Uniform far field asymptotics of internal gravity waves from a source moving in a stratified fluid layer with smoothly varying bottom

Abstract

The far field asymptotic of internal waves is constructed for the case when a point source of mass moves in a layer of arbitrarily stratified fluid with slowly varying bottom. The solutions obtained describe the far field both near the wave fronts of each individual mode and away from the wave fronts and are expansions in Airy or Fresnel waves with the argument determined from the solution of the corresponding eikonal equation. The amplitude of the wave field is determined from the energy conservation law along the ray tube. For model distributions of the bottom shape and the stratification describing the typical pattern of the ocean shelf exact analytic expressions are obtained for the rays, and the properties of the phase structure of the wave field are analyzed.

Asymptotics of the far field generated by a modulated point source in a planarly layered electromagnetic waveguide

“…In the literature, pulse propagation analysis usually makes use of energy, ray, and wave points of view . In the energy approach, the balance of the electromagnetic energy is invoked . With respect to the ray approach, there exist a number of theoretical models that provide a simplified and tractable depiction of the propagation process, which agree with experimental findings.…”

Unsteady regimes of internal gravity wave generation in the ocean

“…This generation pattern can be observed under certain conditions, including the impingement of a stratified flow on an oceanic shelf. In this case in some spatial zones of the shelf the flow velocity may coincide with the local group velocity for a given bottom depth [3]. By means of numerical calculations it was shown that in the case of unsteady motion of a source in a stratified fluid flow the maximum-amplitude waves are generated at near-critical velocities [2].…”