Abstract:
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.
Key words:ice cover, elliptic integral, bifurcation, central manifold, trajectories of fluid particles.
