Effective Roughness Length for Turbulent Flow over a Wavy Surface

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Abstract
A two-equation turbulence model is used to calculate the effective roughness length for two-dimensional turbulent flow over small amplitude, wavy surface topography. The governing equations are solved using the method of matched asymptotic expansions for the case ϵ ≪ 1, δ ≪ 1, where ϵ is the square root of a characteristic drag coefficient for flow over a plane surface and δ is the wave slope. Analytical expressions are derived for the effective roughness length and drag coefficient for flow over stationary topography and over a progressive wave. The results are used to determine the drag coefficient and the form drag for flow over a progressive water wave, and are found to be consistent with observations.

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