a. ARIES II

ARIES II was placed on the seabed in a water depth of about 43.5 m at 53°41.01′N, 4°09.30′ W in the eastern Irish Sea southeast of the Isle of Man at 1408 UTC 12 July 2006 (designated in figures as Julian day 192, where 1 January 2006 is day 0) and was recovered after a continuous recording period of almost 3 days. The English coastline and the estuaries of the Rivers Mersey and Dee are about 70 km to the east. The seabed at the location is very flat and smooth, with no major bed forms in the area of operation. ARIES II carries two 250-kHz linear transducers set to point upward at 25° from the horizontal when their supporting frame is level. The side-scan sonar beam directions were 173 ± 5°true (T) and 83 ± 5°T, fortuitously almost normal and parallel to the near-rectilinear M₂ tidal flow, which runs in directions of 82°T (flood) and 262°T (ebb), roughly due east–west, and has an amplitude of about 2 m during the observations. The orientations greatly simplify the interpretation of sonographs. For brevity the beams are referred to later as the “south” and “east” beams.

The sonars are as described in Thorpe et al. (1998). Each sonar transducer emits 275-μs-long pulses of sound twice a second, giving an effective target resolution of about 0.25 m. Returns from near-surface targets, bubble clouds, or steep waves, are generally detectable to ranges of about 140 m or, given the water depth of (43.5 ± 2) m, to horizontal distances of about 130 m. The main beams are each 33° wide in the vertical and 1.6° in the horizontal (angles measured to the −3-dB points), and isonify strips of the seabed and surface along the beam directions. Because of problems during deployment, the frame carrying the sonar was not level, and as a result the south beam is tilted upward at about 13° from the horizontal and the east beam is tilted at 27.5°. Both beams have sidebands. These make the relatively high scattering sea surface above the sonar detectable in the sonographs. Because of the relative “tilt down” of the south beam, reflections of sidebands from the seabed contribute to stronger signals in this beam than in the east beam. Seabed scattering masks some of the scattering from subsurface bubble clouds immediately above the sonar rig. (We refer to other consequences of the different beam tilts in section 3d.)

During the 3-day deployment, there are 12 periods of maximal tidal flow. Eight periods are selected for sonograph analysis. The other periods occur either when winds were less than about 3 m s⁻¹ or following periods of calm, when the surface scatter is relatively low and the detection of boils is uncertain at best, or when wind direction was highly variable. Boils are detected and their dimensions are estimated in all of the remaining eight periods of large tidal flow.

The processing described by Thorpe et al. (2003) is used to produce sonographs. Figure 2 is an example of a pair of sonographs obtained from the two beams over a period of 15 min. Only the echoes from targets in a range interval from 40 to 120 m are shown. Sonographs at shorter range are dominated by scattering from targets on the bottom at fixed positions in the range. The east beam (see Fig. 2b) provides a record of the advection of targets (relatively dark regions, in some cases probably boils but more often bubble clouds) close to the sea surface along the sonar beam by tide and wind, and thus provides a measure of the surface current. The tilt of targets at ranges of 80–110 m is about 30 m divided by 29 s, giving a current component of about 1.03 m s⁻¹. Small, dark blobs are reflections from breaking waves. The sea surface appears as a line at a range of about 44 m. Reflection from some fixed-bottom targets is visible just beyond this range.

The south beam (see Fig. 2a) shows scatter from targets, including boils, on the sea surface that are advected by the tidally generated and wind-generated flow across the narrow sonar beam. The boils are best seen by viewing the sonograph from below at a small angle to the plane of the figure, when their outlines appear as ghostlike, but definite, crescent-shaped regions of enhanced acoustic scatter. Because the scatter arises predominantly from the regions where convergence causes waves to steepen, and these are of the upwind-facing parts of the divergent regions of rising water as sketched in Fig. 1, only parts of the near-circular boil outlines are generally visible (as crescents) and relatively rarely can their extent be estimated in directions both across and along the tidal flow. The across-tide dimension is the vertical extent that is apparent in the south beam sonograph (Fig. 2a), with the range corrected to the distance along the sea surface. The along-tide dimension is estimated (making the Taylor frozen turbulence hypothesis) from the time a boil is visible in the south beam and from the advection speed estimated from the tilted bands from reflectors carried along in the east beam. [The bands are actually hyperbolas in the range versus time images; see Thorpe and Hall (1983).] It is assumed that the boils move at a speed close to that of the surface flow. The times at which boils are present are shown in Fig. 3a.

b. FLY, ADCP, and CTD

A series of FLY casts (12 h⁻¹) was made from a research vessel, the Prince Madog, steaming at about 0.5 kt through water along a 2-km east–west track about 1.8 km north of the ARIES II position for 24 h from 1207 UTC 13 July. Two further 4-h series were made during flood tides in the following 24-h period. Estimates are made of ε, the rate of loss of turbulent kinetic energy per unit mass (Fig. 3c), using the methods described by Simpson et al. (1996), between a depth of about 5 m (above which turbulence from the vessel’s wake may corrupt the measurements) and a height of 0.15 m from the seabed. Current data, shown in Fig. 3d, were obtained from a bottom-mounted 600-kHz RD Instruments (RDI) ADCP sampling every second about 0.4 km west of ARIES II. There is a gap around Julian day 194 resulting from instrument malfunction.

CTD casts were made every 4 h during the FLY series. For much of this time the density gradient is almost constant with a vertically uniform buoyancy frequency N of 6.2 × 10⁻³ s⁻¹, but in the periods following the westward flow of the ebb tide, the upper 20 m of the water column became stratified with surface temperatures some 0.6°C greater than those at depth, and N reaches 2.4 × 10⁻² s⁻¹ in layers 3–5 m thick. Changes in temperature stratification determined from the FLY series are shown in Fig. 3e.

c. Autosub

The 7-m-long, 0.9-m-diameter AUV Autosub is described by Millard et al. (1998). It was deployed at 1029 UTC 13 July (Julian day 193) and set to run 5-km legs at a constant height of 6 m above the seabed or at constant depths, across and along the tidal flows in a square surrounding the ARIES II position. The AUV was unfortunately underpowered during this mission and its mean speed through the water was limited to about 1 m s⁻¹, which is substantially and critically less than the speed of about 1.25 m s⁻¹ obtained in earlier missions (Thorpe et al. 2003). The AUV was therefore unable either to make progress over the bed when opposed by the maximum tidal flows that exceed 1 m s⁻¹ (Fig. 3b) or to hold course in traverses across such flows. In consequence, the AUV tracks were sometimes irregular, “attack angles” variable or uncertain, and the period over which useful data are recorded is much less than the mission duration of 50 h. The times of the particular legs analyzed later are shown with their respective leg numbers below (Fig. 3e).

The AUV carried a CTD, two ADCPs, a turbulence package with two airfoil sensors, measuring variations in vertical and transverse relative velocity components, and a fast-response thermistor. The CTD and ADCP (and the sub’s internal navigation) logged data every second, whereas the turbulence package sampled at a rate of 512 Hz. Further details of the package and the estimation of ε are given in Thorpe et al. (2003, their appendix A). Values of ε are estimated at 1-s intervals along the AUV track through the water, corresponding to distances of about 1 m. There is a consistent tendency for temperature to rise slightly and for salinity and density to fall in the AUV legs made toward to the east, with reversed trends in westward legs. The depth of the AUV is shown by the black line superimposed on the FLY estimates of ε in Fig. 3c. Arrows on the time axis show when the controlled depth or height above bottom of the AUV is changed.

a. The variation of tidal flow and turbulent dissipation rate

The tidal flows shown in Fig. 3d are not symmetrical, with the ebb currents (typically 1.0 m s⁻¹ near the surface) being less than those in floods (about 1.2 m s⁻¹). The temperature contours (Fig. 3e) show a further asymmetry: much of the water column becomes stratified in temperature toward the end of the westward-going ebb tide (positive in Fig. 3d). Stratification is reduced in the period of increased turbulence of the eastward-going flood tide, and no subsequent stratification is reestablished at the end of the flood flow. These variations are consistent with the effects of tidal straining of the horizontally varying density field (Simpson et al. 1990; Rippeth et al. 2001; see also Fig. 7). The shear in the westward-going ebb tide tilts isotherms, carrying the less dense, warmer, and less saline water observed to the east (see section 2c) over the cooler, more saline, and denser offshore water. This results in the thermal gradients in Fig. 3e. As the flood tide subsequently carries the stratified water eastward, the vertical stratification is affected by the turbulence at the seabed and by the effect of vertical shear acting on the horizontal density gradients. These two effects both act to reduce the vertical density gradients, and even to promote unstable stratification, leaving only weak remnant stratification.

It is evident from the variations of logε measured by FLY (Fig. 3c) that dissipation is high during periods of strong tidal flow (Fig. 3d). Near the seabed ε ∝ z⁻¹ between the bed and z ∼ 3.5 m, which is consistent with the law of the wall. The previously observed phase delay of the onset of high dissipation with distance from the seabed (Simpson et al. 2000) is evident. The mean time delay between the onset of enhanced turbulence near the seabed and that at 35 m above the bottom is 1.75 h. The corresponding vertical spreading speed is (5.6 ± 2.8) × 10⁻³ m s⁻¹, although greater speeds are evident at heights above 30 m from the seabed. Near the surface the relatively high dissipation that sometimes precedes the arrival of this upward-spreading region of enhanced dissipation may be the result of wind mixing (e.g., the wind speed is 9–10 m s⁻¹ at the time of Julian day 194.35).

The periods in which boils were detected on the sea surface are marked in Fig. 3a. The times when boils are present correspond well to the times at which dissipation near the surface is high. In some cases, however (e.g., at Julian days 194.115 and 194.908), boils appear some 30 min earlier than the FLY-measured increase in ε (we shall return to this later; see also section 3e).

The cycle of turbulence is also seen in the AUV measurements of ε. Figure 4 shows measurements of dissipation over a tidal cycle, together with the current and depth of the AUV during a period in which it is set to run legs at a nominal constant depth of 20 m. (The actual mean measured depth is close to 18 m.) Vertical displacements of the vehicle of a meter or more occur during the periods of high dissipation. The observed rms variations in depth are typically 0.8 m with a negative skewness, typically −1.0, suggesting an advective effect of turbulence with relatively large upward motions and with a horizontal scale that is comparable to or greater than the AUV length. The tendency to reach shallower, rather than greater, depths is particularly evident during the flood tide at times between Julian days 194.95 and 195.03.

In contrast, earlier studies in the near-surface mixed layer (Thorpe et al. 2003) found a mean standard deviation in AUV depth of 0.22 m and a positive mean skewness of 0.58 in AUV depth. The vehicle was then operating at 2–10 m below the surface in a mixed layer in the presence of Langmuir circulation that produced substantial downward flows with horizontal widths of about 10 m. It is evident that vertical motion in large eddies can deflect the AUV from its horizontal level course and that the sign of the skewness in depth provides an indication of the mean direction of the vertical motion induced by fluctuations in the flow field, in particular those that lead to boils on the sea surface. The negative skewness in depth implies that the eddies (or bursts) in the present study have associated greater upward than downward mean motion.

Figure 5 shows examples of the decay in logε during the tidal cycle and its relatively abrupt rise (and the increase in rms variations) at several depths. The times of the rise in ε are indicated by black dots in Fig. 3c and agree well with the times of rising turbulence found in the FLY series. Except for the legs made at about 6 m off the seabed, the onset of turbulence is accompanied by a substantial increase, from about 0.2 to 1.3 m, in the root-mean-square displacement of the AUV from constant depth. The abrupt rise in ε shown in Fig. 5 is immediately followed by a temporary reduction in depth; again, this corresponds to turbulence with associated upward vertical motion (see also section 3c). Dissipation levels measured by FLY (Fig. 3c) agree with the AUV estimates to within the measurement uncertainty of about 50% (Thorpe et al. 2003, their appendix A).

Further indication of vertical motions comes from variations in the fall speed of FLY derived from its pressure sensor. The resolution is little better than 0.01 m s⁻¹. The standard deviation of the fall speed, averaged over 2-h-long periods around the time of maximum dissipation rates, is about 7 × 10⁻³ m s⁻¹, and this is greater than in periods of the same duration when the current speed is small and ε is near its minimum value, when the variance is about 4 × 10⁻³ m s⁻¹. At the mean distance between the depths at which the fall speed equals the mean fall speed, a “zero-crossing interval” is about 10.4 m when ε is relatively high, but it is about 6.3 m when ε is low. Although the FLY, like Autosub, does not respond perfectly or in a simply quantified way on encountering vertical motions, this behavior is consistent with the presence of larger and more energetic eddies, with greater vertical velocities, during periods of high dissipation.

Table 1 includes the mean, variance, skewness, and kurtosis of logε measured using the AUV. The selected legs are between 6 m from the seabed and 8 m from the sea surface in fairly steady flows and in the directions specified. Dissipation is generally close to having a lognormal distribution (with logε having 0 skewness and a kurtosis of 3).

The spectra of logε are found to decrease with the horizontal wavenumber k as k^−p in the wavenumber range 0.01–0.80 cyc m⁻¹, where p is about 0.6 (Fig. 6). This value compares fairly well with the value of p = 0.61 ± 0.07 in the wavenumber range of 0.02– 0.2 cyc m⁻¹ found by Thorpe et al. (2003) in turbulence forced by mean winds of 11.6 m s⁻¹ at depths of 2–10 m in the mixed layer. At higher wavenumbers this value is about −2 and, as a reviewer has kindly pointed out, this implies that the variance-preserving spectra have a maximum at about 10-m scale. Because of the difficulties in holding course through the moving water there is only one example (leg 2.4) in which the AUV held course and traveled at an angle to the tidal flow, in this case moving through the water at about 45° to its flow direction. The spectrum for this leg is compared in Fig. 6 to one obtained in a similar flow (leg 2.3) when the AUV is traveling directly downstream. The spectra are not significantly different, except at wavenumbers of about 10⁻² cyc m⁻¹, when the spectra in the direction of the tidal flow exceed that at 45° to the tidal direction. At higher wavenumbers (smaller scales) there is no indication of directional variation or of anisotropy.

The temperature spectra in legs 3.3, 4.1, and 4.2 (see Table 1) are approximately proportional to k^−5/3 in the wavenumber range from 0.012 to 0.16 cyc m⁻¹, falling off with greater negative powers of k at higher wavenumbers. The −5/3 range is narrower than in the mixed layer where (closer to the source of turbulence at the sea surface) it was found to extend from 0.016 to about 8 cyc m⁻¹ (Thorpe et al. 2003).

b. Skewness of dT/dt and d(logε)/dt

The skewness of the time derivatives of temperature and of logε, S(dT/dt) and S(dlogε/dt), respectively, estimated from AUV measurements, are given in Table 1.

In the near-surface mixed layer the skewness of the horizontal spatial derivatives of temperature, or the skewness of the time derivatives for measurements made using sensors moving through the water, is of the order of unity and of a sign that depends on both the direction of traverse through the water relative to the wind and the direction of the heat flux through the water surface; the sign of the skewness is consistent with the presence of enhanced gradients or temperature ramps in braids within a billow structure transporting buoyancy vertically within a wind-driven shear (Thorpe 1985; Soloviev 1990; Thorpe et al. 1991, 2003; Wijesekera et al. 2004; Ozen et al. 2006).

In the tidally strained temperature structure of the present studies, comparable conditions are sketched in Fig. 7. The shear is now generated by the tidal flow, which is the mean current in the water column increasing in height above the seabed, as shown in Fig. 3d. The west-moving ebb tide (Fig. 7a) promotes conditions of stable stratification and a positive vertical temperature gradient, with shear-generated “billows” acting to transfer heat downward. [The billows and their accompanying braids, regions of strain (sketched in Fig. 7), are not intended to describe the size of billows, but rather the general effect of shear in straining eddies of a multitude of scales within the turbulent shear flow.] Autosub legs made to the west of a westerly tidal flow, as in leg 2.3, meet braids where the temperature decreases relatively rapidly. A negative skewness of dT/dt is expected. Legs made to the east, for example, leg 1.5, should have positive skewness. [Leg 2.4 is made to the south in the west-moving ebb tide but, to hold latitude, the AUV has to move upstream relative to the water, and effectively eastward, and so S(dT/dt) should be positive.] Similarly, during the conditions favoring convection during the east-moving flood tide (Fig. 7b), S(dT/dt) should be positive in legs made to the east in the direction of the tide (e.g., legs 3.3 and 4.2). In every case the sign of the skewness values S(dT/dt) in Table 1 is correctly predicted by the model. The magnitude of the observed values is of the order of unity as in the mixed layer.

In the near-surface mixed layer the skewness S(dlogε/ dt) of the time derivatives of logε is nonzero, its magnitude is of the order of 5 × 10⁻² (Thorpe and Osborn 2005). In about 85% of the cases examined, a relation holds between the signs of S(dlogε/dt) and S(dT/dt), consistent with a model in which billows advect small-scale turbulence. In the present observations, the vertical gradient in log ε is generally negative, with ε decreasing with distance from the seabed (Fig. 3c). As can be seen by inspection of Fig. 7, if it is dominated by the changes within braids, S(dlogε/dt) should be positive in the legs made in the direction of the tide and negative in those made against the tide, whether or not the flow is in flood or ebb. Values of S(dlogε/dt) in Table 1 are of similar magnitudes to those in the mixed layer and have the expected sign in legs 1.1, 2.3, and 4.2 made with the tide and in leg 1.5 against the tide. Although the mean skewness in leg 3.3 is negative, one turbulence shear sensor gives positive values while the other gives negative values. Leg 2.4 appears to have an incorrect sign, but the leg being made across the flow may possibly depend on the (presently unknown) across-flow structure of the turbulent eddies and their distortion by tidal shear.

c. Conditional sampling of the Autosub data

The Autosub data are “conditionally sampled” by choosing a variable, for example, temperature gradient dT/dt (the conditional), and finding all of the periods within a selected AUV leg in which this exceeds some selected threshold value, for example, the mean plus some factor times the standard deviation. The times t at the center of these periods are found. One-second average values of similar or other recorded data, say of logε, lying to either side of these times (e.g., from t − 15 s to t + 15 s) are then averaged according to the relative times at which they occur; this forms a section of the mean values of the data, in this case of logε, around the selected extreme values of the conditional variable (dT/dt). If the threshold of the conditional is not set too high, a substantial number of times t are found, and averaging these together to form a single section allows coherent patterns or trends to be detected in data even in the presence of turbulent fluctuations or wave-induced motion (Thorpe et al. 2003).

This methodology has been applied in periods in which the tidal flow is relatively large and steady. Examples of conditional sample plots are shown in Fig. 8, taking dT/dt as the conditional. In Figs. 8a,b, selected values are less than −1.5 times the standard deviation of dT/dt (the mean value is negligibly small), with 1-s averaging over the range of times t − 30 s to t + 30 s. In leg 2.3 (Fig. 8a), which is made with the ebb tide to the west (see Table 1), high negative temperature gradients are consistent with the observed negative skewness of dT/dt (Table 1), and the abrupt increase in logε indicated in Fig. 7a is apparent in the conditional sample plot. The trends in depth induced by the flows of Fig. 7a—downward before the temperature decrease and upward afterward—are reflected in the conditional plot of the depth changes of the AUV, although they are lagged by about 7 s (the time needed for vehicle response to changes in the motion of the surrounding water). A relatively simple interpretation is, however, not always possible. For example, in leg 4.2 (Fig. 8b) the track is eastward in water that, through tidal straining, is possibly convectively unstable. Neither the conditional sample plot with values <1.5 times the standard deviation of dT/dt (Fig. 8b) nor that with values >1.5 times the standard deviation of dT/dt (Fig. 8c) conform to the simple model of Fig. 7b. In the conditional plot of Fig. 8c, where the observed S(dT/dt) > 0 (Table 1) is reproduced, the mean value of logε decreases rather than increases and vertical motions also appear inconsistent with the model. In Fig. 8b, the skewness is incorrect [although because its value in Table 1 of 0.115 is relatively small and the uncertainty in S(dT/dt) is commonly about ±0.2, the sign is of doubtful significance], and although a change in logε is apparent, it appears to be very localized with relatively large variability on either side of the maximum in dT/dt. The indefinite trends may be a consequence of changing conditions, for example, the removal of the stable stratification during the flood tide.

Figure 9 shows mean sections using logε as the conditional from AUV legs at different levels in the water column. The threshold chosen is the mean plus 1.5 times the standard deviation and conditional sample plots are made over the range from t − 15 s to t + 15 s, which is sufficient for averaged values of logε to become reasonably uniform at the extremes. The mean width of regions of elevated logε increases from 4.9 m at the lowest level illustrated by leg 1.5, 6.3 m above the seabed, to 9.0 m in leg 4.2 at a depth of 8.3 m.¹ The most consistent trend in the other variables is that in the mean depth of the AUV; on average, the AUV rises as, or shortly after, it passes through regions of enhanced ε, consistent with regions of the greatest dissipation having vertical velocities transporting turbulent bursts upward from the seabed as suggested in earlier analysis. The temperature variation across the regions of relatively high dissipation is generally very small, only that at 8.3 m in leg 4.2 shows a coherent trend exceeding 1 mK. In this case the mean temperature has a minimum where logε is greatest. Leg 4.2 covers a period in which, as apparent in Fig. 3e, a weak upward vertical temperature gradient is being eroded by turbulence in the flood tide. The temperature minimum is consistent with eddies carrying relatively cold water upward.

Knowing the speed of the AUV through the water, the mean distance between groups of 1-s-average dissipation values exceeding the given threshold can be found. The distance between groups in which logε exceeds two standard deviations is 43.4 m; the peak values are generally single. With a threshold of one standard deviation, the distance is reduced to 19.9 m with an average of 3.13 values within each group. The distances are independent of height above the bed. While (except close to the effects of turbulence generated at the sea surface) the mean dissipation decreases upward, the pdfs of logε measured at a given height are close to lognormal so that the fraction of values exceeding some given threshold based on the standard deviation should remain the same, and the mean distance between them will be independent of height, as observed. The width of the sections in Fig. 9 is consistent with bursts having horizontal dimensions that increase as they move upward.

d. Acoustic scattering from turbulence in the water column

An unexpected feature of the ARIES II observations is a band of acoustic scattering that is visible in the east sonar beam during every period of the eastward-flowing flood tide. An example is shown in Fig. 10a. No similar feature is apparent during ebb or in the south beam. The time periods when the scattering bands are present are marked by horizontal bars in Fig. 3b. At first the echoes, which have a decreasing range, but one that is beyond that of the sea surface, were interpreted as being from some unknown feature approaching from the east and therefore moving against the tide, but a search in the salinity and temperature records for some possible feature, such as a front, failed to find any likely candidate.

The water is stratified during the periods in which the signals are observed and unstratified when they are not. Sound reflection from intense turbulent temperature microstructure is known to occur (Thorpe and Brubaker 1983; Goodman 1990; Seim 1999) and has been used, for example, to identify Kelvin–Helmholtz eddies in internal waves (Moum et al. 2003). In the absence of temperature (or salinity) gradients no scattering occurs, other than that from targets such as fish or zooplankton. The echoes in Fig. 10a are interpreted as being from the top of the upward-spreading region of turbulence during the periods, which is apparent in Fig. 3e, when the stratification is being reduced by turbulence as the tidal currents increase. As expected, no scattering occurs in the periods of upward-spreading turbulence on ebb tides because, relatively, the water column is thermally unstratified. There is then no interface between well-mixed turbulent water and relatively quiescent but stratified water.

Although, on close examination, faint echoes with increasing range are detectable at ranges less than that of the surface, the clearest echoes are at a range beyond that of the sea surface above the sonar. If they represent scattering from the upward-moving interface bounding the top of the highly turbulent region, they must therefore occur after a sound pulse has been reflected from the surface (Fig. 11a) and travels downward toward the turbulent interface.

Why the rising turbulent region is not detected until after sound has been reflected at the sea surface is not entirely clear. Signals by reflectors on the seabed dominate the scattering at ranges less than that of the water surface and perhaps mask the acoustic returns of the upward-going sound from the turbulent interface. The asymmetry of a turbulent laminar interface may also play a part. Viewed from the quiescent side, the turbulent interface appears to be composed of smooth, rounded bulges, but from the turbulent side it appears as multiple wisps of entrained fluid as sketched in Fig. 11b; see Turner (1968, his plate 1, Fig. 2) and Linden (1973). The smoother surfaces and greater temperature contrasts of the bulges produced by eddies impacting the boundary from its turbulent side, from below the case considered here, may be more effective and coherent localized reflectors of downward incident sound than are the diffuse forest of sound-scattering wisps of warmer water entrained into the turbulent region by the eddies—the forest encountered by the upward-propagating beam. The wisps may scatter sound widely and they do not form a coherent localized backscatter layer to reflect the upward-propagating sound.

Why is the scattering layer not visible in the southward-pointing beam? Although the beam patterns of the two transducers are very similar, their inclinations to the horizontal differ (section 2a). A sideband of the east beam, inclined at about 60° to the direction of the center of the main beam, points almost directly toward the sea surface. Only the edge of a sideband in the south beam points directly upward. Although about 15 dB down in strength from the center of the main beam, the center of the sideband of the east beam is about 6 dB greater in strength than the edge of the sideband, which points upward toward the surface in the south beam. Finally, because it is inclined upward at a smaller angle, the scattering from the seabed in the main south beam is greater than that of the east beam, further diminishing the signal-to-noise ratio of the moving interface in the south beam, even at ranges beyond that of the sea surface.

The scattering layers rise at speeds of 7.4 × 10⁻³ to 4.6 × 10⁻² m s⁻¹—rates that are similar to the upward speeds of the spreading turbulence observed in the FLY observations, and occur at times when the enhanced turbulence is approaching the surface (Figs. 3–c). They sometimes persist for 1–2 h within the upper 10 m of the water column, often with a wavelike structure with periods of 2–8 min (Fig. 10b). Turbulence may lead to the generation of internal waves in the near-surface temperature-stratified layer. The bands that are visible in the sonograph image of the scattering layer (e.g., Fig. 10a) have a tilt, a change in range with time, which is roughly equal to the mean flow, suggesting that part of the image derives not simply from a narrow vertically pointing section of the side-scan beam, but also from its horizontal spread. The moving features are separated typically by about 4 m and may be a consequence of scattering from bulges in the turbulent interface as they are carried along the sonar beam by the mean eastward flow.

e. The dimensions of boils; horizontal isotropy?

A total of 870 boils are identified in sonographs during the periods of strong tidal flow within horizontal ranges of 0–110 m from AIRES II. More are poorly resolved and are not included for analysis. The along- and across-tide dimensions are measurable in 303 cases, but only the along-tide dimension can be determined in the remainder. The accuracy of the measurements is about 20%, but with the uncertainty mentioned in section 1. The mean along-tide dimension is 22.4 ± 9.8 m (the uncertainty given being one standard deviation of the set of measurements), or (0.51 ± 0.225)H, and the across-tide dimension is 25.4 ± 12.7 m, or (0.58 ± 0.29)H, where H is the water depth; both values are smaller than the (0.93 ± 0.22)H diameter estimated by Nimmo Smith (2000) but are greater than the estimates of the horizontal dimensions of 4.9–9 m of the upward-moving bursts identified in section 3c.

Probability distribution functions (pdfs) of the boil size distributions are shown in Figs. 12a,b. The pdf of the mean along- to across-tide ratio of boil widths is shown in Fig. 12c. The mean ratio is 0.97, which is not significantly different from unity. There is a peak in the ratio’s pdf near 0.75, suggesting that a number of boils extend further across the tidal flow than along it, consistent with the presence of pairs of eddies as sketched in Fig. 1b and in accordance with many of the images of sediment-linked boils in the North Sea. It was also found that the mean along- to across-tide ratio during 1.5-h periods around the time of maximum tidal flow, about 1.1 m s⁻¹ at the surface, is 1.18, but the mean values are less than unity before and following these periods. The standard deviation of the ratios is about 0.3; data are too few to ascertain whether these differences are significant.