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On the Boussinesq Equations with Non-monotone Temperature Profiles

Zillinger, Christian


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 𝑇â€Č 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–BĂ©nard 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 fĂŒr Analysis (IANA)
Publikationstyp Forschungsbericht/Preprint
Publikationsdatum 04.11.2020
Sprache Englisch
Identifikator ISSN: 0938-8974, 1432-1467
KITopen-ID: 1000133891
Umfang 30 S.
Nachgewiesen in arXiv
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