A new evaluation of the wind stress coefficient over water surfaces

Abstract

An analysis of data from numerous investigators, as well as information obtained directly by the authors, indicates that a large portion of the difficulties encountered in the past in establishing a relationship between the wind stress coefficient C 10 and the wind velocity U 10 can be attributed to computationally induced scatter of the data points. However, plots of the shear velocity u * against U 10 reveal clear trends which show that three regions exist in the development of the wind shear stress: (1) a lower region in which the wind waves have not begun to break, and for which C 10 is approximately constant; (2) a transitional region, after the onset of breakers, for which C 10 varies nonlinearly with U 10 and (3) a limiting region for which C 10 tends again toward a constant value, and corresponds to a condition of breaker saturation. A single general equation to express C 10 as a function of U 10 is proposed, which agrees with the above findings. It is shown that in contrast with the perception of previous investigators, Charnock's coefficient α = z 0 g / u * 2 , where z 0 is the roughness length and g is the acceleration due to gravity, is not constant anywhere in the range of wind velocities 0 < U 10 < 40 m/s. Finally, the data indicate that the wind flow boundary in each one of the three regions described above can be classified as having ‘low roughness,’ ‘transitional,’ and ‘high roughness,’ respectively.