tokens: calculated using Equation ( 30 ) in the Appendix , which are given bywhere represents a horizontal average. Figure 8. Measurements of horizontally averaged density gradients in layers for two low-Ta* simulations. Also shown are predicted density gradients for systems with given rotation rates and layer heights. Both simulations have Pr = τ = 0.1 and . We indeed find that the density gradients in layers are largest for the simulation with the higher rotation rate (Ta* = 0.1), and that the results from this simulation also fit well with prediction. The case with Ta* = 0.01, on the other hand, shows much greater variability in density gradient, particularly at larger layer heights, making it difficult to determine whether or not the theoretical predictions are valid. From Figure 8 we also see that in both cases the steepening of the density gradient is somewhat greater for smaller layers. However, this dependence of density gradient on layer height is weaker than the theory suggests. In Figure 4 we see that the simulation with Ta* = 0.1 spends a greater amount of time in the three- and two-layered phases than either of the other two simulations, and it consequently takes about twice as long as the nonrotating run (Ta* = 0) to reach the one-layered phase. The root cause is related to the lower supercriticality of convection within the layers combined with the increased stability of the interfaces. Through inspection of the density profiles of our layered simulations, we see that the positions and shapes of the interfaces in rotating simulations have less variability with time compared with nonrotating simulations. We also see in Figure 4 that the fluxes in the rotating layered systems oscillate less than they do in the nonrotating ones. Wood et al. ( 2013 ) already discussed these large-amplitude oscillations in nonrotating simulations and attributed them to the presence of large plumes of fluid punching through interfaces, periodically causing spikes in transport. In our layered rotating simulations (particularly the Ta* = 0.1 case), the absence of large-amplitude oscillations in the layered phase suggests that the motion of these plumes is inhibited, possibly because convection is weaker and the interfacial gradients are stronger. Since the plumes could be key players in the layer merger events, their suppression in the rotating simulations could also explain why the merger timescale is longer. All of these effects also contribute to the reduction of mean fluxes of temperature and chemical composition through density staircases in rotating ODDC compared with the nonrotating case. To show this quantitatively, Table 1 presents measurements of and (with standard deviations) for each value of Ta*. For low Ta* simulations, which clearly form convective layers, the fluxes are measured in the one-layered phase. The simulation with Ta* = 0.01 shows 2% and 7% decreases in thermal and compositional fluxes, respectively, compared to the nonrotating
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