A STREAM FUNCTION SOLUTION FOR WAVES ON A STRONGLY SHEARED CURRENT

Christopher Swan

Abstract


A perturbation analysis is presented in which a series of small amplitude progressive gravity waves interact with a strongly sheared current. The solution, which is extended to a second order of wave steepness, shows that if the time averaged vorticity distribution varies with depth the wave motion becomes rotational. An additional wave component, expressed in terms of the first harmonic, is identified at a second order of wave steepness. This does not arise within an irrotational solution and is quite distinct from the Doppler shift associated with the surface current. Explicit solutions are given for the dispersion equation and the wave induced kinematics. These are found to be very different from the existing irrotational solutions, and suggest that the non-linear wave-current interaction terms can become very important if the current profile is strongly sheared in the vicinity of the water surface. In such cases the underlying velocity field should not be predicted by an irrotational solution based upon an "equivalent" uniform current.

Keywords


sheared current; current; stream function

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