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As a first main result, we show that if<jats:inline-formula><jats:alternatives><jats:tex-math>$$T'$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mi>T<\/mml:mi><mml:mo>\u2032<\/mml:mo><\/mml:msup><\/mml:math><\/jats:alternatives><\/jats:inline-formula>is of size at most<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\nu ^{1\/3}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mi>\u03bd<\/mml:mi><mml:mrow><mml:mn>1<\/mml:mn><mml:mo>\/<\/mml:mo><mml:mn>3<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:math><\/jats:alternatives><\/jats:inline-formula>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\u2013B\u00e9nard 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.<\/jats:p>","DOI":"10.1007\/s00332-021-09723-3","type":"journal-article","created":{"date-parts":[[2021,5,24]],"date-time":"2021-05-24T20:02:41Z","timestamp":1621886561000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["On the Boussinesq Equations with Non-monotone Temperature Profiles"],"prefix":"10.1007","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0480-2719","authenticated-orcid":false,"given":"Christian","family":"Zillinger","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,5,24]]},"reference":[{"issue":"5","key":"9723_CR1","doi-asserted-by":"publisher","first-page":"1078","DOI":"10.1016\/j.jde.2010.03.021","volume":"249","author":"D Adhikari","year":"2010","unstructured":"Adhikari, D., Cao, C., Jiahong, W.: The 2d Boussinesq equations with vertical viscosity and vertical diffusivity. 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