Explicit wave-averaged primitive equations using a Generalized Lagrangian Mean

Fabrice Ardhuin (1) , Nicolas Rascle (1, 2) , Kostas Belibassakis (2)

1 CMO - Centre Militaire d'Océanographie
2 Department of Naval Architecture and Marine Engineering [Athens]

The generalized Langrangian mean theory provides exact but implicit GLM equations for general wave-turbulence-mean flow interactions in three dimensions. For practical applications, explicit but approximate glm2-RANS equations for the mean pressure and horizontal momentum are derived from the exact GLM equations. The approximation 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. The glm2-RANS equations are further transformed to yield a non-divergent mass transport in cartesian coordinates. To lowest order, agreement is found with Eulerian-mean theories, and the present work provides an extension of known wave-averaged equations to vertically varying currents or finite current values. The accuracy of the approximations is discussed using comparisons with exact numerical solutions for arbitrary bottom slopes, and an approximate finite amplitude wave theory. These suggest 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.

Mots clés: radiation stresses; waves; GLM

Domaines: Physique Atmosphérique et Océanique [physics.ao-ph]

Fabrice Ardhuin, Nicolas Rascle, Kostas Belibassakis. Explicit wave-averaged primitive equations using a Generalized Lagrangian Mean. 2007. ⟨hal-00129588v1⟩