Waves due to initial disturbances at the interface between two superposed fluids

This paper is concerned with generation of interface waves due to an initial disturbance at the interface between two superposed homogeneous and inviscid fluids, the lower fluid being of finite depth and the upper fluid extending infinitely upwards. Assuming linear theory, the problem is formulated as a coupled boundary value problem in the velocity potentials describing the motion in the two fluids. The interface depression is obtained when the initial disturbance at the interface is in the form of a prescribed depression of the interface or an impulse concentrated at a point. In both the cases, the interface depression is obtained in terms of an infinite integral which is evaluated asymptotically for large time and distance. This is then displayed graphically in a number of figures to visualise the effect of the upper fluid and also the effect of the finite depth of the lower fluid on the wave motion at the interface.