  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. 
Energetic constraints on ocean circulations of icy ocean worlds