Nicolas Rascle | Searcharxiv

arXiv2009

Observation and estimation of Lagrangian, Stokes and Eulerian currents induced by wind and waves at the sea surface

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. The measured currents, with tides filtered out, 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. 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 a part of the wave-induced Stokes drift Uss at the sea surface. Here Uss 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 estimated contribution of Uss to the radar measurement has a 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 elatively weak quasi-Eulerian current with a large deflection angle is interpreted as evidence of strong near-surface mixing, likely related to breaking waves.

physics.ao-ph↗

arXiv2007

Explicit wave-averaged primitive equations using a Generalized Lagrangian Mean

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.

physics.ao-ph↗