Unsteady three-dimensional sources for a two-layer fluid of finite depth and their applications

Abstract

To our friend Ernie Tuck, in celebration of his multi-faceted talents. The velocity potentials of various unsteady point sources are derived in this paper for a two-layer fluid of finite depth. Two-layer fluids are often used to study effects of density stratification on hydrodynamics of marine systems. The sources here are restricted to the upper fluid layer and the potentials of the induced flows are given for the whole fluid domain. The velocity potentials of a transient source of arbitrary strength and in arbitrary three-dimensional motion are derived first. The potentials of a time-harmonic source without forward speed, and then with forward speed, are obtained from the transient source by specifying the appropriate source strength and motion. These potentials are fundamental to the analyses of various types of body motion in finite water depths under the influence of surface and interfacial waves. As a sample application, a numerical solution of the radiation and diffraction problem for a floating rectangular barge is presented. The results indicate that internal waves can have a strong effect on the motions of the floating barge over a wide range of incident-wave frequencies.