Turbulent Mixing in Solitons

Neil S. Oakey and Norman A. Cochrane

Ocean Sciences Division
Bedford Institute of Oceanography
Department of Fisheries and Oceans
Dartmouth, Nova Scotia, Canada B2Y4H2



Simultaneous measurements of microstructure and acoustic backscatter in a packet of mixing solitary waves indicate that the intensity of acoustic backscatter is related to the level of turbulent mixing. We have tested our data with the simple model of Thorpe and Brubaker and found that it is consistent with this formulation.


Solitons or packets of solitary waves are generated in many places but in particular on the Scotian shelf in a region called "The Gulley" near Sable Island it has been easy to predict their generation time and to find them. Essentially at each tidal cycle when the tides are high enough, solitons are generated at the shelf break. Since in very simple terms the development of the internal tide in a modal sense is primarily first mode the development of an appropriate density structure is also necessary. Enhanced mixing associated with these packets has been postulated as a mechanism (Sandstrom, Elliott and Cochrane, 1989) for enhanced nutrient supply and coincident higher biological productivity.

In 1987 we did a short study of Solitons using BATFISH, CTDs, a microstructure profiler (EPSONDE) (Oakey, 1988) and acoustic backscatter instruments. The area was surveyed with BATFISH at the correct time and place to observe solitons until we had fine-tuned our ability to predict exactly where and when to find them. We set up our sampling instruments on the ship to sample the solitary wave packet, as it arrived and passed under us, with a multi-frequency acoustic array and with EPSONDE.

In the paper we will ask the following questions:

Turbulence and Acoustic Backscatter Models

One sees acoustic echoes from a variety of scatterers in the ocean including biological, bubbles and temperature and salinity microstructure. There is a problem in calibration acoustic backscatter intensity in terms of the processes causing it. In the absence of competing processes a particular process such as turbulence may give the largest signal. The soliton provides this special laboratory.

Thorpe and Brubaker (1983) devised a model to describe the acoustic backscatter in terms of the turbulent temperature and velocity field. They derived an equation to describe the backscatter as follows

                   (1) evaluated at (Munk and Garrett, 1973) where  is the sonar wavelength and C is the speed of sound. At 120 kHz,  is 1.3 cm. For isotropic turbulence the Batchelor spectrum is                                             (2) where the Batchelor universal form is given by                     (3) The Batchelor wavenumber is and  where  Evaluating this at gives                     (4) where                              (5) This is typically presented as                           (6) expressed ad dB. Typical values are m2/s and m2/s with K-1. To put the scales into context, at 50 kHz is 3cm and at 120 kHz is 1.3cm. By comparison to the Batchelor cut-off scale  is about 0.81 cm and the turbulence viscous cut-off scale is about 2.7 cm for dissipation  W/kg, remembering that the peak in the dissipation spectrum is at a length scale about a factor of three larger. This means that the overlap in scales of the turbulence and acoustic backscatter overlap well at these scales.

Experimental Setup

The experimental site was on the Scotian Shelf Northeast of Sable Island in a region called "The Gulley" (44o10' N, 58o50' W). The area was surveyed using the BATFISH and CTD Tow YO's to determine accurately when and where the solitons were being generated in respect to a tidal reference (high tide at Halifax). The measurement strategy, which worked reasonably well, was to position the ship where we expected to see the soliton packet and shortly before its predicted arrival and set up our EPSONDE and the Multi-Frequency Acoustic Array. Using such things as the ship radar backscatter to see the surface expression of the Solitons (the surface roughness using long band radar) we were able to confirm the arrival of a soliton packet and initialize sampling. Both acoustic data and microstructure data were recorded on board simultaneously but not on the same computers. The clocks were synchronized to about 1 second. One second represents about 0.7 meters vertically for EPSONDE and about 0.5 meters horizontally for the internal wave. Patches of turbulence may be only a few meters thick. The simultaneity in space and time was a critically important sampling problem. Because EPSONDE is a tethered free-fall vehicle it may be some 10?s of meters separated from the region sampled by the acoustic system which also complicates the notion of simultaneity. After the soliton packet had passed we moved the ship and set up further onshore to wait for another look at the same soliton packet. This was done to try and determine the change in the soliton structure as well as the change in turbulence and acoustic backscatter as the packet moved on the shelf.

Microstructure Measurements

EPSONDE was used in a total of 12 stations including over 200 profiles to depths of about 50 m to obtain velocity and temperature microstructure simultaneously with the acoustic backscatter data. Data were logged on a PC computer. Fifty meter profiles were obtained at intervals as short as 2 minutes. In one instance the ship drifted at a similar speed and direction as the soliton so sampling continued over a period of two hours before the solitary wave packet had passed below the ship. Temperature, temperature microstructure and dissipation profiles were obtained using standard analysis techniques (Oakey, 1982). The depth of an isotherm clearly showed the movement of the base of the mixed layer by the soliton (Sandstrom and Oakey, 1995). The measure of temperature variance, , and the dissipation, , were both seen to be stronger at the interface where mixing was being caused by the shear in the soliton.

Acoustic Backscatter Measurements

Acoustic backscatter signals were logged simultaneously at frequencies of 12, 50.5, 121 and 250 kHz concurrent with repetitive EPSONDE casts. Demodulated signal envelopes furnished by two DATASONICS DFT-210 dual-channel acoustic transceivers were individually digitized at 5kHz every 2 seconds and logged to tape on a computer. The 12 kHz transducer was the ship?s keel transducer and the three higher frequency channels utilized transducers lowered over the side in a weighted "Bucket" to about 6 meters depth in order to minimize near surface bubble attenuation. A selected signal was displayed in real-time on a gray scale recorder at on transmission per second. A failed preamplifier in the 200 kHz channel limited useful data in this channel to a few high signal amplitude events. Intermittent operation of the 120 kHz channel was also experienced but most of the collected data was unaffected. The three high frequency channels were calibrated pre-cruise at BIO. The 12 kHz channel was calibrated at sea by suspending an air filled spherical target (ping-pong ball) beneath the keel axis on a 2-point monofilament suspension.

Data Analysis

The EPSONDE data were analyzed to obtain  and  estimates using standard spectral analysis techniques (Oakey, 1982). Data were analyzed to give microstructure profiles in 2 second (about 1.4 meter) segments. To merge the data with the acoustic data, profile start times were carefully checked. Acoustic data from the different transducers was analyzed to give profiles of backscatter strength averaged over 20 seconds and 1 meter vertical bins. It was later smoothed to 1 minute when merged with the microstructure data.

Using the Thorpe-Brubaker model the microstructure data were used to calculate a "Microstructure Backscatter", , and these data were merged in space and time with the measured "Acoustic Backscatter", .

Each data point represents about 3 meters in the vertical and 3 seconds? acoustic average. For each box a point could be plotted on a regression curve. This produced a scatter of points to which regression statistics could be done. Data from all runs combined to give composite pictures are summarized using box and whisker plots in Figure 1 for 50.5 kHz and in Figure 2 for 121 kHz.


Figure 1: Measured acoustic backscatter intensity is plotted versus the inferred microstructure
backscatter intensity for 50.5 kHz on the left and 121 kHz on the right.


Discussion of Results

From Figure 1 and Figure 2 there is a clear relationship between  and the corresponding . For the 50 kHz data all of the runs were combined and they result in a regression plot with a large scatter. There appears to be a reasonable correlation. The acoustic backscatter data are less than that predicted from the Thorpe-Brubaker theory; about 7dB less at 50 kHz and about10 dB less at 120 kHz. There is less scatter at 120 kHz than at 50 kHz. There is a large excess of high acoustic scatterers that are probably biological in origin.


Sandstrom, H, and N.S. Oakey, 1995: Dissipation in Internal Tides and Solitary Waves. J. Phys. Oceanogr., 25, 604-614.

Munk, W. and C.J. Garrett, 1973: Internal Wave Breaking and Microstructure (the chicken and the egg), Boundary Layer Meteorology, 4, 37-45.

Oakey, N.S., 1982: Determination of the Rate of Dissipation of Turbulent Energy from Simultaneous Temperature and Velocity Shear Microstucture Measurements. J. Phys. Oceanogr. 12, 256-271.

Oakey, N.S., 1988: EPSONDE: An Instrument to Measure Turbulence in the Deep Ocean, IEEE Journal of Oceanic Engineering, 13, 124-128.

Sandstrom, H., J.A. Elliott and N.A. Cochrane, 1989: Observing Groups of Solitary Internal Waves and Turbulence with BATFISH and Echo-Sounder, J. Phys. Oceanogr., 19, 987-997.

Thorpe, S.A. and J.M. Brubaker, 1983: Observations of Sound Reflection by Temperature Microstructure, Limnology and Oceanography, 28, 601-613.