Particle trajectory of nonlinear progressive flexural-gravity waves in Lagrangian coordinates

Abstract

In this paper, we study the particle dynamics of nonlinear flexural-gravity waves propagating in a finite water depth, which is the interaction between ice sheets and water flows. The nonlinear deformation of a floating elastic sheet is modeled by the Cosserat shell theory. The theoretical analysis is performed by a uniform asymptotic perturbation expansion. A third-order explicit parametric solution of particle trajectories in Lagrangian coordinates is presented. Taking the time average of particle motion, the mass transport velocity and the Lagrangian surface setup are also derived. Numerical simulations are computed. The influences of flexural rigidity on the water particle orbits and the mass transport velocity of nonlinear flexural-gravity waves are first discussed.