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We study theoretically the capillary-gravity waves created at the water-airinterface by a small two-dimensional perturbation when a depth-dependentcurrent is initially present in the fluid. Assuming linear wave theory, wederive a general expression of the wave resistance experienced by theperturbation as a function of the current profile in the case of an inviscidfluid. We then analyze and discuss in details the behavior of the waveresistance in the particular case of a linear current, a valid approximationfor some wind generated currents.

Capillary-Gravity Waves on Depth-Dependent Currents: Consequences for the Wave Resistance