# On the Boussinesq Equations with Non-monotone Temperature Profiles

Zillinger, Christian

## 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 Forschungsbericht/Preprint Publikationsdatum 04.11.2020 Sprache Englisch Identifikator ISSN: 0938-8974, 1432-1467 KITopen-ID: 1000133891 Umfang 30 S. Nachgewiesen in arXiv Relationen in KITopen Verweist aufOn the Boussinesq Equations with Non-monotone Temperature Profiles. Zillinger, Christian (2021) Zeitschriftenaufsatz (1000133890)
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