On the Boussinesq Equations with Non-monotone Temperature Profiles

Zillinger, Christian 1
1 Karlsruher Institut für Technologie (KIT)

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 𝜈$^{1/3}$ 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) Publikationstyp Zeitschriftenaufsatz Publikationsmonat/-jahr 08.2021 Sprache Englisch Identifikator ISSN: 0938-8974, 1432-1467 KITopen-ID: 1000133890 Erschienen in Journal of nonlinear science Verlag Springer Band 31 Heft 4 Seiten 64 Vorab online veröffentlicht am 24.05.2021 Nachgewiesen in ScopusWeb of ScienceDimensions Relationen in KITopen Verweist aufOn the Boussinesq Equations with Non-monotone Temperature Profiles. Zillinger, Christian (2020) Forschungsbericht/Preprint (1000133891)
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