Mechanics
Unstable spectrum of a Rayleigh–Bénard system with variable viscosity
Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1165-1178.

This Note studies a Rayleigh–Bénard system in an infinite layer, in the case of temperature-dependent viscosity, with rigid boundary conditions for the velocity at the bottom and free-slip at a top of the layer. It states the linearized problem in the relevant functional operator set-up and identifies, for each nonzero transverse frequency k and Rayleigh number R the (finite) number of modes which are unstable in time. This number is equal to the number of eigenvalues of a particular operator which are smaller than R.

Received:
Accepted:
Revised after acceptance:
Published online:
DOI: 10.5802/crmath.232
Classification: 34L05, 76E15
Lafitte, Olivier 1, 2

1 IRL CRM, UMI3457, Centre de recherches Mathématiques, Université de Montréal, Montréal, Canada.
2 LAGA, UMR7539, Université Sorbonne Paris Nord, 93430 Villetaneuse, France.
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Lafitte, Olivier. Unstable spectrum of a Rayleigh–Bénard system with variable viscosity. Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1165-1178. doi : 10.5802/crmath.232. http://www.numdam.org/articles/10.5802/crmath.232/

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