Aiki, Hidenori and Greatbatch, Richard John (2013) The vertical structure of the surface wave radiation stress for circulation over a sloping bottom as given by thicknessweightedmean theory Journal of Physical Oceanography, 43 . pp. 149164. DOI 10.1175/JPOD12059.1.

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Abstract
Previous attempts to derive the depthdependent expression of the radiation stress have lead to a debate concerning (i) the applicability of Mellor’s approach to a sloping bottom, (ii) the introduction of the delta function at the mean sea surface in the later papers by Mellor, and (iii) a waveinduced pressure term derived in several recent studies. The authors use an equation system in vertically Lagrangian and horizontally Eulerian (VL) coordinates suitable for a concise treatment of the surface boundary, and obtain an expression for the depthdependent radiation stress that is consistent with the verticallyintegrated expression given by LonguetHiggins and Stewart. Concerning (i)(iii) in the above, the difficulty of handling a sloping bottom disappears when waveaveraged momentum equations in the VL coordinates are written for the development of (not the Lagrangian mean velocity but) the Eulerian mean velocity. There is also no delta function at the sea surface in the expression for the depthdependent radiation stress. The connection between the waveinduced pressure term in the recent studies and the depthdependent radiation stress term is easily shown by rewriting the pressurebased form stress term in the thicknessweightedmean (TWM) momentum equations as a velocitybased term which contains the time derivative of the pseudomomentum in the TWM framework.
Document Type:  Article 

Research affiliation:  OceanRep > GEOMAR > FB1 Ocean Circulation and Climate Dynamics > FB1TM Theory and Modeling OceanRep > The Future Ocean  Cluster of Excellence 
Refereed:  Yes 
DOI etc.:  10.1175/JPOD12059.1 
ISSN:  00223670 
Date Deposited:  20 Sep 2012 12:31 
Last Modified:  11 Nov 2013 14:50 
URI:  http://eprints.unikiel.de/id/eprint/15313 
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