Interaction between incident and reflected mechanical waves in the presence of an opposing wind

The interaction between wind and waves largely determines exchanges of mass, momentum, energy, and substances which take place at the air-sea interface. Usually, the parameterization of such interaction considers only the case of progressive waves. However, reflection is practically ubiquitous in the field, especially in coastal areas, and in the lab. Recent experimental studies have extensively treated this subject, showing that even a small amount of wave reflection can significantly modify the free surface elevation and the velocity field on the water side. Nonetheless, a theoretical framework for an exhaustive description of the wave reflection role is still lacking. In this work, an analytical model is developed to emphasize the role of reflection in terms of incident-reflected waves interaction in the 2D momentum equations. A non-null interaction between the incident and the reflected waves is predicted for partially-reflected monochromatic waves, and it is represented by a reflection-induced stress tensor. A phase shift is found among the total wave height, the velocity and the shear stress, with implications on the partition of the wave velocity and stresses. Then, the incident, reflected, and total components of the velocity and of the stresses along the regular wave phase are compared with a set of laboratory experiments, where monochromatic waves in condition of partial reflection are ruffled by an opposing wind. The overlap between experiments and theory is remarkably good, thus validating the entire procedure and assumptions. From the experiments, the fluctuating shear stress and kinetic energy are also extracted for different reflection conditions of the mechanical wave, showing a peak of both quantities near the wave trough (close to the surface). Overall, the experimental analysis gives insights into the velocity, momentum and energy fluxes along the wave phase, based on velocity measurements at one fetch length.