Initial free-surface elevation due to impulsive deflection of a two-dimensional bottom with small slope and small curvature

The incompressible free-surface elevation due to 2D impulsive bottom deformations is investigated analytically. The bottom geometry is arbitrary, with small slope and curvature. The equipotential condition is applied at the initially horizontal surface. The surface and bottom conditions are linearized. The surface elevation produced by an arbitrary bottom deflection is found to leading orders in slope and curvature.