Numerical study of interfacial solitary waves propagating under an elastic sheet.

Zhan Wang,Jean-Marc Vanden-Broeck,Emilian I Părău,Paul A Milewski

doi:10.1098/rspa.2014.0111

Abstract

Steady solitary and generalized solitary waves of a two-fluid problem where the upper layer is under a flexible elastic sheet are considered as a model for internal waves under an ice-covered ocean. The fluid consists of two layers of constant densities, separated by an interface. The elastic sheet resists bending forces and is mathematically described by a fully nonlinear thin shell model. Fully localized solitary waves are computed via a boundary integral method. Progression along the various branches of solutions shows that barotropic (i.e. surface modes) wave-packet solitary wave branches end with the free surface approaching the interface. On the other hand, the limiting configurations of long baroclinic (i.e. internal) solitary waves are characterized by an infinite broadening in the horizontal direction. Baroclinic wave-packet modes also exist for a large range of amplitudes and generalized solitary waves are computed in a case of a long internal mode in resonance with surface modes. In contrast to the pure gravity case (i.e without an elastic cover), these generalized solitary waves exhibit new Wilton-ripple-like periodic trains in the far field.

Highlights

Internal gravity waves are ubiquitous in the ocean owing to density stratification arising from salinity and2014 The Authors
We numerically study steady interfacial gravity waves in a two-layer fluid system with an upper free surface consisting of a flexible elastic sheet modelling the floating ice cover
We show that there is another type of solitary wave which bifurcate from the trivial uniform stream at values of the parameters corresponding to the maxima rspa.royalsocietypublishing.org Proc

Summary

Introduction

This work is devoted to the numerical study of the permanent coherent structures—solitary waves and generalized solitary waves—in an idealization for the physical problem, namely a two-layer fluid system with a density interface and covered by a flexible elastic sheet that resists flexural motion. An extensive numerical study on interfacial solitary waves with free surface was recently carried out by Woolfenden & Parau [14] when the capillary effect was included either on the free surface of the upper layer or on both the top surface and the interface. We numerically study steady interfacial gravity waves in a two-layer fluid system with an upper free surface consisting of a flexible elastic sheet modelling the floating ice cover.

Slow modes

Conclusions