Oblique wave propagation over uneven flexible base in a fluid having free-surface tension

Abstract

A hydroelastic model has been introduced to study the impact of free surface tension on the propagation of oblique incident waves over small distortions on a thin, flexible floor of a fluid region. There are two varieties of time-harmonic propagating waves (free-surface and flexural modes) that exist in the region in the case of any specific frequency. One variety of proliferating waves having smaller wavenumber spreads on the top surface, while another spreads along the thin, flexible base. Using perturbation expansion involving a small parameter $ϵ$, the primary boundary value problem (bvp) is converted to a new bvp for the first-order approximation of the potential function. Subsequently, employing the Fourier transform approach, the first-order approximation of reflected and transmitted energy are acquired in the case of both modes of waves. Two specific examples of irregular floor are taken up to validate the theoretical outcomes flourished in this study. The influence of free-surface tension and flexible floor on the oblique wave propagation over uneven floor are analyzed and depicted graphically for certain sets of parametric values involved in the problem. The presence of free-surface tension on the upper boundary of the fluid introduces a third-order linearized boundary condition into the formulation of the wave-structure interaction problem, unlike the usual homogeneous first-order condition applicable for a free-surface. When a series of obliquely incident waves corresponding to free-surface and flexural modes spread over an irregular flexible floor of the fluid, the free-surface tension acts as a resistive force to the surface gravity waves. It can be inferred from this that the influence of surface tension at the free-surface of the fluid should not always be overlooked while dealing with the linear wave-structure interaction problem. Further, numerical estimation of reflected and transmitted energy for both varieties of time-harmonic waves are presented to confirm the analytical forms of energy relations almost accurately.