Coupled Ostrovsky equations for internal waves in a shear flow

TL;DR

This paper investigates nonlinear internal waves in stratified shear flows using coupled Ostrovsky equations, combining analytical asymptotic methods and numerical simulations to explore diverse wave behaviors.

Contribution

It introduces a novel application of coupled Ostrovsky equations to stratified shear flows and analyzes their complex wave dynamics through combined analytical and numerical approaches.

Findings

Identification of unsteady and steady envelope wave packets

Analysis of the dispersion relation in a three-layer model

Demonstration of various dynamical behaviors of internal waves

Abstract

In the context of fluid flows, the coupled Ostrovsky equations arise when two distinct linear long wave modes have nearly coincident phase speeds in the presence of background rotation. In this paper, nonlinear waves in a stratified fluid in the presence of shear flow are investigated both analytically, using techniques from asymptotic perturbation theory, and through numerical simulations. The dispersion relation of the system, based on a three-layer model of a stratified shear flow, reveals various dynamical behaviours, including the existence of unsteady and steady envelope wave packets.