Physics – Classical Physics
Scientific paper
2005-04-14
Physics
Classical Physics
Submitted to Journal Physical Oceanography, August 2006. Revised, March 2007. Please note that the first version of this docum
Scientific paper
The lowest order sigma-transformed momentum equation given by Mellor (J. Phys. Oceangr. 2003) takes into account a phase-averaged wave forcing based on Airy wave theory. This equation is shown to be generally inconsistent due to 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 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.
Ardhuin Fabrice
Belibassakis Kostas
Jenkins Alastair D.
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