Explicit wave-averaged primitive equations using a generalized Lagrangian mean

By Fabrice Ardhuin, Nicolas Rascle, Kostas Belibassakis. 2007

193 citations recorded by the source corpus.

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.

Subfields: Atmospheric Science, Earth-Surface Processes, Oceanography

View Paper: https://www.semanticscholar.org/paper/55413103d6b5bd341784a51d33082a32c7f3e05b

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Citations in the corpus

A global wave parameter database for geophysical applications. Part 1: Wave-current turbulence interaction parameters for the open ocean based on traditional parameterizations (2008, background): “These include momentum fluxes in and out of the wave field to allow a modelling of the full wave-current coupling (Ardhuin et al., 2008), directional slope statistics for remote sensing studies, i.”
Wave-ice interactions in the marginal ice zone. Part 1: Theoretical foundations (2013, methodology): “Even without the complicating presence of sea ice, the question of how to couple ocean models to the wave field is not yet resolved (e.g. Babanin et al., 2009; Ardhuin et al., 2008).”
A global wave parameter database for geophysical applications. Part 2: Model validation with improved source term parameterization (2013, background): “(6) is a very good approximation of the waveinduced drift, even when finite amplitudes are considered, with the exception of waves in shallow water (Ardhuin et al., 2008).”
Wave-Current Interaction in an Oceanic Circulation Model with a Vortex-Force Formalism: Application to the Surf Zone (2010, unknown): “This can be viewed as mixing-length estimate, with the velocity scale based on the breaker dissipation rate and the length scale based on the local wave height H , modified by the vertical distribution function f(z) and with the depth factor D to retain the depth-average value of Battjes (1975). Apo”
Semiempirical Dissipation Source Functions for Ocean Waves. Part I: Definition, Calibration, and Validation (2009, background): “For example, waves that break are highly nonlinear and thus the effect of breaking waves that is contained in Soc is intrisically related to the non-linear evolution term contained in Snl.”