Commentary on `The Three-Dimensional Current and Surface Wave Equations' by George Mellor

Fabrice Ardhuin (1) , Alastair Jenkins (2) , Kostas Belibassakis (3)

1 HOM - Division Hydrographie Océanographie et Météorologie Militaire
2 BCCR - Bjerknes Centre for Climate Research
3 Department of Naval Architecture and Marine Engineering [Athens]

The lowest order sigma-transformed momentum equation that takes into account a phase-averaged wave forcing based on Airy wave theory is shown to be generally inconsistent due to inadequate approximations in the vertical fluxes of wave momentum. The expression of these fluxes is required to first order in parameters that define the large scale evolution of the wave field, such as the bottom slope. Unfortunately there is no analytical expression for these fluxes, except for fluxes associated with wind-wave generation. Alternative coordinate transforms that allow a separation of wave and mean flow momenta do not suffer from this inconsistency, because the problematic vertical fluxes are part of the wave momentum flux, and are not directly relevant to the mean flow evolution.

Mots clés: surface gravity waves; radiation stresses

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Fabrice Ardhuin, Alastair Jenkins, Kostas Belibassakis. Commentary on `The Three-Dimensional Current and Surface Wave Equations' by George Mellor. 2007. ⟨hal-00004696v3⟩