Convection and gravity waves in two layer models, II. Overstable convection of large horizontal scales

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Abstract
Penetrative convection is studied for idealized two-layer models composed of convectively unstable and stable layers with constant viscosity and conductivity in each layer but different from that in the other layer. The critical Rayleigh number of the unstable layer depends very much on the adjacent stable layer penetrated by the flow. The value is greatly reduced from the usual value of the order of 103 for rigid and free boundaries of fixed temperatures, if the viscosity of the stable layer is very small. The critical mode is an overstable mode having infinite horizontal wavelength. The solar supergranulation is suggested to be similar in nature to such a horizontally large convective cell.

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