The interaction between a steady current and propagating surface waves is investigated
by means of a perturbation approach, which assumes small values of the wave
steepness and considers current velocities of the same order of magnitude as the
amplitude of the velocity oscillations induced by wave propagation. The problems,
which are obtained at the different orders of approximation, are characterized by a
further parameter which is the ratio between the thickness of the bottom boundary
layer and the length of the waves and turns out to be even smaller than the wave
steepness. However, the solution is determined from the bottom up to the free
surface, without the need to split the fluid domain into a core region and viscous
boundary layers. Moreover, the procedure, which is employed to solve the problems
at the different orders of approximation, reduces them to one-dimensional problems.
Therefore, the solution for arbitrary angles between the direction of the steady
current and that of wave propagation can be easily obtained. The theoretical results
are compared with experimental measurements; the fair agreement found between the
model results and the laboratory measurements supports the model findings
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