Generation of surface waves due to initial axisymmetric surface disturbance in viscous fluid of finite depth

The wave generation problem for viscous fluid of finite depth due to an axisymmetric initial surface disturbance is investigated here. Introducing the wave potential function phi and Stoke's stream function psi, the problem is formulated as an initial value problem to describe the motion in the fluid region. Laplace and Hankel transform techniques have been used in the mathematical analysis to obtain the form of the free surface in terms of a multiple infinite integral. This integral is then evaluated asymptotically by the method of steepest descent. The asymptotic form of the free surface is depicted graphically in a number of figures for different values of the viscous parameter and for different types of initial disturbances, and appropriate conclusions are made.