### SPECTRAL WAVE-CURRENT BOTTOM BOUNDARY LAYER FLOWS

#### Abstract

Based on the linearized governing equations, a bottom roughness specified by the equivalent Nikuradse sand grain roughness, fcjv, and a timeinvariant eddy viscosity analogous to that of Grant and Madsen (1979 and 1986) the solution is obtained for combined wave-current turbulent bottom boundary layer flows with the wave motion specified by its near-bottom orbital velocity directional spectrum. The solution depends on an a priori unknown shear velocity, u*r, used to scale the eddy viscosity inside the wave boundary layer. Closure is achieved by requiring the spectral wavecurrent model to reduce to the Grant-Madsen model in the limit of simple periodic plane waves. To facilitate application of the spectral wave-current model it is used to define the characteristics (near-bottom orbital velocity amplitude, U(,r, radian frequency, uir, and direction of propagation, 4>wr) of a representative periodic wave which, in the context of combined wavecurrent bottom boundary layer flows, is equivalent to the wave specified by its directional spectrum. Pertinent formulas needed for application of the model are derived and their use is illustrated by outlining efficient computational procedures for the solution of wave-current interaction for typical specifications of the current

#### Keywords

boundary layer; spectral wave; bottom boundary layer; bottom flow

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