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On the Boussinesq Equations with Non-monotone Temperature Profiles

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


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.

Verlagsausgabe §
DOI: 10.5445/IR/1000133890
Veröffentlicht am 14.06.2021
DOI: 10.1007/s00332-021-09723-3
Zitationen: 2
Web of Science
Zitationen: 2
Zitationen: 5
Cover der Publikation
Zugehörige Institution(en) am KIT Institut fĂŒr 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 Scopus
Web of Science
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