  On icy worlds, the ice shell and subsurface ocean form a coupled system --
heat and salinity flux from the ice shell induced by the ice thickness gradient
drives circulation in the ocean, and in turn, the heat transport by ocean
circulation shapes the ice shell. Therefore, understanding the dependence of
the efficiency of ocean heat transport (OHT) on orbital parameters may allow us
to predict the ice shell geometry before direct observation is possible,
providing useful information for mission design. Inspired by previous works on
baroclinic eddies, I first derive scaling laws for the OHT on icy moons, driven
by ice topography, and then verify them against high resolution 3D numerical
simulations. Using the scaling laws, I am then able to make predictions for the
equilibrium ice thickness variation knowing that the ice shell should be close
to heat balance. Ice shell on small icy moons (e.g., Enceladus) may develop
strong thickness variations between the equator and pole driven by the
polar-amplified tidal dissipation in the ice, to the contrary, ice shell on
large icy moons (e.g., Europa, Ganymede, Callisto etc.) tends to be flat due to
the smoothing effects of the efficient OHT. These predictions are manifested by
the different ice evolution pathways simulated for Enceladus and Europa,
considering the ice freezing/melting induced by ice dissipation, conductive
heat loss and OHT as well as the mass redistribution by ice flow.
