  We numerically calculate the growth and saturation of the Rayleigh-Taylor
instability caused by the deceleration of relativistic outflows with Lorentz
factor {\Gamma} = 10, 30, and 100. The instability generates turbulence whose
scale exhibits strong dependence on Lorentz factor, as only modes with angular
size smaller than 1/{\Gamma} can grow. We develop a simple diagnostic to
measure the kinetic energy in turbulent fluctuations, and calculate a ratio of
turbulent kinetic energy to thermal energy of .03 in the region affected by the
instability. Although our numerical calculation does not include magnetic
fields, we argue that small scale turbulent dynamo amplifies magnetic fields to
nearly this same fraction, giving a ratio of magnetic to thermal energy of ~
.01, to within a factor of two. The instability completely disrupts the contact
discontinuity between the ejecta and the swept up circumburst medium. The
reverse shock is stable, but is impacted by the Rayleigh-Taylor instability,
which strengthens the reverse shock and pushes it away from the forward shock.
The forward shock front is unaffected by the instability, but Rayleigh-Taylor
fingers can penetrate of order 10% of the way into the energetic region behind
the shock during the two-shock phase of the explosion. We calculate afterglow
emission from the explosion and find the reverse shock emission peaks at a
later time due to its reduced Lorentz factor and modified density and pressure
at the shock front. These calculations are performed using a novel numerical
technique that includes a moving computational grid. The moving grid is
essential as it maintains contact discontinuities to high precision and can
easily evolve flows with extremely large Lorentz factors.
