John A. Colosi and James F. Lynch
Woods Hole Oceanographic Institution, Woods Hole, MA 02543
During the past few years much attention has been paid to nonlinear
continental shelf internal waves. This focus has been driven by the important
oceanographic, acoustic, optical, geological, and biological interest related
to this phenomenon. Since these strongly nonlinear continental shelf internal
waves are generated by baratropic tidal interactions with bathymetry and
since the resulting internal tide evolves into an internal bore with trailing
soliton-like waves; we generically call this entity a solibore. Solibores
are extremely common throughout the world's shallow seas, straight, Fjords,
and continental shelves and so in studying their behavior we are not looking
at an isolated curiosity. During the past few years our acoustical oceanography
group here at WHOI has been involved in studying the acoustical and oceanographic
properties of solibores on the New Jersey and New England continental shelves
via the SWARM (Shallow Water Acoustic Random Media) and Shelfbreak front
PRIMER experiments. In these experiments large arrays of acoustical and
oceanographic instrumentation were deployed giving us a first exciting
look at this natural phenomenon. We discuss here some of the important
scientific issues raised by this field work which we will break up into
acoustical and oceanographic issues even though the two are closely related.
The main acoustical issues raised by these experiments center around the idea of the predictability of the acoustical field, that is how well do we need to know the mean state of the ocean, and/or the statistics of the ocean (not withstanding questions of seabed geology) to predict the acoustic field or the statistics of the acoustic field to some level of accuracy. This problem is a function of acoustic frequency, transmission range, and transmission direction relative to the solibore propagation. We have concentrated our efforts at 200 and 400 Hz center frequencies and ranges of 30 to 40 km but we need to explore lower frequencies and longer/shorter ranges. Lower frequencies are interesting since they are less sensitive to small-scale oceanographic variations and they show less chemical absorption but they suffer from increased lossy seabed interactions. Longer and shorter ranges are interesting because we do not know the range scaling for any of the acoustic observables. Predictions for mode spread and bias in a deep water waveguide with Garrett-Munk internal waves indicate spread scales like R3/2 and bias scales like R2 . Furthermore mode intensity variability saturates at 1000km range showing an exponential probability density function . Information like this is not known for a shallow water situation.
In addition, with the exception of Worcester's and Send's Strait of Gibraltar experiment, there is no moored acoustic transmission data for sound propagation perpendicular to the solibore propagation direction. Acoustic scattering in this cross-wave geometry can be severe since the acoustic energy is propagating along the crests or troughs of the solibore. Therefore more work in this geometry is well justified.
Of central importance for signal processing are the acoustic coherence limits that are imposed by solibores. More work is needed on the temporal, spatial and frequency coherence of the field in the presence of solibore internal waves. In particular, no data exists for the spatial coherence of a horizontal line array. This is an important geometry for Navy systems particularly towed arrays.
Another acoustic issue is the forward scattering of sound by solibores at 1 to 10 kHz frequencies. Simple theory would suggest that such scattering would respond to small scale ocean variability of order 10 to 100 m. However spatial structures that small in the solibore have not been routinely measured, and so both first order oceanography and acoustics measurements are needed here. Also in experimental situations where there is acoustic bottom interaction there may be a coupling between volumetric acoustic effects caused by solibores and ocean seabed scattering; that is, the solibore will change how the seabed is ensonified.
There is also the issue of 3-D propagation effects caused by solibores. Transverse gradients of sound speed can cause 3-D scattering of acoustic energy and these gradients become more important as one looks at the cross wave propagation situation. Theoretically we have always treated the propagation, as 2-D and horizontal coherence calculations are generally Nx2D. The use of dense horizontal arrays in future experiments could indicate whether horizontal multipathing is significant and therefore if 3-D effects need to be considered in our theoretical formulations of acoustic wave propagation through solibores.
Finally, we have a wealth of theoretical machinery for calculating acoustic fluctuation quantities like coherence, but what we are lacking are the oceanographic models to be used as inputs to our acoustic fluctuation calculations to test their capabilities in the shallow-water environment. This was the situation in deep-water acoustics nearly 30 years ago before the successful Garrett-Munk internal wave model was used. The key piece of information from an acoustic fluctuation standpoint is the correlation function of the sound speed fluctuations or equivalently the sound speed fluctuation spectrum. Significant simplifications can be made if there is a dispersion relation to link the spatial and temporal scales of the solibore internal wave. Because of the strong non-linearity of the solibore a dispersion relation may not be simply attainable.
Coming full circle to our main issue of the predictability of the acoustic
field, we see that this issue is centrally linked to the predictability
of the solibore field that is addressed in the next section.
Concerning the tidal generation of these waves from bathymetry we have an understanding of the lee wave situation where the tidal flow is super-critical for the internal tide but in many cases we see solibores in strongly sub-critical conditions (PRIMER is one example). One possible mechanism for the sub-critical generation is the Rattray-Baines critical slope mechanism but this has not been studied in detail. In addition there is the issue of the effects of the shelfbreak front (and its associated jet), slope-shelf eddies, and wind stresses on the generation of solibores. In the shelfbreak PRIMER we observed a great deal of variability in solibore generation which must be associated with interactions with the rapidly changing shelfbreak front. In addition we observed the interaction of a Gulf Stream eddy with the shelf region which resulted in no solibore generation. Further there is the issue of the evolution of internal tides into solibores. In general the baratropic tide interaction with the bathymetry results in a symmetric linear-looking internal tide which subsequently through non-linear steepening and some other mechanisms evolves into an asymmetric bore with solitons being generated at the bore face. Since the solitons have a smaller horizontal wavelength than the internal tide they fall behind and therefore a train of solitons develops behind the bore. In shelfbreak PRIMER we observed rapid solibore evolution from the internal tide approximately over 1/8 of an internal tide period. Using fully non-linear models with average stratification profiles we are unable to simulate this rapid development; we find that approximately ½ a tidal cycle is needed for solibore development.
Once a solibore is generated it will propagate up-shelf transferring its energy more and more from a bore-like internal tide to a train of high wavenumber solitons. Proceeding to this propagation the following issues arise. What is the dominant cause of fluctuations in the solibore group velocity, high wavenumber content, energy, and duration? What is the connection between the stochastic background internal wave field and the solibore field? Why are the widths and amplitudes of the solitons on the solibore not related by the simple KDV formulae? What is the significant of dissipation, bathymetric steering, scattering and horizontal refraction in solibore dynamics? Can we treat these waves as essentially 2-D waves? What is the best combination of deterministic and stochastic descriptions of the solibore field?
Turning to dissipation, the first order question is how do solibores break-up? Generally once the solibore is near its break-up point it is more soliton-like than bore-like. Likely candidates for the soliton break-up mechanisms are wave breaking when the thermocline has shoaled to where the solitons cannot exist as waves of depression but must rapidly evolve into waves of elevation, bottom friction, shear dissipation, or interactions with a mixing front. Does the relative importance of these processes shift from site to site? Another big question related to soliton breaking is that we do not know what exactly happens when the solitons rapidly evolve from waves of depression to waves of elevation. Do they break immediately, or do they flip over and break later?
Turning to the oceanography, we advocate an experiment, which would
follow a solibore internal wave from its generation through to its break-up
or dissipation. We advocate a dense line of moorings extending up-slope
from the generation region on the continental slope to the dissipation
region. A few moorings could be placed out of the line plane to look at
3-D effects. The moorings ideally would be equipped with temperature and
conductivity sensors, temperature only sensors, a few micro-structure probes,
and upward looking ADCP. Sea Soar, SAR, acoustic backscatter, and other
measurements would complement the mooring line.
2. The shelfbreak PRIMER Group, "Shelfbreak PRIMER - An integrated acoustic and oceanographic field study in the middle Atlantic bight", In Shallow-Water Acoustics, Editors Rehne Zhang and Jixun Zhou
3. R. H. Headrick, J. F. Lynch, and the SWARM Group, "Acoustic normal mode fluctuation statistics in the 1995 SWARM internal wave scattering experiment", submitted to J. Acoust. Soc. Am., 1997
4. R. H. Headrick, J. F. Lynch, and the SWARM Group, "Modeling mode arrivals in the 1995 SWARM acoustic transmission experiment", submitted to J. Acoust. Soc. Am., 1997
5. J. A. Colosi and S. M. Flatte, "Mode coupling by internal waves for multimegameter acoustic propagation in the ocean", J. Acoust. Soc. Am., V 100 (6), pp3607-3620, (1996)
6. J. C. Preisig and T. F. Duda, "Coupled acoustic mode propagation through continental-shelf internal solitary waves", IEEE J. Oceanic Eng., V22(2), (1997).