Nonlinear ring waves in a two-layer fluid

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.

16 pages, 21 figures

References in corpus (4)

• On Dispersive and Classical Shock Waves in Bose-Einstein Condensates and Gas Dynamics
• Evolution of solitary waves and undular bores in shallow-water flows over a gradual slope with bottom friction
• Initial surface disturbance on a shear current: the Cauchy--Poisson problem with a twist
• Water Waves from General, Time-Dependent Surface Pressure Distribution in the Presence of a Shear Current

Cited by in corpus (3)

• Soliton solutions to the fifth-order Korteweg - de Vries equation and their applications to surface and internal water waves
• Long internal ring waves in a two-layer fluid with an upper-layer current
• Wavefronts and modal structure of long surface and internal ring waves on a parallel shear current