Wavelength scaling of the drag coefficient and dynamic roughness of the ocean surface

Paul A. Hwang

Oceanography Division, Naval Research Laboratory, Stennis Space Center, MS, 39529 U.S.A.      Surface waves are the roughness element of the ocean surface. The parameterization of the drag coefficient of the ocean surface is simplified by adopting the reference wind speed at an elevation proportional to the characteristic wavelength (for example, U_l/2, where l is the wavelength at the spectral peak). The dynamic roughness is analytically related to the drag coefficient through the wind profile function. Drag coefficient computed with U_l/2 is fundamentally different from the drag coefficient computed with the wind speed at fixed 10 m elevation (U₁₀). A comparison is carried out to quantify the difference in wind stress computation using several different parameterization functions of the drag coefficient. The result indicates that the wind stress computed from U₁₀ input using a drag coefficient referenced to U_l/2 is more accurate than that computed with drag coefficient functions referenced to U₁₀. The main independent dimensionless variable of the drag coefficient based on wavelength scaling is the dimensionless frequency of the wave field, which is the inverse wave age in the deep water wave condition. As a consequence of the continuous downshifting of the characteristic wave frequency in a developing sea under steady wind forcing of a constant wind speed, the wind stress input from the atmosphere to the ocean is temporally and spatially (if fetch-limited) varying. The temporal and spatial variation of the wind stress can be quantified by applying the similarity laws of the duration and fetch growth of wind waves and the wavelength scaling of the ocean surface drag coefficient. Numerical computations show that the wind stress input in the first few hours is much larger (about 50 to 100 percent higher) than that at later hours when the wave field reaches a more mature stage.   [NRL/AB/7330--05-xxxx. Abstract prepared for 15th Conf. Atm. Ocean. Fluid Dyna. Cambridge, MA 13-17 June 2005.]