ON THE PENETRATION OF AN ENDOTHERMIC PHASE-TRANSITION BY UPWELLINGS AND DOWNWELLINGS

Using a simple criterion for the deflection of a constant-viscosity up welling or downwelling by an endothermic phase transition, the scaling of the critical phase buoyancy parameter P-crit with the important le ngthscales is obtained. The derived trends match those previously obse rved in time-dependent numerical simulations, implying that geometry i s the dominant factor in determining the propensity to layering. For a sinusoidal temperature anomaly, P-crit is found to be proportional to wavelength, so that a stronger phase change is required to stop longe r wavelengths, in accord with observations from three-dimensional nume rical simulations. For more realistic Gaussian upwelling and downwelli ng features, the dependence of P-crit On width of feature, spacing of features, depth of phase transition and width of phase transition are determined for idealized internally heated and basally heated systems. Narrow upwellings and downwellings are deflected more easily than bro ad ones, providing a first-order explanation for the increased propens ity to layering as Rayleigh number is increased. Internal heating is f ound to strongly favor deflection, particularly when the phase change is at shallow depth. For basally heated systems, the depth of the phas e transition is found to be relatively unimportant in determining the value of P-crit for which both upwellings and downwellings are deflect ed. In contrast, for internally heated systems, a shallower phase tran sition strongly favors layering. Only weak dependence of P-crit on the spacing of upwellings and downwellings is found. A narrower phase tra nsition enhances deflection.