Triad resonance of flexural gravity waves in a two-layer fluid within the framework of blocking dynamics

Abstract

The present study deals with the formation of triads in flexural gravity waves in a two-layer density stratified fluid having a flexible plate-covered surface and an interface within the framework of blocking, which can be used as a mechanism for understanding the spectral distribution of wave energy. The physical model is considered in a two-dimensional Cartesian coordinate system, and the formations of triads are discussed geometrically and validated analytically. The study demonstrates the formation of at most eight triads of three different classes for flexural gravity waves before the threshold of blocking, whereas a maximum of six triads of three different classes have been reported in the case of free-surface gravity waves. However, at least twenty triads are formed for any frequency within the blocking limits for the compressive force lying within the threshold of blocking and buckling limit, irrespective of water depth. On the other hand, 24 triads are formed for a certain frequency in the left neighborhood of the primary blocking point, while thirty triads occur when the frequency is considered in the right neighborhood of the secondary blocking point for specific values of compressive force and density ratio in the case of deep water/short flexural gravity waves in both the layers. In addition, a new class of triad, which is rarely found in the case of surface gravity waves, occurs for a certain frequency within the blocking limits for a suitable choice of compressive force and density ratio in the case of waves in deep/intermediate upper layer depth.