  It has been suggested that the ice shell of Jupiter's moon Europa may drift
non-synchronously due to tidal torques. Here we argue that torques applied by
the underlying ocean are also important and can result in non-synchronous
rotation (NSR). The resulting spin rate can be slightly slower than the
synchronous angular rate that would have kept the same point of the ice shell
facing Jupiter. We develop an ice shell rotation model, driven by ocean stress
calculated using a high-resolution state-of-the-art ocean general circulation
model, and take into account the viscoelastic deformation of the ice shell. We
use the ice shell model results together with observed limits on the ice shell
drift speed to constrain ice shell parameters such as effective viscosity,
which is currently uncertain by at least four orders of magnitude. Our results
suggest, at best, sluggish ice shell convection. Depending on the relaxation
time scale of the ice shell and on the ocean currents, the ice shell may
exhibit negligible drift, constant drift, or oscillatory drift superimposed on
random fluctuations. The expected rotation rate exceeds $\sim$30~m/yr; future
spacecraft observations can be used to test these predictions and yield insight
into the properties of the ice shell and underlying ocean.
