SPECTRAL WAVE ATTENUATION BY BOTTOM FRICTION: THEORY
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Keywords

bottom friction
friction theory
wave attenuation
spectral wave

How to Cite

Madsen, O. S., Poon, Y.-K., & Graber, H. C. (1988). SPECTRAL WAVE ATTENUATION BY BOTTOM FRICTION: THEORY. Coastal Engineering Proceedings, 1(21), 34. https://doi.org/10.9753/icce.v21.34

Abstract

Based on the linearized form of the boundary layer equations and a simple eddy viscosity formulation of shear stress, the turbulent bottom boundary layer flow is obtained for a wave motion specified by its directional spectrum. Closure is obtained by requiring the solution to reduce, in the limit, to that of a simple harmonic wave. The resulting dissipation is obtained in spectral form with a single friction factor determined from knowledge of the bottom roughness and an equivalent monochromatic wave having the same root-mean-square near-bottom orbital velocity and excursion amplitude as the specified wave spectrum. The total spectral dissipation rate is obtained by integration and compared with the average dissipation obtained from a model considering the statistics of individual waves defined by their maximum orbital velocity and zero-crossing period. The agreement between the two different evaluations of total spectral dissipation supports the validity of the spectral dissipation model.
https://doi.org/10.9753/icce.v21.34
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