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Generation of waves due to bottom disturbances in a viscous fluid

The generation of two-dimensional surface waves due to various types of bottom disturbances such as underwater explosions, earthquakes, or volcanic eruptions is investigated here. Assuming linear theory the present problem is formulated as an initial value problem for the wave potential function ϕ and Stokes stream function ψ. Viscosity is considered. The physical model is illustrated by a sketch. Fourier and Laplace transform techniques are applied in the mathematical analysis to obtain the form of the free surface in terms of a multiple infinite integral. This integral is evaluated asymptotically by the method of steepest descent. The asymptotic form of the free surface is depicted graphically in some figures for different values of the viscosity and different types of ground disturbances. Appropriate conclusions are made.