Thomas, T.G. and Takhar, H.S.
Turbulent mass-transport and attenuation in Stokes waves
Applied Scientific Research, 49, (1), . (doi:10.1007/BF00382740).
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The motion of turbulent Stokes waves on a finite constant depth fluid with a rough bed is considered. First and second order turbulent boundary layer equations are solved numerically for a range of roughness parameters, and from the solutions are calculated the mass transport velocity profiles and attenuation coefficients. A new mechanism of turbulent mass transport is found which predicts a reduction and reversal of drift velocity in shallow water in agreement with experimental observations under turbulent conditions. This transpires because the second order Stokes wave motion, in a turbulent boundary layer, can directly influence the mass transport velocity by mode coupling interactions between different second order Fourier modes of oscillation. It is also found that the Euler contribution due to the radiation stress of the first order motion is reduced to half of it's corresponding laminar value as a consequence of the velocity squared stress law. The attenuation is found to be of inverse algebraic type with the reciprocal wave height varying linearly with either distance or time. The severe wave height restriction applicable to the Longuet-Higgins  solution is shown not to apply to progressive waves on a finite constant depth of fluid. The existence of sand bars on sloping beaches exposed to turbulent waves is predicted.
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