Energy propagation in nonlinear internal wave ducts from radiative transport theory.

Abstract

Nonlinear internal waves have 3-D random variability arising from smaller scale physical oceanographic processes. Internal wave fronts form acoustic waveguides, and we examine propagation in directions nearly parallel to the fronts. Intensity fluctuations arising from the variability are treated by 3-D radiative transport methods, which provide insight into the parametric dependence on waveguide randomness. We focus on situations where the frozen field approximation applies, the acoustic modes represent the vertical energy distribution in the waveguide, and the modes propagate adiabatically. Under these conditions, horizontal modal variations are specified by 2-D radiative transport equations. With additional assumptions, the transport equations simplify to diffusion-type equations. An alternative energy scattering interpretation describes the duct in terms of a 2-D Galton’s box, assuming discrete scattering events occur as modes propagate down the duct. The resulting equations also reduce to diffusion-type equations in the continuous limit. We use appropriate spatial variability scales from the SW06 experiment to investigate properties of acoustic intensity. [Work supported by the ONR.]

Shallow Water Propagation

“…As suggested by our WHOI colleagues, one can visualize the acoustic wave interacting with the NIW front elements like a Galton's box with discrete scatterers. Proceeding from this idea, along with appropriate scale and other constraints, a radiative-transport model can be constructed [10] for vertical modes. A fundamental result for the locally-averaged acoustic intensity is a modified diffusion equation, from which predictions can be determined across and down the duct.…”

“…• A modal transport theory is used to develop a scattering model for acoustic energy inside a NIW duct [10] in which wave front segments are treated as scattering elements, and a modified diffusion equation describes the evolution of a grid-averaged intensity in the duct.…”

Shallow Water Propagation

“…• A scattering formalism, based on a limit of discrete scattering events and a modal transport theory, provides an alternative description of intensity variations in a nonlinear internal wave duct [12], and is compared with the standard refractive treatment.…”

“…James Lynch and Timothy Duda and their colleagues [9]- [12] are directed toward propagation effects from waveguides and anti-waveguides of variable structure generated by nonlinear internal waves.…”