Nonlinear ring waves in a two-layer fluid

TL;DR

This paper models weakly nonlinear surface and interfacial ring waves in a two-layer fluid using a 2+1-dimensional cKdV-type equation, revealing the formation of dispersive shock waves and oscillatory wave trains.

Contribution

It introduces a numerical model for 2D weakly nonlinear ring waves in a two-layer fluid based on a recently derived equation, exploring wave phenomena like DSWs and wave trains.

Findings

Distinctive surface and interfacial DSWs observed

Formation of oscillatory wave trains in simulations

Effect of shear flow on wave dynamics analyzed

Abstract

Surface and interfacial weakly-nonlinear ring waves in a two-layer fluid are modelled numerically, within the framework of the recently derived 2+1-dimensional cKdV-type equation. In a case study, we consider concentric waves from a localised initial condition and waves in a 2D version of the dam-break problem, as well as discussing the effect of a piecewise-constant shear flow. The modelling shows, in particular, the formation of 2D dispersive shock waves (DSWs) and oscillatory wave trains. The surface and interfacial DSWs generated in our numerical experiments look distinctively different.