  An approximate dispersion relation is derived and presented for linear
surface waves atop a shear current whose magnitude and direction can vary
arbitrarily with depth. The approximation, derived to first order of deviation
from potential flow, is shown to produce good approximations at all wavelengths
for a wide range of naturally occuring shear flows as well as widely used model
flows. The relation reduces in many cases to a 3D generalization of the much
used approximation by Skop [1987], developed further by Kirby & Chen [1989],
but is shown to be more robust, succeeding in situations where the Kirby & Chen
model fails. The two approximations incur the same numerical cost and
difficulty.
  While the Kirby & Chen approximation is excellent for a wide range of
currents, the exact criteria for its applicability have not been known. We
explain the apparently serendipitous success of the latter and derive proper
conditions of applicability for both approximate dispersion relations. Our new
model has a greater range of applicability.
  A second order approximation is also derived. It greatly improves accuracy,
which is shown to be important in difficult cases. It has an advantage over the
corresponding 2nd order expression proposed by Kirby \& Chen that its criterion
of accuracy is explicitly known, which is not currently the case for the latter
to our knowledge. Our 2nd order term is also arguably significantly simpler to
implement, and more physically transparent, than its sibling due to Kirby &
Chen.
