Open Access
September 2004 Nonlinear Stability of two-layer flows
Fernando Menzaque, Paul Milewski, Ruben Rosales, Esteban Tabak, Cristina Turner
Commun. Math. Sci. 2(3): 427-442 (September 2004).


We study the dynamics of two-layer, stratified shallow water flows. This is a model in which two scenarios for eventual mixing of stratified flows (shear-instability and internal breaking waves) 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 of stratified, sheared flow. Mathematically, for 2X2 autonomous systems of mixed type, a criterium is found 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 elliptic domain is unattainable. Otherwise, there are hyperbolic initial conditions that will lead to incursions into the elliptic domain, and the development of the associated instability.


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Fernando Menzaque. Paul Milewski. Ruben Rosales. Esteban Tabak. Cristina Turner. "Nonlinear Stability of two-layer flows." Commun. Math. Sci. 2 (3) 427 - 442, September 2004.


Published: September 2004
First available in Project Euclid: 3 March 2005

zbMATH: 1084.76031
MathSciNet: MR2118852

Rights: Copyright © 2004 International Press of Boston

Vol.2 • No. 3 • September 2004
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