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 thickness-weighted-mean theory. Journal of Physical Oceanography, 43 . pp. 149-164. DOI 10.1175/JPO-D-12-059.1.

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Abstract

Previous attempts to derive the depth-dependent 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 wave-induced 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 depth-dependent radiation stress that is consistent with the vertically-integrated expression given by Longuet-Higgins and Stewart. Concerning (i)-(iii) in the above, the difficulty of handling a sloping bottom disappears when wave-averaged 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 depth-dependent radiation stress. The connection between the wave-induced pressure term in the recent studies and the depth-dependent radiation stress term is easily shown by rewriting the pressure-based form stress term in the thickness-weighted-mean (TWM) momentum equations as a velocity-based term which contains the time derivative of the pseudomomentum in the TWM framework.

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