As was found by Christensen and Yuen [1985], the propensity to layered convection increases with increasing Rayleigh number, which led them to suggest that the Earth may have undergone a transition from layered to whole-mantle convection as its Rayleigh number decreased due to a combination of secular cooling and a decrease in radiogenic heat production. This trend was confirmed by the two-dimensional studies of Zhao et al. [1992] and in three dimensions by Yuen et al. [1994]. The latter results are illustrated in Figure 2, and show clearly the change in convective style, and in particular the increased propensity to layering, as the Rayleigh number is increased. Most numerical experiments have been performed assuming statistically steady-state conditions, in which heating rate and boundary temperatures do not change with time. Steinbach et al. [1993] have taken the simulations a step further, explicitly modeling convection in a cooling mantle, by using a time-dependent core-mantle boundary temperature. They find that the transition from layered to whole-mantle convection occurs in the form of a very violent avalanche, more vigorous than the avalanches found under steady-state conditions, and that the cooling rate of the Earth increases after the transition has occurred. This was further investigated by Steinbach and Yuen [1994b] and Honda and Yuen [1994]. Furthermore, an instability involving feedback between temperature-dependent viscosity and heatings from latent heat and viscous dissipation may produce melting in the transition zone [ Steinbach and Yuen, 1994a]. These two heat sources produce instabities on different timescales, but with similar magnitudes.