Open AccessComments on “The Three-Dimensional Current and Surface Wave Equations”
Author(s) -
Fabrice Ardhuin,
Alastair D. Jenkins,
Kostas Belibassakis
Publication year - 2008
Publication title -
journal of physical oceanography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.706
H-Index - 143
eISSN - 1520-0485
pISSN - 0022-3670
DOI - 10.1175/2007jpo3670.1
Subject(s) - forcing (mathematics) , momentum (technical analysis) , physics , flow (mathematics) , coordinate system , airy wave theory , mean flow , classical mechanics , flux (metallurgy) , mechanics , stokes wave , transformation (genetics) , mathematical analysis , wave propagation , mathematics , breaking wave , turbulence , geometry , optics , materials science , finance , economics , metallurgy , biochemistry , chemistry , gene
The lowest order sigma-transformed momentum equation given by Mellor takes into account a phase-averaged 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 slope. 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.