Abstract

Limiting Forms of Internal Solitary Waves in a Continuously Stratified Fluid

J.Maltseva (Lavrentyev Institute of Hydrodynamics, Novosibirsk, Russia)

e-mail: maltseva@hydro.nsc.ru

The problem on the limiting forms of nonlinear internal waves in weakly stratified fluid of finite depth is considered. The special type of the steady internal waves, solitary waves with broad flat crests of plateau-type is investigated. The propagation speed of this wave is close to that of a smooth internal bore. The bore describes approximately the forward and back fronts of such a solitary wave. The flow in midsection of solitary wave is close to the flow which is conjugate with uniform flow at infinity. Full description of plateau-type solitary waves in the case of two-layer stratification is given in [1]. This situation takes place for Froude numbers close to critical values which correspond to degeneration of a symmetric solitary wave to asymmetric bore. In the present paper the family of approximate solutions describing plateau-shaped waves in a fluid with density distribution close to exponential is obtained. The neighbourhood of branches of the conjugate flows corresponding to plateau-shape waves is studied. An example of the density profile for which plateau-shaped waves with additional elevation in central region exist is constructed. The work supported by the Russian Foundation for Basic Research (grant 00-01-00850) and Interdisciplinary Program of SB RAS (Project N 1 \"Mathematical modelling of nonhomogeneous fluids flows and its interaction with deformable structures\".) References [1] Maltseva J.L. Flat Solitary Waves in a Two-Layer Fluid. Proc. V Int. Symp. on Stratified Flows, Vancouver, Canada, 2000. p. 804-809.

Section : 6