An investigation of the properties of flexural-gravity wave propagation in a coupled submerged and floating plate system

Abstract

The propagation of flexural-gravity waves in a coupled submerged and floating plate system is studied, and the complex flexural gravity wave propagation properties are investigated in the frequency and time domain, The system exhibits two modes of propagation analogous to the surface and internal waves in a two-layer fluid. The effect of the plate properties on the phase velocities of both the faster (floating plate in general) and the slower (submerged plate in general) modes are analysed in detail. Both modes exhibit complex properties, including waves with negative kinetic energy and points of blocking at which no energy can propagate. They also show complex coupling and energy transfer in the time-domain. Furthermore, the dependency of the blocking frequency and the critical opposing current is analysed in both the shallow and deep water limits. The occurrence of blocking in the internal mode under a specific constraint is also demonstrated. As a special case, the influence of the submerged plate’s position and compressive force on the dynamics of the free surface flexural-gravity wave blocking is studied. The characteristics of the phase speed in both modes are studied, and the occurrences/non-occurrences of optima are mathematically proved. Some of the analytic results are illustrated by time-domain simulations which illustrate the complex wave propagation phenomena of this system.