An exact solution of a linearized problem of the radiation of monochromatic internal waves in a viscous fluid

The eigenvalue method is used to construct an exact solution of the lineari zed boundary-value problem of the generation of internal waves in an expone ntially stratified fluid, when the source is part of a plan which vibrates along its surface. The spatial structure of the solution obtained describes two well-known types of wave beams-unimodal and bimodal. In the limiting c ases the phase pattern of the waves is identical with well-known asymptotic forms and laboratory experiments. The exact solution is compared with the solution of the model problem of the generation of waves by force sources, constructed using homogeneous fluid theory. The phase patterns of the waves in both cases agree everywhere with the exception of critical angles, when the wave propagates along the radiating surface. The amplitudes of the rad iated waves are the same only for certain ratios of the angles of inclinati on of the plane and the direction of propagation of the beams. (C) 1999 Els evier Science Ltd. All rights reserved.