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More recently, work is being conducted under an ONR program called “IODA” (Integrated Ocean Dynamics and Acoustics), which ties in very modern coastal oceanography models, with virtually all of the physical oceanography described above incorporated into it, with fully 3D acoustics models. This is a very ambitious extension for both the acoustics and oceanography, as it attempts to reach down to sampling scales of meters and seconds, as opposed to the hours and kilometer scales that are the usual state of the art. Acous- tics is sensitive to small-scale ocean phenomena with large hori- zontal temperature and sound-speed gradients, so in order to fully model the acoustic field, we need to reach such spatial and temporal resolutions. In weighing whether or not to use such models, one notes that the model generates full 3D acoustics realizations of the pressure field, from which one can generate Lcoh and much more. Moreover, one can generate space-time series and statistics from such a model, and use these instead of running the model for each case.
However, the price you pay is that you have to know how to run (and have the input for) state of the art ocean and acoustics models. These models also have some hefty computer requirements associ- ated with them, and they are not easy-to-use, general public tools.
Another theoretical approach is the “wave propagation in a random medium” approach, which is well known to the public due to its famous application to astronomy (star twinkle). In this approach, as applied to ocean acoustics, one goes from the statistics of the medi- um (e.g. sound-speed) fluctuation to the statistics of the fluctuations in the acoustic amplitude or phase. Calculations in WPRM (Flatte, 1979 and Colosi, 2013) tend to be a bit mathematically involved, but a simple example of what type of form one obtains (from Carey et al, 2002) shows that the phase variance between two receivers goes as a double integral over the paths to the two receivers (includ- ing vertical ocean structure), with the “kernels” of the integrals containing known background quantities and the correlation func- tion containing our statistical knowledge of the ocean. The strength of this approach is that it only asks for basic statistics of the ocean variability as input. However, this is not as easy a thing to provide as it sounds, as the ocean has (as discussed above) numerous processes
going on in shallow water with a variety of scales, and moreover they are spatially and temporally inhomogeneous and anisotropic. However, one can often get adequate answers with even an ap- proximate correlation function, which can be based on either ocean dynamics and scales or direct measurements. Such an approximate correlation function, based on shallow water oceanography mea- sured in the 1996 PRIMER experiment off New England, produced a 30λ average horizontal correlation length, in agreement with the SW06 data above (Lynch et al., 2003). Both PRIMER and SW06 were conducted in the Mid Atlantic Bight region, and close to the shelf-break and its associated front, so the agreement between these two results is less surprising than it would be for two very distantly separated sites. These two measurements also make one begin to think that the shelf-break oceanography (perhaps the front) is a large contributor to the 30 wavelength result.
The question now arises – how do we separate the effects of the various pieces of oceanography and the seabed from one another? We can turn various pieces of oceanography “on and off” in the large numerical models, and even do so (using individual process dynamic models) in the correlation functions. But while this tactic may produce answers, it produces comparatively little insight into the physics, and one has to run models over large, multidimensional parameter spaces to get a complete set of answers. So where do we go?
“Simple” feature Models and Lcoh
A recent, and ongoing, attempt to answer that question has been to employ simple “feature models” of the ocean and seabed. In this approach, which has been successful in both oceanography and acoustics (A. Robinson and D. Lee (eds.), 1994 and Lynch et al., 2010), one reduces the ocean features to simple geometric forms (e.g. eddies become circles, fronts become straight linearly sloping (in depth) features, nonlinear internal waves become square shaped instead of hyperbolic cosecant squared shaped, etc.). The feature’s internal structure (i.e. the ocean interior sound-speed profile) also can be simplified, so that the vertical and horizontal temperature/ sounds-speed profiles of the ocean features become very convenient to deal with geometrically. Indeed, this allows one to use simple
14 | Acoustics Today | Winter 2014