Impact of bottom explosions on wave formation in the presence of an inertial surface and wave current in a viscous fluid

Abstract

This study examines the impact of a bottom explosion on wave generation in an inertial surface, considering the roles of fluid viscosity, wave current, and the nature of a slippery porous sea bottom. The Fourier and Laplace transform techniques are employed to calculate the surface elevation in terms of an infinite integral. Further, the infinite integral is evaluated asymptotically using the stationary-phase approach for larger time and distance values. The influence of viscosity, inertial surface, current, and slip parameters on wave generation is analyzed for different times and distances. The study reveals that the presence of an inertial surface lessens the amplitude of free surface elevation. Further, the free surface elevation's amplitude reduces as the current speed and liquid viscosity approach closer to a small value. In the case of a slippery porous bottom, as the slip parameter increases, the free surface elevation's amplitude decreases.