The influence of bottom disturbances on wave generation in a viscous liquid in the presence of uniform current

Abstract

In the present paper, the effect of bottom disturbances on wave generation in a viscous liquid in the presence of uniform current is studied. The wave potential and Stokes stream function are used to formulate this problem. Multiple integrals representing the free surface elevation are obtained by mathematical analysis using the Laplace transform in time and the Fourier transform in space. This is divided into various multiple integrals, using the steepest descent method to evaluate them asymptotically for a large time and distance. There are three types of ground disturbances taken into consideration: D0(x)=e(−x2/2), D0(x)=e−|x|, and D0(x)=δ(x). The effect of uniform current speed (U) and viscosity (ν) on the free surface elevation is illustrated for the three forms of ground disturbances. It is observed that the presence of current often amplifies the energy of the propagating wave and also increases its amplitude. Moreover, as viscosity increases, the amplitude of free surface elevation decreases with respect to time, and further, the period of oscillation of surface elevation becomes smaller for a large time.