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

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 soluti...

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Bibliographic Details
Published inApplicable analysis Vol. 99; no. 12; pp. 2026 - 2044
Main Authors Fan, Xiaoting, Xu, Wen-Qing, Wang, Shu, Wang, Wei
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 09.09.2020
Taylor & Francis Ltd
Subjects
asymptotic expansion
Asymptotic methods
Asymptotic series
Boundary layers
Boussinesq equations
Boussinesq system
Diffusivity
Ming Mei
Multiscale analysis
Perturbation theory
Rayleigh-Benard convection
Rayleigh-Bénard convection
Singular perturbation
vanishing diffusivity limit
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Summary: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.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2018.1553035