Internal solitons in the ocean and their effect on underwater sound

Abstract

Nonlinear internal waves in the ocean are discussed (a) from the standpoint of soliton theory and (b) from the viewpoint of experimental measurements. First, theoretical models for internal solitary waves in the ocean are briefly described. Various nonlinear analytical solutions are treated, commencing with the well-known Boussinesq and Korteweg-de Vries equations. Then certain generalizations are considered, including effects of cubic nonlinearity, Earth's rotation, cylindrical divergence, dissipation, shear flows, and others. Recent theoretical models for strongly nonlinear internal waves are outlined. Second, examples of experimental evidence for the existence of solitons in the upper ocean are presented; the data include radar and optical images and in situ measurements of wave forms, propagation speeds, and dispersion characteristics. Third, and finally, action of internal solitons on sound wave propagation is discussed. This review paper is intended for researchers from diverse backgrounds, including acousticians, who may not be familiar in detail with soliton theory. Thus, it includes an outline of the basics of soliton theory. At the same time, recent theoretical and observational results are described which can also make this review useful for mainstream oceanographers and theoreticians.

Instability in internal solitary waves with trapped cores

“…[1][2][3][4] In the open ocean, typically, the waves are highly nonlinear and may attain very large amplitudes. [5][6][7] It is well known that at such large amplitudes, ISWs of depression (elevation) may exhibit trapped cores if the density gradient at the surface (bottom) of the water column is finite (and waves are supported in which the local horizontal fluid velocity exceeds the wave speed).…”

Transformation of surface and internal waves at the bottom step

“…Проведено числен-ное моделирование на основе уравнений Навье-Стокса в приближении Буссинеска. Показано, что процесс трансформации для волн умеренной амплитуды адекватно описывается в рамках модели Гарднера, однако при бóльших амплитудах следует пользоваться моделью Мияты-Чоя-Камассы (см., [42]). При столь больших амплитудах процесс трансформации сопровождается сдвиговой не-устойчивостью и генерацией мелкомасштабных волн на пикноклине, что приводит к его постепен-ному размытию и утолщению.…”

Decay of Benjamin–Ono solitons under the influence of dissipation

“…The propagation of small amplitude long waves in a stratified fluid consisting of a relatively thin layer overlying a very deep passive layer is described by the well-known Benjamin-Ono (BO) equation [1,2,8] ∂u ∂t + αu ∂u ∂x…”

“…Here, u(x, t) is the perturbation of a pycnocline (a layer with a constant density) and α and β are parameters which depend on the particular stratification (for details see [2,8]). The symbol ℘ denotes the principal value of the integral.…”