Shear observations in the deep thermocline

Deep-Sea Research, 1975, VoL 22, pp. 831 to 836, Pergamon Press. Printed in Great Britain.

Shear observations in the deep thermodine* JOHN C. VAN LEER~ and CLAESG. ROOTH~" (Received 13 May 1974; in revised form 14 March 1975; accepted 19 March 1975) Abstraet--Photogrammetric evaluation of the rate of distortion of vertical dye streaks within the main oceanic thermocline indicates that spiraling perturbation structures overlay the large-scale vertical shear. The data show pronounced shear structure with vertical scales of a meter or less at depths of hundreds of meters. The shapes as well as strengths of the observed shear structure have a strong dependence on depth. At 400 m the major variations in shear had vertical length scales of about I0 to 20 m ; the velocity amplitudes were of the order of 1 era s -x, and the predominant spiral pitch was consistent with downward propagation of energy by internal gravity, waves. Shallower observations suggest a lateral intrusion process as a predominant shear source.

INTRODUCTION

MANY OBSERVATIONSof salinity and temperature microstructure have been made at sea in the main thermocline (SrOMMEL and FEOOROV, 1967; STOM~mL and COOPER, 1967; TAIT and HowE, 1968; and Cox, NAGATAand OSBORN, 1969). With the exception of WOODS' (1968) near-surface Malta data, there are few published records of fine-scale velocity structure in the thermocline. Our data, taken on the research submarine Alvin, dive no. 219, on September 1967, are the only records of fractional meter resolution known to us of shear as a function of depth "taken in and below the permanent thermocline. The dive took place at the 2000-m contour on the continental slope due south of Martha's Vineyard, Massachusetts (70°25'W, 39°45'N). TECHNIQUE

The submarine was equipped with stereo cameras and a dye dispensing apparatus (see Fig. 1). A temperature gradient device was also included, but it malfunctioned. During each experiment, a pair of fluorescein dye pellets was released and allowed to fall, leaving two straight vertical trails separated horizontally by about 1 m. Each cylindrical pellet left a small spiral wake of

ring vortices and plumes that grew to about 20or 30-cm diameter as the wake decayed. These vertical streaks were then distorted according to the time integral of the shear (Fig. 2). By using a redundant pellet, it was clearly verified that streak shape was not due to any random wake phenomenon. After several minutes, the submarine followed the trails, taking photographs at 6- or 8-s intervals. Lateral distortions for 5- to 10-min elapsed time (E.T.) are typically many meters, requiring alert submarine piloting. After 20 min, the distortions become so great that the streaks are very difficult to follow. The most dramatic spiral dye streaks were particularly hard to follow and photograph. Of the 400 exposure pairs made, 76 pairs were reduced on a Ballplex Stereo Projector. These were selected for their photographic clarity, continuity from pair to pair, and lack of submarine interference. In all, seven sequences of photographs were reduced between 167- and 905-m depth, covering 9% of the total depth range. A *Contribution from the Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida 33149. "l-University of Miami, Rosenstiel School of Marine and Atmosphere Science, 4600 Rickenbacker Causeway, Miama, Florida 33149, U.S.A.

831

832

JOHN C. VAN LEFmand CLAESG. Roo'r~

sequence consists of 3 to 20 pairs, which could be joined by three or more common, distinctly identifiable, small-scale wake features between adjoining pairs. The shear was computed from discrete data points sampled from a continuous dye streak while it was projected in stereo. The images were projected in two contrasting colors (red and green). The intersection of both images of the same dye feature corresponded to its scaled spatial position. It was clear that the continuous dye streak could be closely approximated by a series of layers in which the shear was constant. Such a layer projects as a straight line segment on a single, sloping planar screen. This process has a visualaveraging effect, reproducing only the streak features with lateral distortion larger than the dye pellet wake diameter. Thus, only those points where a change of slope or direction of the streak occurred were sampled. This accounts for the nonuniform thickness of the shear layers shown in Fig. 4. Each layer represents the average vector shear between two sampled points and includes both magnitude and direction (in local dye streak coordinates). Successive layers in depth may have either changes in magnitude or direction or both. Because no compass was observed during these measurements, succeeding sequences cannot .be related in direction, except the ones between 418 and 465 m shown in Fig. 3. In Fig. 4, the information on shear magnitude as a function of depth is shown on the right with a dot at the center of the averaged interval, while the angle data are presented on the left in the same manner. The error bars were computed assuming a + 5° error in the position of the assumed vertical about both x and y axes. (These error estimates were found to be quite conservative during a dive in the summer of 1971 where r.m.s. submarine angle variations observed on Alvin's inclinometer were typically less than I°.) MAGNITUDE OF THE SHEAR The average magnitude of the shear, S, was about 10-2 s-x at 167 m. It became smaller with increasing depth until, at 450 m, it became nearly constant, of the order 10-~ s-L Averaging weights

4~5~

48d6'6

4~4 8

!

457e

I

Yr

....

/

•Z

\

42~

/, y /

/

""x,/",0~-,4 xq~L..~o "~"

r%o

" %o 45a,0 45; ~

4304

451.0 456.4 4~.l,y 43545

4524)

434.Z

Fig. 3. Hodograph of the horizontal velocity as a function of depth between 4t8 and 464 m. The vectormean shear of

0"2 × i0-s s-t has been removed. used in computing the average shear for each sequence are the layer thicknesses seen in Fig. 4. The standard deviations, 8, were computed with the same weights. They decreased more sharply with depth than the mean itself.In fact, the ratio ~/~ decreased exponentially from 0.9 in the shallowest sequence to 0.1 in the deepest (Fig. 5). Hence, the shallow shear had small-scale spatial fluctuations in magnitude of the same order as the average shear,while near 9 0 0 m the fluctuations were only one.tenth of the average. Woods' Malta data give ~/~q-----1.28at 30 + 10-m depth in the seasonal thermocline with a mean shear of about 0.011 s-I, which is rather close to the mean shear for the uppermost Alvin data. Examination of the magnitude of the shear in Fig. 4 shows that regions of relatively intense shear tend to be thin compared to the intervening regions in the shallow observations. In deeper measurements, these regions have nearly equal thickness. In the terminology of WOODS (1968), the thin intense shear regions are called sheets, and the thick regions of low shear are called layers. Woods' shallow Malta data are plotted in Fig. 5

r

~o~

m"

Fig. 4.

m

Vector shear as a function of depth from Alvi~ dive 2! 9, I 0 Seplember 1967.

Depth,

0

o

0

0

834

JOHNC. VAN LEERand CLAF~G. ROOm

iO01

T

o.I

i

0

z

i

s

l

i

JLI,I

wood's data-~7 mean

,/ /

.o"

~'0o

/

:sOO

/

400

/

500-

t

1.0

o/°

/

/o o

* 0 0 -~

/ 700 -

sac

L ,/

/

/

/

gap. Each hodograph has the same shape as the dye streak when viewed along the direction of the mean shear. The displacements are arbitrarily normalized to the displacement 2 s after streak formation. The large-scale angular features of these shear records can be seen best in the hodograph in Fig. 3 where complete direction reversals often occurred on an approximately 10-m scale. The angular variations with somewhat smaller depth scale with 90 ° or less direction changes were also present. These streaks are spiral-like, suggesting several physical processes.

900'

SUPPORTIVE TEMPERATURE, SALINITY, AND DENSITY RECORDS

t000'

Fig. 5. Ratio of the standard deviation from the average shear to a v e r a ~ magnitude of the shear as a function of depth for Alvin dive 2i9.

(inverted triangle); they appear more sheeflike than even the shallowest Alvin shear data. THE A N G L E OF THE SHEAR

The angle of the shear vector changed significantly on the same vertical scale as its magnitude. Variations of 90 to 180° on vertical scales of 1 m or less occurred in all dye streak records reduced. The correlation between changes in angle and changes in magnitude as a function of depth does not generally appear strong. The shear angle changed more rapidly with depth near the surface than at greater depth, similarly to the magnitude changes discussed above. The two longest records were between 418 and 464 m (see Fig. 4). The single 3-m gap in these records represents only a 24-s loss of information. This makes is possible to fit the two angle records together with minor error (probably less than 4- 10°). These data are presented hodographically in Fig. 3. The vector mean shear of 0.2 × l0 -3 s-1 was removed from both hodographs, forcing the shallowest and deepest point on each to coincide. The origin o f the lower hodograph has been displaced by an arbitrary amount from the origin of the upper one, reflecting the unknown displacement change over the 3-m data

Because of equipment failures no usable temperature or salinity data were obtained during the dives; hence, other data were used for interpreting the shear data. STD Stas. I to I0, taken on Wunsch's Atlantis H cruise No. 47, ran down the continental slope past the Alvin dive site and on to site D (39°20'N, 70°00'W); These stations were taken in mid=November and should give salinity and temperature information similar to that at the site of Alvin dive No. 219, except perhaps in the near-surface region. In particular. the large salinity-stabilized temperature inversion is seen on most of the slope and shelf stations at about 75 ± 20 m. Below I00 m, smaller temperature inversions, which decrease in amplitude and frequency with depth, are present but becoming rare below 300 m. Similar inversions were noted on the Alvin dive because they interrupted sonic communications with the surface and registered on the sphere's temperature indicator. These features are clearly shown in the profiles from Sta. 8 (Fig. 6). Below 150 m, warmer, saltier water overlies colder, fresher water so that the temperature and salinity gradients are generally in the proper sense for salt fingers to be present. Between 150 and 275 m, the average salinity gradient was 0.003%0 m -I, which is about the same gradient found in the main thermocline near Bermuda at 500- to 700-m depth. The smallest shear measured in a single layer was 3 4- 1 x I0 -as -I at 236.3m

Shear observations in the deep thermocline

835

~ i 4°

5°

6°

3oo:: 400:

'7 °

~?;o IB°

~ ii

~,;o i 9°

iii

Salinity, %, 2,io i i I0 °

=

~io

~fio

Temperature, I to

12o

I~ °

I

*C 14 e

J

,~L 15°

i

, ~?;o,,, ;~?,,,

lip

~

I'~

lip

IItO

/

/

E

60o!

I 1400 ~

Fig. 6.

Temperature, salinity, and at profiles near the Alvin dive site Atlantis//cruise 47, Sta. 8, 16 October 1968.

(Fig. 2b, below and to the left of the kink in the center of the pictures). The difference in velocity over this 40-era layer was 1.2 4- 0.6 mm s-1. This extreme resolution is made possible by the dye streaks' time integration over an approximate 15-min period. There were long, laminar-looking filaments streaming out of the spot on the left streak. The filaments were clearly sheared, even in the weakly sheared layer. These fingerlike filaments were doubtlessly enhanced or triggered by the presence of the fluorescein dye. This structure looks unlike that seen in locations with stronger shears, and it may give some idea of the appearance of an actual salt finger layer. DISCUSSION

If one considers steplike variations in density and velocity with depth to be evidence of some mixing process, then variations of their vertical gradients compared to their mean vertical gradient at some location may be a measure of the intensity of this mixing. This same reasoning should hold for the intensity of intermingling o f sliding layers. The ratio of O/S appears to decrease exponentially from the surface with an e-folding scale of 350 m. (Fig. 5). This may be evidence that internal mixing is more intense near the surface. Internal wavelike motions could propagate downward from a nearsurface energy source, decaying as they propagate and causing progressively less intense mixing with

increasing depths. In the following discussion, we will examine an internal wave and adveeting layer explanation of these dye streak data. Consider a packet of plane waves propagating in the x - z plane with the dominant component exp i ( k x + lz - - cot). We have then, according to standard WKBJ (WENTZV-L,KRAMERS, BRILLOUIN, JEFFREYS) approximation, the dispersion relation: (N 2 -- co~) k 2 = (co~ - - f ~ ) F.

(1)

The vertical component of the group velocity is: boo

co

Ol

1 k ~ + lS

l3

o

N 2 --

o~ 2

1 N 2-f2'

(2)

i.e. the vertical group propagation is in the opposite sense to the phase propagation. The momentum equation in the ),-direction is

icov + f u = 0.

(3)

Thus, if u = exp i ( k x + lz - - 030, then v = / f o ) -1 exp ( k x + lz - - 030, and the local time hodograph is a clockwise ellipse with the axis ratio o i l A spatial hodograph of the form of a right-handed spiral implies then an upward phase propagation, with associated downward propagation of energy. Both data sets in Fig. 3 grossly appear to be right-handed spirals with eccentricity of one in

836

JOHN C, VAN LF.~Rand CLAESG. ROOTH

three. At the latitude of the experiment, this eccentricity would correspond to a downward propagating internal gravity wave packet with an approximately 6-h period, i.e. possibly a second harmonic of the semidiurnal tide.

Advecting layers The temperature and salinity records (Fig. 6) have numerous strong salinity-stab'flized temperature inversions in the upper 200 m. These suggest advective intermingling of water masses from the continental shelf, 40 km away, with the local slope water. At greater depths, the source of possible advected layers becomes less dear. These layers might be formed by mixing processes such as breaking internal waves on the continental slope as proposed by CACCmONE (1970). The 180 ° reversals look similar to those shown in his Fig. 68. F o r Cacchione's mechanism to be valid, a horizontal propagation of these layers of 20 or more kilometers from the slope would be required. Since N f -1 ~- 25, the horizontal scale o f d d o r m a tion is about 250 m for a layer 10 m thick in local geostrophic balance. Thus, the + 0 . 7 cm s-~ layer velocities cannot he associated with the direct intrusive process from the shelf. I f these features oh#patted 20 k m distant, they could only have arrived at the dive site through advection, owing to geostrophie processes of a much larger vertical scale. CONCLUSIONS

The direct visual observations of dye streak distortion made during several Alvin dives have indicated the frequent occurrence of pronounced shear with spiral-like vertical structure in the sense of a right-hand screw. The photogrammetric evaluation of a few dye streaks sugsests that the main contender for generation o f such structure is horizontal advection near the surface where the streaks have a more two-dimensional character and gravity-inertial wave propagation at depths greater than 400 m. Considering Richardson number variations as a function of local static stability, the occurrence of a sharply defined layersheet combination of the type described by WOODS (1968) appears mainly limited to the seasonal thermocline. The detailed mechanics for the maintenance of the near-surface structure cannot be deduced from our data. At greater depth, the smoother shear profiles

with spiral-like structure and predominant wavelengths of about 10 or 20 m suggest a downward propagating internal gravity wave packet with ~ 6-h period. Its r.m.s, velocity amplitude was about 0-5 cm s -1. While it is true that frictional coupling in a rotating fluid leads to a spiral hodograph tbr the horizontal velocity as a function of z, the associatedd amping of amplitude with depth rules outthis mechanism as an explanation for our observations. The time-dependent Ekman problem leads to spiral solutions with scales of [u/(c0 ± f)]*, but always effectively damped in half a wavelength [exp ( - - n ) is about 0.05]. Relatively close cominental shelf topography or surface disturbances seem to be the source of gravity wave energy packets propagating past the observation site that is most compatible with our observations. It appears that currem measuring devices, even at these depths, must either sample with a few meters vertical resolution or encompass an integrating mode of velocity recording to avoid spatial aliasing problems in the main thermocline.

AcknowledfementsmWe gratefully acknowledge the assistante of Mr. Ttmooo~ Si,~qc~ in the construction of the dye di~etut~. ~ . DAvm N t a o ~ , GOgUONBaOWN, and DAVIDDlttrmaONO am thanked for their labors in the stereo ~ o n of the clam. This work was carried out at M.I.T. under NSF grants GA-1015, GA-1613, GA-12773, and GA-21172. ONR supported the work at Woods Hole (keanostaphic Institution involving the use of Alvin under Contr~t No. N00014-66-C-0241, Project NR 053-004. Finally, we wish to ae.knowkstgethe support and e n c o ~ t

of Profa~m" HmcRY STOIeI~L. REFERENCES

CACCHIONB D. A. (1970) Experimental study of internal gravity waves over a slope, Ph.D. dissertation, Mas~:hu~tts Institute of Technology and Woods Hole Oceanolraphie ~ t i t u t i o n . Cox C., Y. NAOATA, and T. OSBORN (1969) Oceanic fine structura and internal waves. Bulletin of the

Japanese Society of Fisheries Oceanography, special number (Professor Uda's commemorative papers), 67-71. STOtm~m. H. and J. Coot~Sit (1967) Regularly.spaced steps in the main thermoetine near Bermuda. Journal of GeophyMeal Re.sem.eh,73(18), 5849--5854. STOMMm. H. and K. N. ~DORoV (1967) Small scale structure in temperature and salinity near Timor and Mindanao. Tellus, 19, 306-325. TAIT R. I. and M. R. Hown (1968) Some observations of the~xiohaline stratification in the deep ocean. Deep-Sea Research, l& 275-280. WooDs J. D. (I968) An investigation of some physical processes associated with the vertical flow of heat through the upper ocean. Meteorological Magazine. 65-72.