The Reynolds wave shear stress in partially reflected waves

Wind--waves play a relevant role in the downward flux of mass, momentum and heat, {and in their balances.} {Thus, they} are quite significant in {small- and large-scale processes like} global warming{,} especially in continental shelf. There is still no consensus on the effectiveness of different mechanisms in enhancing, e.g., the carbon dioxide ($\mathrm{CO}_2$) uptake in the continental shelves with respect to the open ocean {. To} our best knowledge, the role of partial reflections of short and long waves in the budget has been largely neglected {without a specific justification, even though reflection in water waves is a recurring phenomenon}. Presumably, this is a consequence of the difficulties in performing experiments with variable reflection coefficient and phase shift of the {waves approaching coastal} structures. We report experiments on the vertical momentum transfer in partially reflecting waves propagating on a flat horizontal bottom{. We measured the free surface level and the fluid velocity, and estimated} the Reynolds wave{--generated} shear stress. A set of experiments using paddle waves or a paddle plus wind waves and a reflection coefficient ranging from $0.10-0.75$, with a phase shift of $\pi/4-\pi$ rad, confirm{s} the theoretical model. The results indicate that reflection must be carefully considered in the correct interpretation of data, particularly when considering momentum transfer in the vertical. The new contributions in the paper are (i) the adoption of a generation--absorption system that controls the reflection coefficient and phase {shift between incident and reflected waves}; (ii) the quantification of the {phase shift} influence on the vertical momentum transfer and its horizontal variability; (iii) the consequences for locally{--}generated wind{--}waves and wind generated surface currents. To our knowledge, these are the first experiments where the characteristics of the reflected waves have been imposed, allowing a thoroughly analysis of their effects on the flow field.