Non linear stability of a two layer flows

MENZAQUE, F.; MILEWSKI, P.; ROSALES, R.; TABAK, E.; TURNER, C.

INT PRESS BOSTON, INC

Año: 2004 vol. 2 p. 427 - 427

We study the dynamics of two-layer, stratified shallow water flows. This is a modelin which two scenarios for eventual mixing of stratifed flows (shear-instability and internal breakingwaves) are, in principle, possible. We find that unforced flows cannot reach the threshold of shear-instability, at least without breaking first. This is a fully nonlinear stability result for a model ofstratified, sheared flow. Mathematically, for 2X2 autonomous systems of mixed type, a criterium isfound deciding whether the elliptic domain is reachable -smoothly- from hyperbolic initial conditions.If the characteristic fields depend smoothly on the system´s Riemann invariants, then the ellipticdomain is unattainable. Otherwise, there are hyperbolic initial conditions that will lead to incursionsinto the elliptic domain, and the development of the associated instability.