THE COUPLING OF GRAVITY-WAVES AND CONVECTION - AMPLITUDE EQUATIONS AND PLANFORM SELECTION

Convective motion in a layer of fluid heated from below is considered where the boundaries are stress free and the upper surface supports in terfacial gravity waves. Inviscid, immiscible, constant density, ambie nt fluid is separated from the convecting layer below by a stable dens ity jump. An important parameter in the problem is delta representing the ratio of the interfacial density jump to the density change across the convecting layer. Amplitude equations are derived describing conv ective motion in the plane and a planform selection analysis performed . It is demonstrated that the breaking of the translational and Galile an invariance of the problem allows a strong coupling between a large- scale interfacial mode and convection. The resulting phase dynamics is third order in time.