Fig. 4: Mean wave-coherent airflow velocities.

Horizontal (\(\tilde{u}\)) and vertical (\(\tilde{w}\)) velocity components are shown. Slow waves (a, b) and fast waves (c, d) induce broadly differing patterns in the airflow. The phase-averaged water surface elevation is shown below the velocity fields (gray shading) for the slow waves, and in (e) and (f) for the fast waves. The gray dashed line represents the height L_i of the ''inner region'', which satisfies kL_i(U(L_i) − c) = 2κu_*, where κ is the von Karman constant, c the peak phase speed of the waves, k the wavenumber, and U(z) the mean wind velocity profile (Belcher and Hunt⁸ (their equation 26, see also Grare et al.¹⁰, Buckley and Veron³¹).