Dimensionally Consistent Similarity Relation of Ocean Surface Friction Coefficient in Mixed Seas*

Applying wavelength scaling, dimensionally consistent expressions of the ocean surface friction coefficient can be developed for both wind sea and mixed sea in the ocean. For a wind sea with a monopeak wave spectrum, the natural choice of the scaling wavelength is that of the spectral peak component. For a mixed sea with a multipeak spectrum, the peak component in the wind sea portion of the wave spectrum is not a good reference wavelength. A much better scaling wavelength is the weighted average of swell and wind sea following the consideration of equivalent momentum in the wave field. The resulting friction coefficient Cλ/2 is referenced to the wind speed at one-half of the scaling wavelength Uλ/2 instead of C10 referenced to the neutral wind speed at 10-m elevation U10. Although referencing the wind speed at a fixed elevation such as U10 is of practical necessity, Uλ/2 is physically significant as the free-stream velocity in wave-modulated boundary layer flows. A simple procedure to apply the similarity relation of Cλ/2 to obtain C10 is described.