Physical parameters of envelope solitary waves at a water-ice interface

Abstract

In this note we focus our attention on physical parameters of so-called envelope solitary waves beneath an ice cover. The form and propagation of waves in water basins under the ice cover are described by the 2D Euler equations. The ice cover is modeled by an elastic Kirchhoff-Love plate and is assumed to be of considerable thickness so that the inertia of the plate is taken into account in the formulation of the model. The Euler equations involve the additional pressure from the plate that is freely floating at the surface of the fluid. We consider the self-focusing case, when envelope solitary waves exist, for which the envelope speed (group speed) is equal to the speed of filling (phase speed). The indicated families of envelope solitary waves are parameterized by the speed of the waves, and their existence is proved earlier for speeds lying in some neighbourhood of the critical value corresponding to the quiescent state. The envelope solitary waves, in turn, bifurcate from the quiescent state and lie in some neighbourhood of it. Analysing the form of the envelope solitary wave and the critical parameters for it we determine characteristic values of length and speed of the wave. These physical parameters can be compared with possible observations detecting such waves in practice.