Stability properties and nonlinear mappings of two and three-layer stratified flows

L. Chumakova, F. E. Menzaque, P. A. Milewski, R. R. Rosales, Esteban Tabak, C. V. Turner

Research output: Contribution to journalArticle

Abstract

Two and three-layer models of stratified flows in hydrostatic balance are studied. For the former, nonlinear transformations are found that map [baroclinic] two-layer flows with either rigid top and bottom lids or vertical periodicity, into [barotropic] single-layer, shallow water free-surface flows. We have previously shown that two-layer flows with Richardson number greater than one are nonlinearly stable, in the following sense: when the system is well-posed at a given time, it remains well-posed through the nonlinear evolution. Here, we give a general necessary condition for the nonlinear stability of systems of mixed type. For three-layer flows with vertical periodicity, the domains of local stability are determined and the system is shown not to satisfy the necessary condition for nonlinear stability. This means that there are wave-motions that evolve into shear unstable flows.

Original languageEnglish (US)
Pages (from-to)123-137
Number of pages15
JournalStudies in Applied Mathematics
Volume122
Issue number2
DOIs
StatePublished - Feb 2009

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Stratified Flow
Nonlinear Mapping
Nonlinear Stability
Periodicity
Shear flow
Vertical
Shallow Water Flow
Necessary Conditions
Nonlinear Transformation
Free Surface Flow
Hydrostatics
Local Stability
Unstable
Water
Motion

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Stability properties and nonlinear mappings of two and three-layer stratified flows. / Chumakova, L.; Menzaque, F. E.; Milewski, P. A.; Rosales, R. R.; Tabak, Esteban; Turner, C. V.

In: Studies in Applied Mathematics, Vol. 122, No. 2, 02.2009, p. 123-137.

Research output: Contribution to journalArticle

Chumakova, L. ; Menzaque, F. E. ; Milewski, P. A. ; Rosales, R. R. ; Tabak, Esteban ; Turner, C. V. / Stability properties and nonlinear mappings of two and three-layer stratified flows. In: Studies in Applied Mathematics. 2009 ; Vol. 122, No. 2. pp. 123-137.
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