Comments on "The Three-Dimensional Current and Surface Wave Equations"

Fabrice Ardhuin, Alastair D. Jenkins, Konstadinos A. Belibassakis
2008 Journal of Physical Oceanography  
The lowest order sigma-transformed momentum equation given by Mellor takes into account a phaseaveraged wave forcing based on Airy wave theory. This equation is shown to be generally inconsistent because of inadequate approximations of the wave motion. Indeed the evaluation of the vertical flux of momentum requires an estimation of the pressure p and coordinate transformation function s to first order in parameters that define the large-scale evolution of the wave field, such as the bottom
more » ... . Unfortunately, there is no analytical expression for p and s at that order. A numerical correction method is thus proposed and verified. Alternative coordinate transforms that allow a separation of wave and mean flow momenta do not suffer from this inconsistency nor do they require a numerical estimation of the wave forcing. Indeed, the problematic vertical flux is part of the wave momentum flux, thus distinct from the mean flow momentum flux, and not directly relevant to the mean flow evolution. Corresponding author address: Fabrice Ardhuin, Centre Militaire d'Océanographie, Service Hydrographique et Océanographique de la Marine,
doi:10.1175/2007jpo3670.1 fatcat:oe2s3cfsojbptfdh2rtojkbjqu