Time-Dependent Wave Motion in a Viscous Fluid Covered by a Poroelastic Plate

Abstract

Time-dependent wave motion coupled with bottom disturbances and poroelastic plate in a viscous incompressible fluid of finite depth is studied here. The problem is framed as an initial value problem in terms of potential and stream functions by assuming linear water wave theory. Three objectives are met in this work: first, the behaviour of the root of the dispersion relation is analyzed for plane progressive waves; second, the effect of viscosity on the asymptotic form of the plate deflection is studied. Third, the effect of plate porosity and other crucial parameters on fluid velocity are examined through various contour plots. Using Laplace and Fourier transform techniques, the expression for plate deflection is derived in terms of a highly oscillatory infinite integral and then evaluated asymptotically by using the steepest descent method. Different numerical analyses are performed by varying physical parameters such as viscosity, porosity, flexural rigidity and frequency of the wave motion. It is observed that, with an increase in the value of viscosity, the values of the real and imaginary parts of the complex root of the dispersion relation increase for frequency above a cut-off value; the maximum amplitude of the plate deflection decreases, and the vertical velocity decreases.