Capillary-Gravity Waves on Depth-Dependent Currents: Consequences for   the Wave Resistance
  We study theoretically the capillary-gravity waves created at the water-air interface by a small two-dimensional perturbation when a depth-dependent current is initially present in the fluid. Assuming linear wave theory, we derive a general expression of the wave resistance experienced by the perturbation as a function of the current profile in the case of an inviscid fluid. We then analyze and discuss in details the behavior of the wave resistance in the particular case of a linear current, a valid approximation for some wind generated currents. 
Michael Benzaquen and Elie Raphael
cond-mat.soft physics.flu-dyn