TY  - JOUR
T1  - Weakly nonlinear analysis of Rayleigh–Bénard convection problem in extended Boussinesq approximation
A1  - Dostalík, Mark
A1  - Matyska, Ctirad
A1  - Průša, Vít
JA  - Applied Mathematics and Computation
Y1  - 2021
VL  - 408
SP  - 126374
SN  - 0096-3003
UR  - https://www.sciencedirect.com/science/article/pii/S009630032100463X
M2  - doi: 10.1016/j.amc.2021.126374
KW  - Extended boussinesq approximation
KW  - Thermal convection
KW  - Weakly nonlinear analysis
N2  - We investigate Rayleigh–Bénard convection problem in an extended Boussinesq approximation suitable for conditions in the Earths mantle. The aim is to evaluate the influence of depth-dependent material parameters, dissipation, adiabatic heating/cooling and heat sources on qualitative characteristics of thermal convection. We identify the critical values of dimensionless parameters that determine the onset of convection, and we characterize the dominating convection patterns in marginally supercritical states. These issues are addressed by the application of linear stability analysis and weakly nonlinear analysis. We have found that the character of convection differs substantially from the standard case of Rayleigh–Bénard convection.
ER  -