Convection with temperature dependent viscosity in a porous medium: nonlinear stability and the Brinkman effect.
Lorna Richardson, Brian Straughan (1993)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Similarity:
We establish a nonlinear energy stability theory for the problem of convection in a porous medium when the viscosity depends on the temperature. This is, in fact, the situation which is true in real life and has many applications to geophysics. The nonlinear analysis presented here would appear to require the presence of a Brinkman term in the momentum equation, rather than just the normal form of Darcy's law.