Motion of Fluid Particles in the Field of a Generalized Surface Solitary Wave in a Fluid under Ice Cover

We consider a fluid layer of finite depth described by the Euler equations. The ice cover is modeled by a geometrically nonlinear elastic Kirchhoff–Love plate. The fluid particles move under the ice cover in the field of generalized solitary wave type nonlinear surface traveling waves of small but finite amplitude. The equations of the model admit a solution describing such surface waves. Generalized solitary waves are solitary waves up to terms that are exponentially small in amplitude; therefore, for approximations of algebraic order in amplitude, the trajectories of particles are determined by the surface solitary wave. In the analysis we use explicit asymptotic expressions for solutions describing wave structures at the water–ice interface, such as a generalized solitary wave, as well as asymptotic solutions for the velocity field generated by these waves in the bulk of the fluid.