2 in equation (2), the non-linearity condition is satisfied. A question of importance is whether there is any observational evidence to support the conjecture that the internal wavegroup shown in Fig. 2 is moving in an easterly or southeasterly direction. There are four data sets that can possibly shed light on this question: (i) additional 20-kHz observations by the authors; (ii) coherent imaging radar observations by ELACHI, CAILLAT and Ross (1977); (iii) hydroglider (a towed variable depth device) data gathered by MOLLO-CHRISTENSEN,MOREY and STRIMAITIS(1975); and (iv) Batfish (a towed variable depth device) data gathered by WOODS(1974). Examination of the ship's track (Fig. 1) suggests that the R.V. Columbus Iselin may have traversed the internal wave packet more than once. The acoustic data between 1200 and 1400 U.T. suggest the idea of an east-southeasterly traveling wave packet. Suppose (as a working hypothesis), that one has an easterly traveling wave packet and that the ship overtook the wave packet while traveling in an easterly direction. At about 1210 U.T., the vessel has passed over the leading oscillation of the wave packet. At about 1218 U.T., the ship turned toward the south and thus should have crossed the wave packet along a trough or crest; this should have resulted in diminished internal wave oscillations (as seen in the acoustic data) but an overall depression of the acoustic reflector level (compared to the reflector level before the onset of the wave group--e.g, at 1210 U.T.) should have been present. That this is the case may be seen by an examination of Fig. 6. As the vessel turned west (about 1237 U.T. Fig. 6) it encountered the latter part of the wave group and apparently once again encountered the depression (identified in Fig. 2 as 'another wave group') following the wave packet of interest. The length of the southerly leg (1210 to 1230 U.T.) was about 3 km, suggesting at least this lateral (i.e. along a crest) horizontal extent for the wave group. Imaging radar observations by ELACHI et al. (1977), show the presence of surface bands of low radar reflectivity. [For a discussion of imaging radar techniques in oceanography see the paper by BROWN, ELACHI and THOMPSON(1976)]. If these bands are interpreted as surface manifestations of an internal wave field, then an east-southeasterly (or west-northwesterly) direction of propagation is indicated. Imaging data gathered by Elachi and his colleagues on September 16, 1974 in the large rectangle shown in Fig. 1, are presented in Fig. 7(a). These data are not precisely coincident with the acoustic data shown in Fig. 1. Also shown in Fig. 7(b) are imaging radar observations in the same general GATE area on September 5, 1974. Several long surface bands, marked 'internal waves' in Fig. 7, appear in the data from September 16. From the alignment of the bands, it can be inferred that internal waves, assumed to be associated with the bands, travel in a southeasterly (or northwesterly) direction. More dramatic records were obtained on September 5, 1974. In these data, two areas that may be internal wave packets are evident. Once again an east-southeasterly direction of propagation is indicated. The imaging radar data, while not confirming the acoustic data in detail, generally support the existence of discrete internal wave groups in the GATE area at the time the acoustic data were gathered. Mollo-Christensen has published a preliminary analysis of his hydroglider observations, which were simultaneous with the acoustic observations aboard the R.V. Colombus Iselin (MOLLO-CHRISTENSENet al., 1975). Temperature and salinity data (obtained by towing the hydroglider) also indicate the presence of an internal wave field propagating either in the southeasterly or northwesterly direction.
306
J.R. PRONI,F. OSTAPOFEand R. L. SELLERS
To facilitate comparison with other data obtained from the hydroglider (MOLLOCHRISTENSEN et al., 1975) and the Batfish (WOODS, 1974, 1976), the acoustic data were analyzed to determine the mean depth of the acoustic reflecting layer for each of the R.V. Columbus Iselin track segments (Fig. 1) and for the standard deviation of the reflector depth, (Table 1). A deepening of the average reflector depth during the passage of the ship over the packet is indicated. Table 1. Mean depths and standard deviations of the acoustic reflecting layers for certain R.V. Columbus Iselin track segments shown in Fig. 1. TIME
INTERVAL
MEAN
(m)
STANDARD
DEVIATION
0820
-
0905
50.4
3.8
0905
-
1015
56.0
3.3
1015
-
1210
58.3
5.2
1210
-
1230
56.7
2.1
1230
-
1330
57.3
2.9
1330
-
1420
56.2
(m)
A substantial amount of additional acoustic data were gathered during GATE. However, although much internal wave activity was detected, few wave packets were detected. A typical example of the internal wave activity frequently seen is shown in Fig. 5(b). CONCLUSIONS
The main conclusions of this study are: (i) acoustic data indicate the presence in the deep ocean of spatially discrete, high-frequency internal wave packets; (ii) the form of the internal wave packet is similar to that of internal wave packets along continental shelves. The main features of the wave packet include (a) a weak non-linearity, (b) a downgoing first oscillation, and (c) a slight deepening of the reflecting acoustic layer; (iii) the place of origin is estimated to be on the order of 30 km from the place of observation. A referee of this paper has asked about the possibility that the wave groups reported in this paper might arise from periods of 'intermittency' in a general background of quasirandom, high-frequency internal waves. To define an internal wave packet, two calm periods (i.e. periods of no high-frequency internal wave activity) are required to define the beginning and the end of the packet. Two such calm periods can arise either by being genuinely calm (i.e. truly devoid of high-frequency internal wave activity) or as a consequence of a momentary nulling of a superposition of quasi-random internal waves. The authors believe that, while it is not impossible, it is highly unlikely that the structural form required of the internal wave group (as stated on page 303) would be produced by a chance (double) nulling of the quasi-random internal wave field. The calm periods on either side of the wave group shown in Fig. 2(a) are several kilometers long, the calm area being terminated by the abrupt onset of the internal wave group. Had the calm period been produced by an extensive null, it is unlikely that such an abrupt large amplitude internal wave onset should occur, rather, one should expect a gentle period of
.-. E
0
T am
"' 50
XBT
_
10-
~i4-n.
~1
uJ uJ k-
.t.6 iB ,I 0
I
iO00
I
I
I
2000 3000 4000 DISTANCE (m)
I
5000
APPENDIX Fig. A 1. The figure is a reproduction of Fig. 2 in PRONI and APEL (1975). The leading edge of the wave packet is on the right. The water depth is about 110 m (New York Continental Shrift.
[facing p. 306]
Acoustic observations in the deep ocean during GATE
307
wave amplitude growth as the null departed. At the present time, the authors can offer no information on the processes of generation of the internal wave groups. Acknowledgements--Useful suggestions and comments were made to the authors at the Southampton (England) GATE data review in the summer of 1975. Thanks are extended to our colleagues at this meeting, particularly STEVENTHORPE,JOHN WOODS,ERIC MOLLO-CHRISTENSEN,and KLAUSHASSELMANN.CHARLESELACHIhas been most generous in allowing us to use a portion of the imaging radar data he gathered in 1974, we sincerely thank him for his kindness. DUNCAN ROSSmade the original suggestion that the imaging radar data lend support to the acoustic wave packet interpretations. T. BROOK BENJAMIN was also kind enough to review this manuscript. CHARLES LAUTER carried out, in expert fashion, the electronics work required in the acoustic observations. REFERENCES APEL J. R., H. M. BYRNE, J. R. PRON1 and R. L. CHARNELL (1975) Observations of oceanic and internal surface waves from the Earth Resources Technology Satellite. Journal of Geophysical Research, 80, 865-881. BENJAMIN, B. (1967) Internal waves of permanent form in fluids of great depth. Journal of Fluid Mechanics, 29, 559-592. BREKHOVSKIKHL. M., K. V. KONJAEV,K. O. SABININ and A. N. SERIKOV(1975) Short period internal waves in the sea. Journal of Geophysical Research, 80, 856. BROWN W. E., JR., C. ELACHI and T. W. THOMPSON (1976) Radar imaging of ocean surface patterns. Journal of Geophysical Research, 81, 2657-2667. ELACHI C., J. CAILLAT and D. Ross (1977) Imaging radar observations in GATE. To be submitted to
Journal of Geophysical Research. GAR6ETr A. E. and B. A. HUCHES (1972) On the interaction of surface and internal waves. Journal of Fluid Mechanics, 52, 179-191. HALPERN D. (1971) Semidiurnal internal tides in Massachusetts Bay. Journal of Geophysical Research, 76, 6573-6584. HUNKINS K. and M. FLIEGEL(1973) Internal undular surges in Seneca Lake: a natural occurrence of solitons. Journal of Geophysical Research, 78, 539-548. LAFOND E. C. (1961) Boundary effects on the shape of internal temperature waves. Indian Journal of Meteorology, 12, 335. LEE C. and R. C. BEARDSLI~Y(1974) The generation of non-linear internal waves in a weakly stratified shear flow. Journal of Geophisical Research, 79, 453-462. MIROPOL'SKIY YU. Z. (1973) Probability distribution of certain characteristics of internal waves in the ocean. lzvestiya, Atmospheric and Ocean Physics, 9, 411. MOLLO-CHRISTENSENE., K. A. MOREYand D. STRIMAITIS(1975) Towed probe observations of upper ocean; made from R.V. Columbus Iselin during GATE III, September 1974, Vols. 1 and 2, Massachusetts Institute of Technology, Department of Meteorology Report, October 1975. pp. 32-34. OSTAPOFF F., J. R. PRONI and R. L. SELLERS(1975) Preliminary analysis of ocean internal wave observations by acoustic soundings. GATE Report, 14, World Meteorological Organization, Geneva, 392-397. PRONI J. R. and J. R. APEL(1975) On the use of high-frequency acoustics for the study of internal waves and microstructure. Journal of Geophysical Research, 80, 1147-1151. SABININ K. D. (1971) Measurement of the parameters of internal waves by means of a moving, spatially separated system of sensors, lzvestiya, Atmospheric and Oceanic Physics, 7, 379. THORPE S. (1968) On the shape of progressive internal waves. Philosophical Transactions of the Royal Society London, Series A, 263, 563. THORPE S. (1974) Near-resonant forcing in shallow two-layer fluid: a model for the internal surge in Loch Ness ? Journal of Fluid Mechanics, 63, 509. WOODSJ. (1974) Batfish experiments on RRS Discovery. Part 1 : Measurements and analysis at sea. Oceanography Department, Southampton University, pp. 1-3. WOODS J. (1976) Batfish experiments on RRS Discovery during Phase III of GATE, 2-16 September, 1974. Part 2: Data processing at Southampton. Oceanography Department, Southampton University, 2nd revised edition, January 1976, 413-414. ZIEGENnEIN J. (1969) Short internal waves in the Strait of Gibraltar. Deep-Sea Research, 16, 479.
Acoustic observations of high-frequency, near-surface internal wave groups in the deep ocean during GATE* J. R.
PRONIt,
F
OSTAPOFFt
and R. L SELLERSt
(Received 14 February 1977, zn rewsedform 18 August 1977, accepted 31 August 1977) Abstract--High-frequency, near-surface mternal wave groups m the deep ocean were observed during G A T E '~The wave groups have several structural features m c o m m o n with internal wave groups observed on continental shelves It is suggested that the wave groups are (a) &stlngulshable because of their structural features from the generally present h~gh-frequency internal wave background and (b) that these same features are to be expected on a theoretical basis from the work of T B BENJAMIN(Journal ol Fluid Mechanics, 29, 559-592, 1967) Some evidence supporting the acoustic data is derived from simultaneously observed temperature and sahmty data and from some imaging radar gathered m the same overall area_
INTRODUCTION
PART OF the oceanographic subprogram of the GARP (Global Atmospheric Research Program) Atlantic Tropical Experimant (GATE) addresses the problem of couphng between the motions in the mixed layer and in the interior ocean. Internal gravity waves in the main thermochne may locally enhance the shear flow, thus providing a mechanism for turbulence and mixing. During the third phase of GATE (August 30 to September 21, 1974) a high resolution experiment that included an internal wave program was carried out. The main components of this program were a two-legged mooring instrumented with current meters and temperature sensors with a horizontal spatial separation resolution of 500 m (University of Klel) and the acoustic probmg that will be discussed in this paper. Acoustic data on the detailed spatial structure of some internal wave groups near the ocean's surface but in deep ocean water will be presented. The observed wave groups have certain structures that &stmgmsh them from the generally present high-frequency internal waves. Observations of high-frequency mternal wave groups along the United States and on other continental shelves have been made m the last several years (LAFOND, 1961, GARGETT and H U G H E S , 1 9 7 2 ; ZIEGENBEIN, 1 9 6 9 ; H A L P E R N , 1971), and internal surges in lakes (a closely related phenomenon) have been reported (THORPE, 1968, HUNKINS and FLIEGEL, 1973, THORPE, 1974). Recent measurements of continental shelf wave packets have been made by satelhte (APEL, BYRNE, PRONI and CHARNELL,1975) and acoustically (PgONI and APEL, 1975). The theory governing the propagation of these wave groups or wave packets for the continental shelf was developed by LEE and BEARDSLEY(1974) and * A GATE Contnbutlon t Atlantic Ooeanographtc and Meteorological Laboratories, Sea-Air Interaction Laboratory, 15 Rlckenbacker Causeway, Mlama, FL 33149, U S A ~_G A T E is the acronym for the G A R P (Global Atmospheric Research Program) Atlantic Tropical Experiment
299
300
J R. PRONI, F OSTAPOFFand R L. SELLERS
for lakes (Loch Ness in particular) by THORPE (1974). A feature shared by shelf and lake theories is that they apply to shallow water (more precisely, the ratm of depth to wavelength of the internal waves is small) The existence of wave packets or groups having hmited spatial extent has been described particularly in recent Soviet literature (SAmNIN, 1971, MIROPOL'SKIV, 1973; BREKHOVSKIKH,KONJAEV,SABININand SERIKOV,1975). The inferences on the existence of internal wave groups are based on the assumption that (i) certain characteristics of internal waves have non-Gausslan probability distributions, (li) certain time series of internal waves are non-stationary, and (ili) the high-frequency Internal wave field is dlrectionally anisotroplc. Relatively little attention was paid to the detailed structure of the internal wave packets. METHOD
Deep-occan internal waves were observed acoustically. The acoustic device, which was towed behind the R.V. Columbus Iselin during the third phase of GATE, utilized 1-ms-long pulses with a carrier frequency of 20kHz. The beamwldth was 12 by 18 °. Normally the acoustic transducer (1.e. the actual sound emlttmg element) is towed in a hydrodynamically streamlined towbody The tow depth is normally a few meters below the surface. For the acoustic device to be able to detect subsurface water movements, some acoustic scatterers must be present It is presently known on theoretical and experimental grounds that at least three classes of acoustic scatterers exist. These include (1) biological scatterers and suspended material both organic and inorgamc, (il) turbulence, and (111) small-scale temperature and density microstructure. Acoustic scatterers often have a clear vertical stratification The scatterers ahgn themselves in layers separated vertically by regions of much lower acoustic reflectivlty. Examples of such layering have been published by PRONI and APEL (1975) (see the Appendix of this paper for an example of layering). Upon passage of internal waves, these layers are caused to oscillate and thus outline the internal wave structure Internal wave amplitude can then be obtained directly from the acoustic records. Acoustically derived layer depth variations and simultaneous temperature variations from the scattering layer have shown good agreement (OSTAPOFF,PRONI and SELLERS,1975). OBSERVATIONS
The R.V. Columbus lselin track for September 16, 1974, is shown in Fig. 1, as are the areas (hatched) in which synthetic aperture radar data were gathered by the Natlonal Aeronautics and Space Administration dev:ce CV990 on September 16, 1974. Fig. 2(a) shows a portion of the acoustic record from 1130 to 1215 U.T. on September 16, 1974. Time runs from left to nght with a total record length of about 4.4 km (ship's speed = 1 6 m s-1). There is evidence that an internal wave packet is portrayed between the pomts marked 'front' and 'end' of a wave packet in Fig. 2(a). The packet seems to be proceeding toward the right in Fig. 2(a); (see the discussion on page 303). Figure 2(b) delineates graphically the acoustic scattering layer to faohtate the &scusslon. The wave group begins with a sharp downgoing oscillation. A range of wavelengths is visible m the wave packets ranging from a few hundred meters to about 600 m. Because the direction of the propagation of the wave packet IS not known exactly (see, however, the discussion in the analysis section), the distances of a few hundred meters to 600 m must be regarded as upper hmzts on the distance between downgoing oscillations. The packet
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302
J R PRONI,F OSTAPOFF and R L SELLERS
length (again an upper limit) is estimated to be roughly 3.2 km. At a depth of 30 m, the horizontal resolution of the acoustic system is roughly 7 m Any oscillation of this order or larger should be detected (assuming of course, that an acoustic scatterer IS present). The maximum amplitude in the packet is approximately 10 m. The acoustic scatterer before the onset of the wave packet is at a fixed depth (i.e. no oscdlatlons at or near the 350-m-wavelength range*); the scattering layer after the passage of the packet is shghtly lower ( ,-, 4 m) than before the passage of the packet A second observation of a possible internal wave packet was made between 0240 and 0320 U.T. on September 16, 1974 (Fig. 3). There was an area of high acoustic return ranging from a depth of about 25 m to a depth of about 70 m This area of high acoustic return is a manifestation of the deep scattering layer, which is known to be biological in origin. A second area of acoustic return ranges from a depth of about 220 to 230 m. Time runs from left to right in the figure. The ship was underway at a speed of approximately 2.0 m s- ' A sequence of four expendable bathythermograph (XBT) observations was made during and after the ship's passage through the lnterr~al wave group. The launching times of the four XBTs are indicated m Fig 3, and the XBT records are shown in Fig 4 TEMP ('C) 5
SURFACE
so ~ ioe -
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Fig 4
X B T records obtained during the traversal o f the wave g r o u p shown m Fig 3
The wave packet begins with a downgoing oscillation (the packet is thought to be propagating from left to right in Fig. 3; see page 303 for a discussion of this choice of propagation direction) as did the packet shown in Fig. 2 Note also the depression of 2 to 3 m in the mean depth of the uppermost portion of the deep scattering layer, which results upon passage of the internal wave packet Consider now the XBT taken at 0320 U T. (Fig 4) This observation was before the wave group had arrived at its location (Lat. 08°55.4'N, Long. 22°46 3'W) The mixed layer extended to a depth of about 32m. A second layer of uniform temperature is visible in the depth range 162 to 200 m. Consider now the XBT observation at 0310 U.T., the upper mixed layer had Increased its depth to about 25 m. This XBT appears to have * There may be present~ of course, oscillations of the scattering layer m other lower frequency bands, such as the seml-dmrnal tide, for example
SURFACE
SURFACE
150
150 1215 U.T
(a)
ANOTHER WAVE GROUP
SURFACE
2
-END
OF WAVE PACKET
“FRONT” OF WAVE PACKET SURFACE
50-
-50
z I
z ti 0
: 100
-
150
-
100
150
(b) Fig 2 (a) Acoustic record of an Internal wave group observed from September 16. 1974 The record length IS roughly 44km (b) SchematIc packet record III (a)
1130 to 123OUl on portrayal of the wave
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(b) Fig 5 (a) Example of typlcal Internal wave actlvlty observed m the GATE area (no clearly defined wave packets dre \lslble) (b) Temperature. sahmty. and (computed) density profiles for September 16 1914
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ACOUSTIC SEPT. Fig 6
‘150
(20KHz)
16.1974, Acoustlc
OBSERVATION
OF AN INTERNAL
IN THE AREA OF 8.37’NORTH record
LAT
WAVE GROUP MADE ON 22’30’
obtamed from about 1210 to 1245U T These Immediately after the data shown m Fig 2
WEST data
LONG. were
obtamed
17km
WEST lM&lNG RADAR DATA GATHERED ON SEPT. I6 1974 BY ELACHI ET AL. (a) LIO Krn-hJTH IMAGING RADAR DATA GATHERED BY ELKHI ET. AL ON SEPT 5,19?4 (b) Fig 7 (a) Imagmg radar data west to east (b) Imagmg radar
from September 16. 1974 by ELACHI et a/ (1977), whde flying data gathered by ELACHI et al. on Sepkmber 5. 1974 while flying on a north-south course
U
‘. & t XBT
0
1000
2000 3000 4000 DISTANCE (ml
I I I
5000
APPENDIX Fig Al
The figure 1s a reproduction of Fig 2 In PRONI and APEL (1975) The leadlng edge of the wave packet 1s on the nght The water depth 1s about IlOm (New York Contmental Shelf) ~icrng
p 3061
Acoustic observations in the deep ocean during G A T E
303
been taken between a trough and a crest of the internal wave packet. The remaining two XBT records (0300 and 0250 U.T.) were made during the passage of the vessel over a trough. The latter three XBTs clearly show the depression (the depth extension of the mixed layer) generated by the passage of the internal wave group. Another interesting comparison can be made between acoustic and XBT information by examining the acoustic scattering layer in the 220- to 230-m range. In the data from the XBT taken at 0320 U.T. (Fig. 4) a deep mixed layer (i.e. a layer of uniform temperature) is evident between 158 and 200m. In the XBT at 0310U.T., this deep mixed layer occupies the range 156 to 190m. At 0300U.T., the deep mixed layer was in the depth range 180 to 212 m. The general trend of the vertical movement of the mixed layer depth is in agreement with the trend observable in the acoustic data in Fig. 4. For example, at 0320U.T., the acoustic scattering layer was several meters deeper than at 0310U.T. Also the shorter internal waves visible within the packet at a depth of about 25 m are absent from the deeper oscillations. Such short wavelength oscillations would have been detected if they were present, because the horizontal resolution of the acoustic system at 200 m is approximately 50 m. ANALYSIS
An attempt is made to interpret the acoustic data using an open ocean internal wave surge as a model. The original interpretation of the GATE data as an internal surge was inspired by the similarity of the structural form of the GATE wave packet to the form of continental shelf wave packets.* A typical continental shelf internal wave packet is shown in Fig. 2 of the paper by PRONI and AVEL(1975).;" This wave packet shows several features in common with wave packets observed in the GATE area. These features are as follows: (i) the wave packets begin with a downgoing oscillation; (ii) the largest oscillations are at the leading edge of the packet; (iii) the mean scatterer depth before the onset of the wave packet is less than the mean scatterer depth after the onset of the wave packet. (This effect is more marked in the continental shelf wave packet than in the GATE data.) Similarity in form alone is not enough to have confidence in a surge interpretation. The next step in establishing a surge interpretation is to determine what are the expected governing equations and then to determine whether these governing equations admit surges as solutions. The propagation of the continental shelf wave packet (LEEand BEARDSLEY,1974) is known to be described by the non-linear Korteweg~teVries-Burger equation. The downward initial oscillation of the continental surge follows as a natural consequence of energy dissipation. The initial oscillations are thought to be so-called solitons. The causative mechanism for shelf packets is thought to be the interaction of tides with bottom topographic features. BENJAMIN (1967) appears to have pioneered the study of non-linear internal waves in fluids of great depth. He has shown that: (i) the non-linear governing equations of a two-fluid system, one of finite thickness, h, and the other of infinite depth, admit solitary waves as solutions; (ii) these same non-linear equations admit the existence of internal bores or surges. The above conclusions are derived using (and are valid only to the limit of) a first * This does not mean to imply that the mechanism of generating the deep ocean internal wave group under consideration need be the same as that of continental shelf internal wave groups. t T h i s figure is reproduced in the Appendix of this paper.
304
J.R. PRONI,F. OSTAPOFF and R. L. SELLERS
approximation to the effects of finite wave amplitude. The necessary condition for nonlinear effects to manifest themselves and for the applicability of Benjamin's theory is: a'2 h2 ~ 0(1),
(1)
where a is the internal wave amplitude, 2 is the internal wave length, and hi is the depth o f the mixed layer. A typical density profile from the GATE area is shown in Fig. 5. From that figure, we have hi ~ 35m. From Fig. 2, we have a ~ 10m, 2 ~ 400m, hence: a.)~ h~- ~ 4.
(2)
Therefore, we assume the applicability of Benjamin's theory and its consequences (i) and (ii) listed earlier. According to BENJAMIN (1967), the speed of propagation, CNL, for a deep ocean solitary wave is: 3p2 a'x
C2L = C 2 1 + T r o T - J , °tpl nl ]
(3)
where Pl is the mixed layer density, P2 is the density of the lower layer (Benjamin has a two-layer model), and CL is the speed of propagation of a linear internal wave and is given by
. C~= ~{P2--Pl"~ ~ - ) gn,,
(4)
where g is gravitational acceleration. It is of interest to try to estimate the place of origin of the internal wave packet. This can be done if it is assumed that the leading edge of the packet travels CNL and the tail of the packet travels at CL. It is also necessary to know the true length of the packet, Lp. From Fig. 2 the observed length, L, of the packet is roughly 3,5 km. From Fig. 5 one obtains P2 = 1.0265 and Pl = 1.0234. Then, using equation (4), it is estimated that CL = 87 cm s- 1 NOW,
Lp = (CNL-- CL) (tobs -- torigin),
(5)
where tobs is the time of observation of the wave packet and torigin is the time of origin of the wave packet• If r is the distance from the point of observation of the wave packet and L the observed packet length, then
Lp r = CNL(tobs--torigin ) = CNL •(CNL--CL) ~ CNL (c~LL_cL) •
(6)
Thus the maximum value for r is roughly 30 km. Benjamin also gives an estimate for the width of a soliton A: A
4(Pl~z(~) = 3\p-~EJ
~ 83 m.
(7)
Acousticobservationsin the deep ocean during GATE
305
Note that the condition [equation (2)] for the appearance of non-linearity is relatively weakly dependent on 2, so that even if A replaced 2 in equation (2), the non-linearity condition is satisfied. A question of importance is whether there is any observational evidence to support the conjecture that the internal wavegroup shown in Fig. 2 is moving in an easterly or southeasterly direction. There are four data sets that can possibly shed light on this question: (i) additional 20-kHz observations by the authors; (ii) coherent imaging radar observations by ELACHI, CAILLAT and Ross (1977); (iii) hydroglider (a towed variable depth device) data gathered by MOLLO-CHRISTENSEN,MOREY and STRIMAITIS(1975); and (iv) Batfish (a towed variable depth device) data gathered by WOODS(1974). Examination of the ship's track (Fig. 1) suggests that the R.V. Columbus Iselin may have traversed the internal wave packet more than once. The acoustic data between 1200 and 1400 U.T. suggest the idea of an east-southeasterly traveling wave packet. Suppose (as a working hypothesis), that one has an easterly traveling wave packet and that the ship overtook the wave packet while traveling in an easterly direction. At about 1210 U.T., the vessel has passed over the leading oscillation of the wave packet. At about 1218 U.T., the ship turned toward the south and thus should have crossed the wave packet along a trough or crest; this should have resulted in diminished internal wave oscillations (as seen in the acoustic data) but an overall depression of the acoustic reflector level (compared to the reflector level before the onset of the wave group--e.g, at 1210 U.T.) should have been present. That this is the case may be seen by an examination of Fig. 6. As the vessel turned west (about 1237 U.T. Fig. 6) it encountered the latter part of the wave group and apparently once again encountered the depression (identified in Fig. 2 as 'another wave group') following the wave packet of interest. The length of the southerly leg (1210 to 1230 U.T.) was about 3 km, suggesting at least this lateral (i.e. along a crest) horizontal extent for the wave group. Imaging radar observations by ELACHI et al. (1977), show the presence of surface bands of low radar reflectivity. [For a discussion of imaging radar techniques in oceanography see the paper by BROWN, ELACHI and THOMPSON(1976)]. If these bands are interpreted as surface manifestations of an internal wave field, then an east-southeasterly (or west-northwesterly) direction of propagation is indicated. Imaging data gathered by Elachi and his colleagues on September 16, 1974 in the large rectangle shown in Fig. 1, are presented in Fig. 7(a). These data are not precisely coincident with the acoustic data shown in Fig. 1. Also shown in Fig. 7(b) are imaging radar observations in the same general GATE area on September 5, 1974. Several long surface bands, marked 'internal waves' in Fig. 7, appear in the data from September 16. From the alignment of the bands, it can be inferred that internal waves, assumed to be associated with the bands, travel in a southeasterly (or northwesterly) direction. More dramatic records were obtained on September 5, 1974. In these data, two areas that may be internal wave packets are evident. Once again an east-southeasterly direction of propagation is indicated. The imaging radar data, while not confirming the acoustic data in detail, generally support the existence of discrete internal wave groups in the GATE area at the time the acoustic data were gathered. Mollo-Christensen has published a preliminary analysis of his hydroglider observations, which were simultaneous with the acoustic observations aboard the R.V. Colombus Iselin (MOLLO-CHRISTENSENet al., 1975). Temperature and salinity data (obtained by towing the hydroglider) also indicate the presence of an internal wave field propagating either in the southeasterly or northwesterly direction.
306
J.R. PRONI,F. OSTAPOFEand R. L. SELLERS
To facilitate comparison with other data obtained from the hydroglider (MOLLOCHRISTENSEN et al., 1975) and the Batfish (WOODS, 1974, 1976), the acoustic data were analyzed to determine the mean depth of the acoustic reflecting layer for each of the R.V. Columbus Iselin track segments (Fig. 1) and for the standard deviation of the reflector depth, (Table 1). A deepening of the average reflector depth during the passage of the ship over the packet is indicated. Table 1. Mean depths and standard deviations of the acoustic reflecting layers for certain R.V. Columbus Iselin track segments shown in Fig. 1. TIME
INTERVAL
MEAN
(m)
STANDARD
DEVIATION
0820
-
0905
50.4
3.8
0905
-
1015
56.0
3.3
1015
-
1210
58.3
5.2
1210
-
1230
56.7
2.1
1230
-
1330
57.3
2.9
1330
-
1420
56.2
(m)
A substantial amount of additional acoustic data were gathered during GATE. However, although much internal wave activity was detected, few wave packets were detected. A typical example of the internal wave activity frequently seen is shown in Fig. 5(b). CONCLUSIONS
The main conclusions of this study are: (i) acoustic data indicate the presence in the deep ocean of spatially discrete, high-frequency internal wave packets; (ii) the form of the internal wave packet is similar to that of internal wave packets along continental shelves. The main features of the wave packet include (a) a weak non-linearity, (b) a downgoing first oscillation, and (c) a slight deepening of the reflecting acoustic layer; (iii) the place of origin is estimated to be on the order of 30 km from the place of observation. A referee of this paper has asked about the possibility that the wave groups reported in this paper might arise from periods of 'intermittency' in a general background of quasirandom, high-frequency internal waves. To define an internal wave packet, two calm periods (i.e. periods of no high-frequency internal wave activity) are required to define the beginning and the end of the packet. Two such calm periods can arise either by being genuinely calm (i.e. truly devoid of high-frequency internal wave activity) or as a consequence of a momentary nulling of a superposition of quasi-random internal waves. The authors believe that, while it is not impossible, it is highly unlikely that the structural form required of the internal wave group (as stated on page 303) would be produced by a chance (double) nulling of the quasi-random internal wave field. The calm periods on either side of the wave group shown in Fig. 2(a) are several kilometers long, the calm area being terminated by the abrupt onset of the internal wave group. Had the calm period been produced by an extensive null, it is unlikely that such an abrupt large amplitude internal wave onset should occur, rather, one should expect a gentle period of
.-. E
0
T am
"' 50
XBT
_
10-
~i4-n.
~1
uJ uJ k-
.t.6 iB ,I 0
I
iO00
I
I
I
2000 3000 4000 DISTANCE (m)
I
5000
APPENDIX Fig. A 1. The figure is a reproduction of Fig. 2 in PRONI and APEL (1975). The leading edge of the wave packet is on the right. The water depth is about 110 m (New York Continental Shrift.
[facing p. 306]
Acoustic observations in the deep ocean during GATE
307
wave amplitude growth as the null departed. At the present time, the authors can offer no information on the processes of generation of the internal wave groups. Acknowledgements--Useful suggestions and comments were made to the authors at the Southampton (England) GATE data review in the summer of 1975. Thanks are extended to our colleagues at this meeting, particularly STEVENTHORPE,JOHN WOODS,ERIC MOLLO-CHRISTENSEN,and KLAUSHASSELMANN.CHARLESELACHIhas been most generous in allowing us to use a portion of the imaging radar data he gathered in 1974, we sincerely thank him for his kindness. DUNCAN ROSSmade the original suggestion that the imaging radar data lend support to the acoustic wave packet interpretations. T. BROOK BENJAMIN was also kind enough to review this manuscript. CHARLES LAUTER carried out, in expert fashion, the electronics work required in the acoustic observations. REFERENCES APEL J. R., H. M. BYRNE, J. R. PRON1 and R. L. CHARNELL (1975) Observations of oceanic and internal surface waves from the Earth Resources Technology Satellite. Journal of Geophysical Research, 80, 865-881. BENJAMIN, B. (1967) Internal waves of permanent form in fluids of great depth. Journal of Fluid Mechanics, 29, 559-592. BREKHOVSKIKHL. M., K. V. KONJAEV,K. O. SABININ and A. N. SERIKOV(1975) Short period internal waves in the sea. Journal of Geophysical Research, 80, 856. BROWN W. E., JR., C. ELACHI and T. W. THOMPSON (1976) Radar imaging of ocean surface patterns. Journal of Geophysical Research, 81, 2657-2667. ELACHI C., J. CAILLAT and D. Ross (1977) Imaging radar observations in GATE. To be submitted to
Journal of Geophysical Research. GAR6ETr A. E. and B. A. HUCHES (1972) On the interaction of surface and internal waves. Journal of Fluid Mechanics, 52, 179-191. HALPERN D. (1971) Semidiurnal internal tides in Massachusetts Bay. Journal of Geophysical Research, 76, 6573-6584. HUNKINS K. and M. FLIEGEL(1973) Internal undular surges in Seneca Lake: a natural occurrence of solitons. Journal of Geophysical Research, 78, 539-548. LAFOND E. C. (1961) Boundary effects on the shape of internal temperature waves. Indian Journal of Meteorology, 12, 335. LEE C. and R. C. BEARDSLI~Y(1974) The generation of non-linear internal waves in a weakly stratified shear flow. Journal of Geophisical Research, 79, 453-462. MIROPOL'SKIY YU. Z. (1973) Probability distribution of certain characteristics of internal waves in the ocean. lzvestiya, Atmospheric and Ocean Physics, 9, 411. MOLLO-CHRISTENSENE., K. A. MOREYand D. STRIMAITIS(1975) Towed probe observations of upper ocean; made from R.V. Columbus Iselin during GATE III, September 1974, Vols. 1 and 2, Massachusetts Institute of Technology, Department of Meteorology Report, October 1975. pp. 32-34. OSTAPOFF F., J. R. PRONI and R. L. SELLERS(1975) Preliminary analysis of ocean internal wave observations by acoustic soundings. GATE Report, 14, World Meteorological Organization, Geneva, 392-397. PRONI J. R. and J. R. APEL(1975) On the use of high-frequency acoustics for the study of internal waves and microstructure. Journal of Geophysical Research, 80, 1147-1151. SABININ K. D. (1971) Measurement of the parameters of internal waves by means of a moving, spatially separated system of sensors, lzvestiya, Atmospheric and Oceanic Physics, 7, 379. THORPE S. (1968) On the shape of progressive internal waves. Philosophical Transactions of the Royal Society London, Series A, 263, 563. THORPE S. (1974) Near-resonant forcing in shallow two-layer fluid: a model for the internal surge in Loch Ness ? Journal of Fluid Mechanics, 63, 509. WOODSJ. (1974) Batfish experiments on RRS Discovery. Part 1 : Measurements and analysis at sea. Oceanography Department, Southampton University, pp. 1-3. WOODS J. (1976) Batfish experiments on RRS Discovery during Phase III of GATE, 2-16 September, 1974. Part 2: Data processing at Southampton. Oceanography Department, Southampton University, 2nd revised edition, January 1976, 413-414. ZIEGENnEIN J. (1969) Short internal waves in the Strait of Gibraltar. Deep-Sea Research, 16, 479.