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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 12
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Articles

Boundary layers associated with the 3-D Boussinesq system for Rayleigh–Bénard convection

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Pages 2026-2044 | Received 23 Apr 2018, Accepted 24 Nov 2018, Published online: 04 Dec 2018
 

Abstract

We investigate the boundary layer effects of the 3-D incompressible Boussinesq system for Rayleigh–Bénard convection with vanishing diffusivity limit. By adopting the multi-scale analysis and the asymptotic expansion methods of singular perturbation theory, we construct an exact approximating solution for the viscous and diffusive Boussinesq system with well-prepared initial data. In addition, we obtain the convergence result of the vanishing diffusivity limit.

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Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by National Natural Science Foundation of China [grant number 11771031, 11531010] and by Natural Science Fund of Qinghai Province [grant number 2017-ZJ-908].

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