Nonlinear stability problem of a rotating porous layer. (English) Zbl 0816.76035
After presenting the basic perturbation equations, the evolution equation is derived for an energy functional adopted for the viscous rotating Bénard problem. The a priori estimate of the energy functional is then given which ensures the nonlinear stability under some sufficient conditions. We then solve the variational problem and carry out numerical calculations to determine the critical energy bounds.
MSC:
76E30 | Nonlinear effects in hydrodynamic stability |
76S05 | Flows in porous media; filtration; seepage |
76U05 | General theory of rotating fluids |
76E15 | Absolute and convective instability and stability in hydrodynamic stability |
76M30 | Variational methods applied to problems in fluid mechanics |