  Refraction of a Longuet-Higgins Gaussian sea by random ocean currents creates
persistent local variations in average energy and wave action. These variations
take the form of lumps or streaks, and they explicitly survive dispersion over
wavelength and incoming wave propagation direction. Thus, the uniform sampling
assumed in the venerable Longuet-Higgins theory does not apply following
refraction by random currents. Proper handling of the non-uniform sampling
results in greatly increased probability of freak wave formation. The present
theory represents a synthesis of Longuet-Higgins Gaussian seas and the
refraction model of White and Fornberg, which considered the effect of currents
on a plane wave incident seaway. Using the linearized equations for deep ocean
waves, we obtain quantitative predictions for the increased probability of
freak wave formation when the refractive effects are taken into account. The
crest height or wave height distribution depends primarily on the ``freak
index", gamma, which measures the strength of refraction relative to the
angular spread of the incoming sea. Dramatic effects are obtained in the tail
of this distribution even for the modest values of the freak index that are
expected to occur commonly in nature. Extensive comparisons are made between
the analytical description and numerical simulations.
