Vertical profiles of the wave-coherent airflow over ocean waves
Amplitude and phase of the wave-induced components of the wind relative to the waves for various wind-wave conditions at each height were computed spectrally. Results show that the wave-induced fluctuations depend on both the critical height zc and the normalized height kz. The critical height zc is defined as the height where the mean wind speed U(zc) equals the phase speed of the waves c. The normalized height kz is the height of the anemometers z normalized by the wavenumber k of the waves with k = g/c2.
In the neighborhood of the critical height, results are qualitatively consistent with the critical layer theory of Miles (1957). Across the critical height, the wave-induced vertical and horizontal velocities change significantly in both amplitude and phase. Below the critical layers, a suitable normalization of the wave-induced fluctuations collapses the data from all the anemometers, on a curve which follows an exponential decay with the normalized height kz.
Miles J. W. (1957). On the generation of surface waves by shear flows. J. Fluid. Mech., Vol 3, 185-204.
Sullivan et al. (2014). Large eddy simulation of marine atmospheric boundary layers above a spectrum of moving waves. J. Atmos. Sci., Advance online publication. doi: 10.1175/JAS-D-14-0095.1