FUNDAMENTAL SOLUTION OF THE INTERNAL-WAVE EQUATION FOR A MEDIUM WITH A DISCONTINUOUS BRUNT-VAISALA FREQUENCY

A two-layer stratified medium with constant, but different, values of the Brunt-Vaisala (BV) frequencies in the layers is considered An inte gral representation of the fundamental solution of the internal-wave e quation is constructed in the Boussinesq approximation. The wave patte rns in the upper and lower layers are investigated under the assumptio n that the source is located in the lower layer. It is shown that the fundamental solution in the lower layer is expressed in terms of the s ame standard functions as in the case of a single layer. The situation is more complicated in the upper layer and the investigation is based on a study of the branching points of a certain multivalued function. For long. times, approximate solutions are obtained by the stationary -phase method. The limiting case when the BV frequencies in the layers are only slightly different is investigated. In another limiting case , a surface exists (a circular cone or a cylinder, depending on the ra tio of the BV frequencies in the layers) close to which the formulae o btained using the stationary-phase method are inapplicable. The specia l asymptotic form of the fundamental solution :on this surface is calc ulated. (C) 1997 Elsevier Science Ltd. All rights reserved.