# 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.

 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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