Effect of compressive stress on the dispersion relation of the flexural–gravity waves in a two-layer fluid with a uniform current

Abstract

The explicitly analytical solution is derived for the dispersion relation of the flexural-gravity waves in a two-layer fluid with a uniform current. The upper fluid is covered by a thin plate with the presence of the elastic, compressive and inertial forces. The density of each of the two immiscible layers is constant. The fluids of finite depth are assumed to be inviscid and incompressible and the motion be irrotational. A linear system is established within the framework of potential theory. A new representation for the dispersion relation of flexural-gravity waves in a two-layer fluid is derived. The critical value for the compressive force is analytically determined. The dispersion relation for the capillary-gravity with an inertial surface in a two-layer fluid can be obtained in parallel. Some known dispersion relations can be recovered from the present solution.