Motion of Fluid Particles in the Field of a Nonlinear Periodic Surface Wave in a Fluid Beneath an Ice Cover

A finite-depth fluid layer described by the Euler equations is considered. The ice cover is simulated by a geometrically nonlinear elastic Kirchhoff–Love plate. The trajectories of fluid particles under the ice cover are in the field of nonlinear surface periodic traveling waves of small, but finite amplitude. A solution describing such surface waves is allowed by the equations of the model. Periodic waves are described by Jacobi elliptic functions. The analysis uses explicit asymptotic expressions for solutions describing wave structures at the water–ice interface, such as a periodic wave against a zero‑displacement surface, as well as asymptotic solutions for the velocity field in a fluid column generated by these waves.