Nonlinear equilibrium solutions for travelling waves in a free convection between vertical parallel plates
Abstract
Nonlinear stability of free convection between vertical parallel plates with different uniform temperatures is investigated on a weakly nonlinear basis. The Landau equation for P less than Pc, two coupled Landau equations for P greater than Pc, and three coupled Landau equations for P = Pc are derived for disturbance amplitudes in the neighborhood of the criticality where P is the Prandtl number and Pc = 12.45425644. Coefficients involved in the equations are determined numerically, and equilibrium solutions of the amplitude equations are classified into several categories.
 Publication:

European Journal of Mechanics B Fluids
 Pub Date:
 1991
 Bibcode:
 1991EJMF...10...25F
 Keywords:

 Equilibrium Equations;
 Flow Stability;
 Free Convection;
 Parallel Plates;
 Traveling Waves;
 Branching (Mathematics);
 Nonlinear Equations;
 Prandtl Number;
 Fluid Mechanics and Heat Transfer