A LINEAR-STABILITY ANALYSIS OF THE COUPLING OF GRAVITY-WAVES AND CONVECTION

The problem of convection in a fluid layer heated from below is studied when the lower boundary is rigid and stress-free and the upper boundary is deformable and stress-free. The upper boundary is taken as a material surface with a specified stable density change across it. This gives rise to a parameter delta-which is a nondimensional measure of the density change across the upper interface. The linear stability problem for isothermal boundary conditions is studied in detail and the neutral curve is defined in terms of the Rayleigh number and the interface parameter delta. The critical wave number k(c) and the critical Rayleigh number Ra(c) increase with increasing delta. An asymptotic representation for the neutral curve has been obtained for large delta-and, as delta --> infinity, the corresponding results for a rigid upper boundary are recovered.