| Abstract: | The three-dimensional problem of finite-depth stratified flow over a small bottom irregularity is considered in mixed Euler-Lagrange variables. The Brunt-Väisälä frequency is assumed to be constant and small, and the free surface condition is replaced by the rigid roof condition. Investigation of the far field showed that the principal wave perturbations lie within an angle which for large values of the internal Froude number is much less than theKelvin angle, while the wave amplitude at infinity is of the order of l/ r, where r is the polar radius. The ring perturbations are exponentially damped. As distinct from point source models, the model in question does not lead to divergence of the integrals on the flow axis 1-3]. Appproximate expressions for the radial and ring waves in terms of certain universai functions were obtained for investigating the near and far fields when the bottom irregularity is hemispherical. For the radial waves a law of similarity was obtained for which the characteristic dimension in the direction of the flow axis is the ratio of the flow velocity to the Brunt-Väisälä frequency, and the characteristic dimension in a direction perpendicular to the flow axis the depth of the fluid. In the first approximation the ring perturbations do not depend on the Brunt-Väisälä frequency. It is shown that in the near field the zone of intense wave perturbations is of the order of the fluid depth and not of the dimensions of the obstacle as for Kelvin ship waves on the surface of a homogeneous fluid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 86–94, September–October, 1987. |
