Observation and Estimation of Lagrangian, Stokes, and Eulerian Currents Induced by Wind and Waves at the Sea Surface

Abstract

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.

HF Radar Activity in European Coastal Seas: Next Steps toward a Pan-European HF Radar Network

“…Bragg scattering is also responsible for the second order bands in the radar spectrum but here the scatter is from non-linear ocean waves which propagate at different speeds and hence results in a different Doppler shifts and also from multiple scattering. The surface current estimated by HFRs has been suggested to include the entire, or parts of, the wave-induced Stokes drift Law, 2001;Ardhuin et al, 2009), while other authors provide evidences against this assumption . In any case the magnitude of this component is expected to be typically smaller than the uncertainties contained in the observation of the Eulerian currents by HFRs (Ardhuin et al, 2009;Röhrs et al, 2015).…”

“…Indeed, the spatial and temporal scales measured with HFR are not the same that those of point-wise acoustic Doppler current profilers or drifters, so it can be expected that vertical or horizontal shear in currents contribute also to the RMSDs observed between measurements. The differences between HFRs and fixed current profilers might be also affected by the contribution of the Stokes drift (Ardhuin et al, 2009), which will not be measured by the later. This can explain the significant scatter found in the literature concerning point to point comparison between HFR and other in situ measurements.…”

Ocean forecasting for the German Bight: from regional to coastal scales

“…The Stokes drift components are subtracted from the wave processes to transfer the problem to the Eulerian framework. Moghimi et al (2013) studied the effects of two approaches (radiation stress, Mellor, 2011; and vortex force, Ardhuin et al, 2008) using GETM-SWAM coupled models and showed that the results for the longshore-directed transport are similar for both formulations. Recently, Aiki and Greatbatch (2013) showed that radiation stress parameterization is applicable for small bottom slopes.…”

Effects of waves on coastal water dispersion in a small estuarine bay

“…s aw and s wo are computed from spectral wave energy source terms S in and S oc , respectively (introduced in paragraph 3.2. ), according to Ardhuin et al [2009Ardhuin et al [ , 2010.…”