Fig. 9. Dynamical parameter space for Enceladus.

The black points represent our simulations; the blue blocks represent the possible position of Enceladus in this space. The minimum value of κ on Enceladus is assumed to be 1.4 × 10⁻⁷m² s⁻¹. This is the estimated molecular diffusivity (9), but tidal mixing will likely produce much elevated values. The solid lines show the parameters for the corresponding meridional heat flux predicted by Eq. 26. Because the ocean heat transport is unlikely larger than 3 GW, the diffusivity must be smaller than ∼10⁻³m² s⁻¹. E_k and $R_a^{\star }$ are defined in Eqs. 28 and 30, respectively.