Surface Wave-Aerodynamic Roughness Length Model for Air-Sea Interactions

Abstract: A recently introduced model to evaluate the equivalent hydrodynamic length scale $z_0$ for turbulent flow over static rough surfaces is reformulated and extended to enable evaluation of $z_0$ for moving surface waves. The proposed Surface Wave-Aerodynamic Roughness Length model is based on maps of the surface height and its vertical speed as function of position, and Reynolds number. Pressure drag is estimated by approximating the local flow as ideal inviscid ramp flow (Ayala et al., 2024). Wave history effects are included through dependence on the local velocity difference between the air and wave speed. The model is applied to monochromatic and multiscale surfaces, and the predicted surface roughness length scales are compared to measured values and to commonly used wave parametrization methods found in the literature. The proposed model shows significantly improved agreement with data compared to other models.