The three-dimensional planform of the infinite Prandtl number convection is studied in one and two layers, with a numerical code which combines spectral and finite difference methods. The equations are solved in rectangular cavities supposing mirror symmetry on the sides. The one-layer experiments serve mainly for testing the code. These experiments reveal the outstanding importance of the initial and boundary conditions in the evolution of the flow pattern. The main emphasis of this paper is on two-layer convection models, with implications for the Earth's mantle and its gravity anomaly field. In this case, the interface between the two layers is fixed at a given depth, and coupling of the two circulations is ensured by the continuity of velocities and horizontal stress across the interface. The two-layer cases have been run with Rayleigh numbers up to 130 times the critical value, the thickness of the lower layer being twice that of the upper one. The ratio of the lower layer viscosity to the upper one is gradually increased.

When this ratio is small (between 1 and 10), viscous coupling prevails, and bimodal or square cells formed in the lower layer induce similar, but counterrotating cells in the thin upper layer. When the viscosity ratio is high (several hundred), thermal coupling becomes dominant: again, the convective structure of the lower is more or less duplicated in the upper layer, but now the flows of both layers rotate in the same sense. In these situations the gravity anomalies are postively correlated with the topography of the upper surface. When the viscosity ratio is moderate (e.g. 25), the flow direction of the rolls in the thin upper layer becomes perpendicular to that observed in the lower layer, leading to a balance between the conflicting effects of the viscous and thermal couplings. This allows the upper rolls to have an aspect ratio close to 1. In this case, gravity is positively correlated with deflection of the interface, but no more correlation can be seen with surface topography, which is determined by small-scale flow of the upper layer. These results suggest that the gravity and bathymetry anomalies of the Earth should be either postively correlated or not correlated at all. This has to be contrasted with earlier findings of two-dimensional modeling which allow the possibility of having anticorrelation between gravity and topography. ¿ American Geophysical Union 1988