Mantle convection at marginal stability
Warford, Andrew Craig
Master of Arts
The horizontal extent of convection cells in the earth's mantle can be estimated from the geometry of plate boundaries. The vertical dimensions can perhaps be estimated from the theory of marginal stability in variable viscosity fluids. For viscosity laws symmetrical about mid-depth the aspect ratio increases with increasing viscosity contrast, but the law of variation with depth has little effect. The value of the Rayleigh number is affected by both the viscosity law and the contrast. The aspect ratio for the asymmetric cases studied is much less affected except at very high contrasts (>3) and then only in the case of an exponentially varying viscosity. In all cases studied, the variation of the Rayleigh number with wavelength is smaller as the viscosity contrast increases, thus allowing for a fairly wide range of aspect ratios. The variation of velocity with depth indicates that motion takes place in the entire depth range except in the case of viscosity decreasing exponentially with depth and then only at high viscosity contrast (>2).