  Globally ice-covered oceans have been found on multiple moons in the solar
system and may also have been a feature of Earth's past. However, relatively
little is understood about the dynamics of these ice-covered oceans, which
affect not only the physical environment but also any potential life and its
detectability. A number of studies have simulated the circulation of icy-world
oceans, but have come to seemingly widely different conclusions. To better
understand and narrow down these diverging results, we discuss energetic
constraints for the circulation on ice-covered oceans, focusing in particular
on Snowball Earth, Europa, and Enceladus. Energy input that can drive ocean
circulation on ice-covered bodies can be associated with heat and salt fluxes
at the boundaries as well as ocean tides and librations. We show that heating
from the solid core balanced by heat loss through the ice sheet can drive an
ocean circulation, but the resulting flows would be relatively weak and
strongly affected by rotation. Salt fluxes associated with freezing and melting
at the ice sheet boundary are unlikely to energetically drive a circulation,
although they can shape the large-scale circulation when combined with
turbulent mixing. Ocean tides and librations may provide an energy source for
such turbulence, but the magnitude of this energy source remains highly
uncertain for the icy moons, which poses a major obstacle to predicting the
ocean dynamics of icy worlds and remains as an important topic for future
research.
