Nonlinear Stability of Natural Convection in an Inclined Fluid Layer

nonlinear stability analysis of convection in an inclined layer of a viscous, incompressible fluid is carried out using energy method. The nonlinear stability boundary determined by the Rayleigh number Ra for the underlying dynamical system is found to depend upon the inclination of the layer with respect to the horizontal and Prandtl number of the fluid. A comparison with the linear instability boundary for the considered hydrodynamic system indicates a parametric region where the nonlinear stability of the basic flow is uncertain.