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On the Boussinesq equations with non-monotone temperature profiles

Zillinger, Christian

Abstract:
Abstract. In this article we consider the asymptotic stability of the two-dimensional Boussinesq equations with partial dissipation near a combination of Couette flow and temperature profiles $T(y)$. As a first main result we show that if $T′$ is of size at most $\nu^{1/3}$ in a suitable norm, then the linearized Boussinesq equations with only vertical dissipation of the velocity but not of the temperature are stable. Thus, mixing enhanced dissipation can suppress Rayleigh-Bénard instability in this linearized case.
We further show that these results extend to the (forced) nonlinear equations with vertical dissipation in both temperature and velocity.

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Volltext §
DOI: 10.5445/IR/1000125789
Veröffentlicht am 06.11.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 11.2020
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000125789
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 30 S.
Serie CRC 1173 Preprint ; 2020/32
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter Boussinesq equations, partial dissipation, hydrostatic imbalance, enhanced dissipation, shear flow
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