a b s t r a c tA multi-scale global hindcast of ocean waves is presented that covers the years 1994-2012, based on recently published parameterizations for wind sea and swell dissipation [, Aouf, L., Collard, F., 2010. Semi-empirical dissipation source functions for wind-wave models: Part I. Definition, calibration and validation. J. Phys. Oceanogr. 40 (9), 1917Oceanogr. 40 (9), -1941. Results from this hindcast include traditional wave parameters, like the significant wave height and mean periods, and we particularly consider the accuracy of the results for phenomenal sea states, with significant heights above 14 m. Using unbiased winds, there is no evidence of a bias in wave heights even for this very high range. Various spectral moments were also validated, including the surface Stokes drift and mean square slopes that are relevant for wave-current interactions modelling and remote sensing, and also spectra of seismic noise sources. The estimation of these parameters is made more accurate by the new wave growth and dissipation parameterizations. Associated air-sea fluxes of momentum and energy are significantly different from what is obtained with the WAM-Cycle 4 parameterization, with a roughness that is practically a function of wind speed only. That particular output of the model does not appear very realistic and will require future adjustments of the generation and dissipation parameterizations.

The surface current response to winds is analyzed in a two-year time series of a 12 MHz (HF) Wellen Radar (WERA) off the West coast of France. Consistent with previous observations, the measured currents, after filtering tides, are of the order of 1.0 to 1.8% of the wind speed, in a direction 10 to 40 degrees to the right of the wind, with systematic trends as a function of wind speed. This Lagrangian current can be decomposed as the vector sum of a quasi-Eulerian current U E , representative of the top 1 m of the water column, and part of the wave-induced Stokes drift U ss at the sea surface. Here U ss is estimated with an accurate numerical wave model, thanks to a novel parameterization of wave dissipation processes. Using both observed and modelled wave spectra, Uss is found to be very well approximated by a simple function of the wind speed and significant wave height, generally increasing quadratically with the wind speed. Focusing on a site located 100 km from the mainland, the wave induced contribution of Uss to the radar measurement has an estimated magnitude of 0.6 to 1.3% of the wind speed, in the wind direction, a fraction that increases with wind speed. The difference U E of Lagrangian and Stokes contributions is found to be of the order of 0.4 to 0.8% of the wind speed, and 45 to 70 degrees to the right of the wind. This relatively weak quasi-Eulerian current with a large deflection angle is interpreted as evidence of strong near-surface mixing, likely related to breaking waves and/or Langmuir circulations. Summer stratification tends to increase the UE response by up to a factor 2, and further increases the deflection angle of U E by 5 to 10 degrees. At locations closer to coast, Uss is smaller, and UE is larger with a smaller deflection angle. These results would be transposable to the world ocean if the relative part of geostrophic currents in U E were weak, which is expected. This decomposition into Stokes drift and quasi-Eulerian current is most important for the estimation of energy fluxes to the Ekman layer.

Morrow et al. SWOT Fine-Scale Global Ocean Topography This presents both a challenge in reconstructing the 4D upper ocean circulation, or in the assimilation of SSH in models, but also an opportunity to have global observations of the 2D structure of these phenomena, and to learn more about their interactions. At these small scales, ocean dynamics evolve rapidly, and combining SWOT 2D SSH data with other satellite or in situ data with different space-time coverage is also a challenge. SWOT's new technology will be a forerunner for the future altimetric observing system, and so advancing on these issues today will pave the way for our future.

The generalized Langrangian mean theory provides exact equations for general wave-turbulence-mean flow interactions in three dimensions. For practical applications, these equations must be closed by specifying the wave forcing terms. Here an approximate closure is obtained under the hypotheses of small surface slope, weak horizontal gradients of the water depth and mean current, and weak curvature of the mean current profile. These assumptions yield analytical expressions for the mean momentum and pressure forcing terms that can be expressed in terms of the wave spectrum. A vertical change of coordinate is then applied to obtain glm2z-RANS equations (55) and (57) with non-divergent mass transport in cartesian coordinates. To lowest order, agreement is found with Eulerian-mean theories, and the present approximation provides an explicit extension of known wave-averaged equations to short-scale variations of the wave field, and vertically varying currents only limited to weak or localized profile curvatures. Further, the underlying exact equations provide a natural framework for extensions to finite wave amplitudes and any realistic situation. The accuracy of the approximations is discussed using comparisons with exact numerical solutions for linear waves over arbitrary bottom slopes, for which the equations are still exact when properly accounting for partial standing waves. For finite amplitude waves it is found that the approximate solutions are probably accurate for ocean mixed layer modelling and shoaling waves, provided that an adequate turbulent closure is designed. However, for surf zone applications the approximations are expected to give only qualitative results due to the large influence of wave nonlinearity on the vertical profiles of wave forcing terms.