Green functions for impulsive free-surface flows due to bottom deflectionsin two-dimensional topographies

An analytical investigation is performed of the initial free-surface flow s ubject to an impulsive concentrated unit flux through an arbitrary point at an otherwise impermeable boundary. The flow is assumed incompressible, inv iscid, irrotational and two-dimensional. It obeys a zero-potential conditio n at the horizontal free surface. This problem of impulsive Green functions is solved for various bottom topographies, such as sloping beaches, submer ged ridges, and finite basins. The basic result in each case is the normal derivative of the velocity potential along the free surface, which represen ts the initial surface velocity due to the concentrated impulsive flux. The results have relevance to tsunami modeling. (C) 2000 American Institute of Physics. [S1070-6631(00)50811-3].