Analytical solutions of tsunami waves induced by sea floor collapses

This paper considers tsunami generation by sea floor collapses. Sea floor collapse is considered by both moving sea bottom or by rapid water discharge into a sea floor collapsing hole. The mathematical formation is done through the use of linear potential theory for fluid. The problem is specified in terms of velocity potential with appropriate boundary conditions imposed on water surface as well as at the sea bottom. Time dependence of impulsive movements of sea bottom is modeled as Dirac delta function. Green;s function method is used to provide a framework for analyzing arbitrary sea floor movement in a circular domain. Exact solutions were derived for some special cases of vertical sea bottom movements. In general, the solution is expressed in terms of infinite integral, but for the case of far field and long time solution, the asymptotic form of the integral can be evaluated by using Kelvin's stationary phase method. This corresponds to the leading waves of a tsunami generated by sea floor collapse. The solutions of the present study can provide the initial phase of sea surface conditions and can be used as input for tsunami simulations using TSUNAMI-N2, COST and COMCOT.