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A simple model of wave–current interaction

Published online by Cambridge University Press:  23 June 2015

Nicoletta Tambroni ,
Paolo Blondeaux  and
Giovanna Vittori
Nicoletta Tambroni
Affiliation:
Department of Civil, Chemical and Environmental Engineering, University of Genoa, Via Montallegro 1, 16145 Genova, Italy
Paolo Blondeaux*
Affiliation:
Department of Civil, Chemical and Environmental Engineering, University of Genoa, Via Montallegro 1, 16145 Genova, Italy
Giovanna Vittori
Affiliation:
Department of Civil, Chemical and Environmental Engineering, University of Genoa, Via Montallegro 1, 16145 Genova, Italy
*
†Email address for correspondence: blx@dicat.unige.it
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Abstract

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.

JFM classification

Geophysical and Geological Flows: Coastal engineering Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 775 , 25 July 2015 , pp. 328 - 348
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Copyright
© 2015 Cambridge University Press 

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