Particle trajectory of nonlinear progressive flexural-gravity waves in Lagrangian coordinates - Hsu, Hung-Chu; Li, Meng-Syue (Frontiers in Marine Science, 2022)
In this paper, we consider the particle dynamics of nonlinear flexural-gravity waves in finite water depth, which is the interaction between ice sheets and water flows. The deformation of ice sheet is described as a nonlinear elastic model based on the Cosserat theory proposed by Toland [1]. 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 averaged of particle motion, the new fourth-order expression for the mass transport velocity and Lagrangian mean level are also derived. Numerical simulations are computed. The influences of flexural rigidity on the water particle orbits, mass transport velocity and Lagrangian mean level of nonlinear flexural-gravity waves are first discussed.