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While it has long been recognized that Lagrangian drift at the ocean surface plays a critical role in the kinematics and dynamics of upper ocean processes, only recently has the contribution of wave breaking to this drift begun to be investigated through direct numerical simulations (Deike et al. ,  J. Fluid Mech. , vol. 829, 2017, pp. 364–391; Pizzo et al. ,  J. Phys. Oceanogr. , vol. 49(4), 2019, pp. 983–992). In this work, laboratory measurements of the surface Lagrangian transport due to focusing deep-water non-breaking and breaking waves are presented. It is found that wave breaking greatly enhances mass transport, compared to non-breaking focusing wave packets. These results are in agreement with the direct numerical simulations of Deike  et al. ( J. Fluid Mech. , vol. 829, 2017, pp. 364–391), and the increased transport due to breaking agrees with their scaling argument. In particular, the transport at the surface scales with $$S$$ , the linear prediction of the maximum slope at focusing, while the surface transport due to non-breaking waves scales with $$S^{2}$$ , in agreement with the classical Stokes prediction. 

As reported in 1954, more than a half century ago, C. Cox and W. Munk developed an empirical model of the slope distribution of ocean surface waves that has been widely used ever since to model the optical properties of the sea surface and is of particular importance to the satellite remote sensing community. In that work, the reflectance of sunlight was photographed from a Boeing B-17G bomber and was then analyzed. In this paper, surface slope statistics are investigated from airborne scanning topographic lidar data collected during a series of field experiments off the coast of California and in the Gulf of Mexico, over a broad range of environmental conditions, with wind speeds ranging from approximately 2 to 13 m s −1 . Unlike the reflectance-based approach of Cox and Munk, the slope distribution is computed by counting laser glints produced by specular reflections as the lidar is scanned over the surface of the ocean. We find good agreement with their measurements for the mean-square slope and with more recent (2006) results from Bréon and Henriot that were based on satellite remote sensing. Significant discrepancies for the higher-order statistics are found and discussed. We also demonstrate here that airborne scanning lidar technology offers a viable means of remotely estimating surface wind speed and momentum flux. 

An analysis of coherent measurements of winds and waves from data collected during the ONR Southern California 2013 (SoCal2013) program from R/P FLIP off the coast of Southern California in November 2013 is presented. An array of ultrasonic anemometers mounted on a telescopic mast was deployed to resolve the vertical profile of the modulation of the marine atmospheric boundary layer by the waves. Spectral analysis of the data provides the wave-induced components of the wind velocity for various wind-wave conditions. Results show that the wave-induced fluctuations depend both on the spectral wave age [Formula: see text] and the normalized height [Formula: see text], where c is the linear phase speed of the waves with wavenumber k and [Formula: see text] is the mean wind speed measured at the height z. The dependence on the spectral wave age expresses the sensitivity of the wave-induced airflow to the critical layer where [Formula: see text]. Across the critical layer, there is a significant change of both the amplitude and phase of the wave-induced fluctuations. Below the critical layer, the phase remains constant while the amplitude decays exponentially depending on the normalized height. Accounting for this double dependency, the nondimensionalization of the amplitude of the wave-induced fluctuations by the surface orbital velocity [Formula: see text] collapses all the data measured by the array of sonic anemometers, where a is the amplitude of the waves. 

Using direct numerical simulations (DNS), Deike et al. found that the wave-breaking-induced mass transport, or drift, at the surface for a single breaking wave scales linearly with the slope of a focusing wave packet, and may be up to an order of magnitude larger than the prediction of the classical Stokes drift. This model for the drift due to an individual breaking wave, together with the statistics of wave breaking measured in the field, are used to compute the Lagrangian drift of breaking waves in the ocean. It is found that breaking may contribute up to an additional 30% to the predicted values of the classical Stokes drift of the wave field for the field experiments considered here, which have wind speeds ranging from 1.6 to 16 m s⁻¹, significant wave heights in the range of 0.7–4.7 m, and wave ages (defined here as c_m/ u_*, for the spectrally weighted phase velocity c_mand the wind friction velocity u_*) ranging from 16 to 150. The drift induced by wave breaking becomes increasingly more important with increasing wind friction velocity and increasing significant wave height.