The generalized Lagrangian mean (GLM) formulation is used to describe
the interaction
of waves and currents. In contrast to the more conventional Eulerian formulation
the GLM description enables splitting of the mean and oscillating motion
over the
whole depth in an unambiguous and unique way, also in the region between
wave crest
and trough. The present paper deals with non-breaking long-crested regular
waves on
a current using the GLM formulation coupled with a WKBJ-type perturbation-series
approach. The waves propagate under an arbitrary angle with the current
direction.
The primary interest concerns nonlinear changes in the vertical distribution
of
the mean velocity due to the presence of the waves, but modifications of
the orbital
velocity profiles, due to the presence of a current, are considered as
well. The special
case of no initial current, where waves induce a so-called drift velocity
or
mass-transport velocity, is also studied.