STABILITY OF NATURAL CONVECTION IN A SHALLOW CAVITY
The stability of natural convection in a shallow cavity is presented. The flow is two dimensional and is driven by a horizontal temperature gradient between isothermal vertical side walls. The top and bottom boundaries are taken to be highly conducting.
The eigenvalue problem arising from the linear stability theory is solved pseudospectrally by Chebyshev polynomials. The critical wavelength and Grashof number is determined for a set of Prandtl numbers in a wide range. For Pr < 0.14 the shear instability leads to stationary transverse cells; for higher values of Pr the instability is a convection type, and it sets in as oscillating longitudinal rolls in the range 0.14 < Pr < 0.45, and as stationary longitudinal rolls for larger Prandtl numbers. The energy transfer from the base flow and the buoyancy field to the disturbance kinetic energy is presented to obtain a physical interpretation of the reasons for the instability.