Impulsive Tsunami generation by rapid bottom deflections at initially uniform depth

An analytical small-time expansion is developed for impulsive tsunami generation at initially uniform depth in two and three dimensions. The flow is due to impulsive bottom deflections that are rapid, with duration shorter than the gravitational time scale for the given depth. The bottom deflection is assumed separable in space and time. A third-order small-time expansion is given. The first and second-order solutions are general, while only the gravitational effect is included. The solutions are given as Fourier transforms and Green function integrals. The solutions are integrated numerically for the simple case of a rising block.