We study theoretically the capillary-gravity waves created at the water-air interface by a small two-dimensional perturbation in the frequently encountered case where a depth-dependent current is 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 illustrate the use of this expression in the case of constant vorticity. Copyright (C) EPLA, 2012
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