Comments on "A Combined Derivation of the Integrated and Vertically Resolved, Coupled Wave-Current Equations"
|Author(s)||Ardhuin Fabrice4, Suzuki Nobuhiro1, McWilliams James C.2, Aiki Hidenori3|
|Affiliation(s)||1 : Univ Brest, CNRS, IFREMER, IRD,Lab Oceanog Phys & Spatiale, Plouzane, France.
2 : Univ Calif Los Angeles, Dept Atmospher & Ocean Sci, Los Angeles, CA USA.
3 : Nagoya Univ, Inst Space Earth Environm Res, Nagoya, Aichi, Japan.
|Source||Journal Of Physical Oceanography (0022-3670) (Amer Meteorological Soc), 2017-09 , Vol. 47 , N. 9 , P. 2377-2385|
|WOS© Times Cited||17|
|Note||The original article that was the subject of this comment/reply can be found at http://journals.ametsoc.org/doi/abs/10.1175/JPO-D-14-0112.1.|
|Keyword(s)||Currents, Mixed layer, Sea state|
Several equivalent equations for the evolution of the wave-averaged current momentum have been proposed, implemented, and used. In contrast, the equation for the total momentum, which is the sum of the current and wave momenta, has not been widely used because it requires a less practical wave forcing. In an update on previous derivations, Mellor proposed a new formulation of the wave forcing for the total momentum equation. Here, the authors show that this derivation misses a leading-order term that has a zero depth-integrated value. Corrected for this omission, the wave forcing is equivalent to that in the first paper by Mellor. When this wave forcing effect on the currents is approximated it leads to an inconsistency. This study finally repeats and clarifies that the vertical integration of several various forms of the current-only momentum equations are consistent with the known depth-integrated equations for the mean flow momentum obtained by subtracting the wave momentum equation from the total momentum equation. Several other claims in prior Mellor manuscripts are discussed.