Near-Bottom Speed and Temperature Observations on the Blake-Bahama Outer Ridge

Speed and temperature measurement made in the bottom boundary layer (BBL) in the region of the Western Boundary Undercurrent at 28/sup 0/22'N, 74/sup 0/13'W over an approx.11 day period are presented. The observations suggest that the BBL structure is consistent with that of a turbulent Ekman layer formed in an initially stably stratified fluid over a uniform surface even though they were obtained in and above an abyssal furrow. The inferred friction velocities u/sub asterisk/ (u-bar/sub asterisk/=0.66 cm/s) generally are larger than those inferred by Weatherly (1972) under the Florida Current and at times sufficiently large to result in erosion of some of the finer cohesive sediments if the criterion for their erosion summarized in McCave (1978) is assumed to apply at the site of the observations.

The first factor is the accuracy of (1) as a representation for U(z) near the bottom.The furrows, being oriented downcurrent and spaced about two boundary layer thicknesses apart, may be due to Langmuir-like circulation patterns or 'vortex rolls' in the bottom boundary layer (BBL).Such vortex rolls are thought to be ubiquitous features of turbulent stream flows including turbulent Ekman layers [Tennekes, 1973].Regions of horizontal convergence (divergence) near the surface owing to these secondary circulations are regions of enhanced (reduced) turbulence production [Tennekes, 1973].Thus the presence of secondary circulation patterns may not conflict with the flow being logarithmic near the surface.Logarithmic layers are observed near the surface in nearly all turbulent shear flows.However, whether a logarithmic layer can be expected to form over a longitudinally furrowed surface is not clear.This study indicates that, at least in the smaller furrowed region, this does happen.It appears that locally the BBL settles smoothly into the furrow in such a way that the local velocity profile is everywhere like that of a turbulent Ekman layer over a uniform surface.
The second factor hinges on the value of von Karman's constant g used in (1) to evaluate u,.As was discussed in Tennekes and Lumley [1972], g is a constant only in the limiting sense of the turbulent Reynolds number Re, --u,h/•,--> oo, where h is the boundary layer thickness and •, is kinematic viscosity.In the large Re, encountered in the atmospheric layer there is some reason to believe that g --0.35 rather than the traditional value of 0.4 deduced from laboratory studies done at lower Re, [Businger et al., 1971).Since Re, in this study is about 2 orders of magnitude smaller than that of the atmo-Paper number 80C0238.0148-0227/80/080C-0238501.00 spheric boundary layer, we take K --0.4.If indeed the value of 0.35 as was suggested by Businger et al. [1971] is appropriate for the present data set, the u, values presented here are overestimated by about 14%.A second uncertainty in choosing a value of K arises when the fluid is no longer clean but is sediment laden.Large concentrations of sediment in water lead to an apparent reduction in • by as much as 50% [Yalin, 1977].However, because of the low u, values inferred in this study, in comparison with those in Smith and McLean [1977], the suspended sediment concentration gradients are thought to be sufficiently small not to affect • and hence the speed profile.within the logarithmic layer was six, which is considerably greater than the required minimum of two.So far as these statistical considerations are concerned, we feel that the u, values have a standard error of about 0.5 cm/s.

EXPERIMENT
The site of the observations, 28ø22'N, 74 ø IYW, is on the western flank of one of the two ridges which comprise the BBOR (Figure 1) in water of depth 4750 m.The Western Boundary Undercurrent supposedly flows along isobaths northward at this site; further downstream it is believed to be deflected counterclockwise still following isobaths and to flow southward at the base of the Blake Escarpment [Heezen and Hollister, 1971].Furrows are nearly ubiquitous features in the BBOR area, being absent only on the crests of the two ridges [Flood, 1978].The site is about 11 km downslope (west) of the Bahama Outer Ridge crest and about an equal distance upslope from the eastern edge of a region of large abyssal mud waves (amplitudes tens of meters and wave lengths about 2 km) [Flood, 1978].The sediments in this area are cohesive muds of composition 2-11% sand, 31-36% silt, and 58-63% clay [Flood, 1978].
The instrument used to measure the speed profile is shown schematically in Figure 3.It is very similar to an instrument described by Weatherly [1972], which was used to measure the speed profile in the bottom boundary layer of the Florida Current.It is a different instrument, however, not previously described, and a brief description follows.On the instrument are ten Savonious rotors and four thermistors.The height above bottom, during the experiment, of each sensor's midpoint is given in Table 1  A second instrument deployed in the area consists of a tripod frame, in which is mounted a camera system to take time sequences of bottom photographs, and a single vector averaging current meter (VACM), to record the current speed and direction at elevations of 70 and 92 cm, respectively.A similar apparatus is described in Wimbush and Lesht [1979].
This A total of three dives were made by the submersible Trieste H in the vicinity of these instruments.The information on the sediment given earlier was deduced from bottom cores taken on one of those dives [Flood, 1978].

a. The Near-Bottom Current
Since simultaneous measurements of currents at various heights in the benthic boundary layer are not yet common, it may be of interest to consider the speed time series obtained.

c. Time Averaging
In (1) the speed U is an average speed.For the atmospheric boundary layer it has been found that the appropriate averaging interval is about 15-20 min.Monin [1970] justifies the use of this interval on the basis of a deep minimum in the spectrum at this point.Wyngaard [1973] estimates that for (a x 100)% accuracy the averaging interval T should be where *i is the integral time scale which he approximates by z/ U.For 1% accuracy in the atmospheric logarithmic layer, he estimates T = 15 min.
No comparable minimum has been noted for spectra obtained in the bottom boundary layer.However, this may be due to the spectral density E(n), where n is frequency, being examined [Wimbush and Munk, 1970;Weatherly, 1972]   In section 3c the appropriate averaging interval is estimated to be of the order of several hours.In Figure 10 are shown time series of u,, Zo, and t a determined from 6-hour averaged speeds.The input data are the six 6-hour averaged and decimated time series obtained from the rotors at z = 0.18, 1.05, 1.33, 1.89, 3.67, and 5.65 m.As is noted above, the 0.99 confidence level for a 6-point fit is that ?_> 0.84.All the computed ?were greater than 0.84 (Figure 10d).One might conclude that all the 6-hour averaged profiles were logarithmic up to z --5.65 m.However, as we try to demonstrate below, one must be careful in making conclusions from such a test.
In part from examination of sample profiles and the meanspeed profile (Figure 8b), we conclude that the flow was logarithmic up to about 6 m above the furrow bottom but never up to 19 m.The observed speed at 19 m (more precisely 18.75 m) was consistenly larger than the value predicted for that level from the six-point fit curves (i.e., using speeds obtained for z < 6 m).Thus, for example, in Figure 8b the observed speed at this level falls to the right of the dashed curve.However, if we assume the logarithmic layer extended to 19 m and do a seven-point fit to (1) (i.e., use the speed data for z _< 19 m), the computed t a is always larger than that necessary for a 0.99 confidence level for a seven-point according to the t test.Thus using this test one might conclude (we believe erroneously) that the speed profile was logarithmic up to 19 m.
By examining sample profiles we subjectively conclude that for a six-point fit when r 2 •> 0.987, the speed profile was logarithmic up z = 5.65 m.About 7% of the r 2 displayed in Figure 10d are less than 0.987.If we neglect the t a value determined from profiles obtained during the first 24 hours (see below), less than 2% were less than 0.987.In the sense that the ?values exhibit smooth behavior and are generally large (much greater than 0.84), and the inferred u, and Zo values also exhibit smooth behavior, an averaging time of 6 hours apparently yields reliable estimates of u, and Zo.
During the first day of the experiment the current speeds are largest and the six-point fits are poorest (Figure 10).In other speed data from a similar instrument we have noticed that the measured profiles are relatively less logarithmic during the first few hours of observation.We suspect that the relatively poor fit for the first day's data in Figure 10 is not owing to the speeds being largest then but rather to an instrumental effect (e.g., grit in the motor bearings which gets washed out after a few hcurs).
One might expect a correlation between the current direction and ?.For example, one might expect a better fit (larger t a) when the flow was along the furrow axis and a worse fit (lower t a) when the current direction was at an angle to the furrow.Figure 10e shows the current direction as a function of time measured concurrently by the VACM on the tripod instrument.Somewhat surprisingly there is little visual associaton in the t a and direction curves shown in Figure 10.Even a polar scatter plot of t a with current direction (not shown) shows no apparent pattern.This may be due to the fact that the current direction was rather constant 330 ø + 25 ø.
While there is no apparent dependence of ? on current direction, t a values are found to be somewhat correlated with current speed.From Figure 11 1).However, while the 9-min average fits are the worst, they still are not bad.Over 60% of these fits had t a _> 0.987, and over 85% had t a _> 0.960.For time scales of 9 min the flow profile is sufficiently logarithmic that reasonable estimates of u, and Zo can be obtained by using

g. Sediment Erosion
Shown as a time-lapse motion picture of the seabed, the film record from the tripod camera shows only one clear indication of hydrodynamic disturbance of the bottom.This is the washing away of one small (--,« cm) lump of sediment in the field of view of the camera at the beginning of the experiment.It is probably that this lump was a product of the disturbance caused by the apparatus landing on the seabed.Hence its erosion may not be significant, except that it suggests the likelihood of erosion of biogenic forms in the environment.After the tripod is moved to the furrow flank, no erosional activity is visible in the film.In particular, we see no perceptible migration of the three flank ripples in the field of view of the camera.
However, our measurements of u, suggest that erosion may  8, recalculated from data of Southard and coworkers) show that material may be eroded by stresses as low as u, = 0.4 cm/s.However, that is for calcareous ooze with high water content.The sediment of these furrows has 38-45% CaCo3 and 52-58% water [Flood, 1978].
For calcareous ooze with this water content the critical erosion stress corresponds to u, = 0.6 cm/s.We conclude from our inferred u, values that u, > 0.6 cm/s about 68% of the time.If this critical u, = 0.6 cm/s for erosion applies, then erosion of some of fine calcareous ooze presently occurs in the furrow floor.However, the presence of red clay which has a higher critical u, for erosion (u, •> 3.5 cm/s [McCave, 1978]) in the cohesive sediment at our site [Flood, 1978]  mixed layer, or in the stably stratified water above the thermocline.Only when the current at 19 m attains a speed of about 20 cm/s does the noise level in the highest thermistor reduce to that of the other three thermistors.This suggests that at such times the mixed layer extends above z = 30 m.No conductivity, temperature, and depth or salinity, temperature, and depth casts were made during the time of the observations.However, a mixed layer of thickness -•30 m is not inconsistent with observations of these layers made at other times in the general area [Flood, 1978;Greenwalt and Gordon, 1978].

Fig. 1 .
Fig. 1.Sketch of bathymetry in the Blake-Bahama Outer Ridge area inferred from Flood [1978, Figure 2.1].Numbers are depths in kilometers.The two ridge crests are indicated by dashed lines and the site of the measurements by a cross.

Fig. 2 .
Fig. 2. Photograph of the furrow in which the profiling instrument (Figure 3) landed.The anchor weight indicated in Figure 3 is buried beneath the furrow floor.For reference the dimensions of the lowest rotor cage are 23 cm x 21 cm.

Fig. 3 .
Fig. 3. Schematic of the profiling instrument.The lowest part of this instrument appears in Figure 2.
tripod instrument was launched on September 18, 1977, and reached the bottom at about 0130 UT on September 19.It was found by Trieste II on September 24 a few meters from the edge of a furrow and about 800 m east of the other instrument.(Only our dislike of being thought ridiculous prevents us from suggesting that horizontal convergence owing to furrow-associated vortex rolls in the B BL was responsible for one instrument landing directly in a furrow and the other landing a few meters from a furrow rim.)The submersible then maneuvered the tripod to the rim of the furrow so that the camera was looking at the ripples in the upper part of the furrow wall.Figure 4 is a photograph taken just after the instrument has been repositioned.At the end of the experiment the release system failed, and the instrument was lifted off the bottom by Trieste II at 2305 UT October 1, 1977.

Figure
Fig. 4. Photograph of the tripod instrument after repositioning by Trieste H on a furrow flank.The length of one side of the tripod is 1.6 m.

Fig. 5 .
Fig. 5. Time series plot of the ten 9-min averaged speed records obtained from the profiling instrument.

Fig. 7 .Fig. 9 .
Fig. 7. Time series of the VACM record from the tripod instrument.Shown are current direction (in øT), speed, eastward and northward components, temperature, and compass heading.The temperature measuring circuit apparently took about 12 hours to stabilize at the beginning.The disturbance in compass heading, early September 24, is due to repositioning by Trieste H.

Figure 8b indicates that
Figure 8b indicates that the mean speed profile was logarithmic for O. 18 m _< z _< 5.65 m.The straight line in this figure is the least squares fit of (1) throught the lowest six points.The computed coefficient of determination r 2 (r is the correlation coefficient) of the data about this least squares fit is 0.9995.For a 0.99 confidence level in a six-point fit, the t test requires that t a _> 0.84.This test reinforces what is suggested by a visual examination of Figure 8, namely, that (1) is a very good approximation to the mean speed data over the range 0.18 m _< z _< 5.65 m.The u, and Zo values determined from this least square fit are 0.66 cm/s and 0.49 cm, respectively.In section 3c the appropriate averaging interval is estimated to be of the order of several hours.In Figure10 are shown

Fig. 12 .
Fig. 11.Scatter plot of the r • values in Figure 8 and 6-hour averaged speed at 3.67 m.Circled values are those for the first day of the experiment.

( 1 )
. Increasing the averaging intervals results in a smoothing of the u, and the Zo series.The histograms of u, and Zo in Figure 12 only become narrower as th• averaging time increases.Consistently better fits (larger t a) are obtained as the averaging interval is increased.For a stationary flow this is expected ((2)).However, for a nonstationary flow (i.e., in (1) U = U(t)) it is not apparent that this should be the case.The mean values of the u,, the Zo, and the t a values inferred from consecutive 9 rain, 1.5 hour, 6 hour, 24 hour, 256 h profiles are given in Table 2.The mean u, value for the 24-hour averaged data is somewhat smaller than the others because the last 16 hours of data, when the current was relatively strong, does not contribute to this mean but does contribute to the others.Implicit in the above is the assumption that the logarithmic layer extended to 5.65 m even when the current was relatively weak.If this were not the case one would expect relatively low t a values (poorer fits) for six-point fits to be associated with periods of weaker flow.A comparison of Figure 10c and 10d shows that this is not the case.Earlier in discussing the speed spectrum for the record obtained at z --1 m, the rise in the energy level occurring for n •> 0.6 cph was attributed to shear generated turbulent fluctuations in the BBL.If this is correct, then with E(n) being the observed spectrum, Eb(n) the estimated background spectrum, rtl • 0.6 cmph and n2 = 3.33 cph (the Nyquist frequency)

Fig. 13 .
Fig. 13.Segment of the raw temperature time series measured by the four thermistors.For presentation purposes, some of the time series have been offset vertically by an arbitrary amount.
' data which we have obtained consists principally of current speeds above the bottom of a small furrow and simultaneous current speed and direction over the flank of a similar furrow.The most distinctive feature of these records is the steadiness of the current both in speed and in direction.Presumably because of this steadiness we find the logarithmic law fit to the data to be the best that we have seen for a benthic boundary layer (though at first we thought the furrow might prevent a log layer from forming).This logarithmic layer was characterized by friction velocity u, = 0.66 cm?s, Zo --0.5 cm, and thickness/•, = 5.6 m.The shear stress is larger than that determined for the BBL of the Florida Current (u, which the boundary layer is assumed horizontal!y uniform.The input parameters to the model IVl, f, Zo, and No were assigned the values quoted above.The model predicted u, = 0.66 cm/s,/•,, --6 m and hmix --27 m, which is in close agreement with values inferred from the data.The data presented here a re insufficient to determine whether the smaller furrows in the B BOR region are relic or active features.The presence of weed in the furrow may help scour and maintain the furrows.The sharpness of corners at which the floor and walls meet suggests that these furrows are not just relic features.The inferred u, values for the furrow floor may be sufficiently large to result in erosion of some of the finer cohesive sediments.The results summarized in McCave [1978] suggest that calcareous ooze may be eroded for u, •> 0.6 cm/s.This, together with the observation of coarsest sediments in the furrow bottom, less coarse in the furrow wall, and least coarse outside [Flood, 1978], leads us to speculate that the data are not inconsistent with these furrows being active features resulting from vortex rolls which cause the u, values inside a furrow to be slightly larger than outside.The region of horizontal convergence near the surface is where the turbulence is largest [Tennekes, 1973] and should coincide with the furrow axes.If such vortex rolls do exist in this region of the BBOR, the reason for their existence (the postulated ubiquitous existance of such features in turbulent wall boundary layers [Tennekes, 1973] or Taylor-Goertler vortices associated with boundary layers on concave walls (see Figure 1 and Schlichting [1968, p. 504-509])) remains the subject for future work.