Hydrodynamic stability in the presence of a stochastic forcing: a case study in convection. (English) Zbl 07868599
Summary: We investigate the stability of statistically stationary conductive states for Rayleigh-Bénard convection that arise due to a bulk stochastic internal heating. Our results indicate that stochastic forcing at small magnitude has little to no effect, while strong stochastic forcing has a destabilizing effect. The methodology put forth in this article, which combines rigorous analysis with careful computation, provides an approach to hydrodynamic stability which is applicable to a variety of systems subject to a large scale stochastic forcing.
MSC:
| 76E06 | Convection in hydrodynamic stability |
| 76E30 | Nonlinear effects in hydrodynamic stability |
| 76R10 | Free convection |
| 76M35 | Stochastic analysis applied to problems in fluid mechanics |
| 80A19 | Diffusive and convective heat and mass transfer, heat flow |
Keywords:
Rayleigh-Bénard convection; Boussinesq approximation; nonlinear stability analysis; eigenvalue problem; bulk stochastic internal heating; critical growth factorReferences:
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