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Chao Ji, Qinghe Zhang, and Yongsheng Wu
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Chao Ji, Qinghe Zhang, and Yongsheng Wu

Abstract

A new approach has been proposed to derive the expressions for three-dimensional radiation stress using solutions of the pressure and velocity distributions and the coordinate transformation function that are derived from a Lagrangian description wherein the pressure is zero (relative to the atmospheric pressure) at the sea surface. Using this approach, analytical expressions of horizontal and vertical depth-dependent radiation stress are derived at a uniform depth and for a sloping bottom, respectively. The results of the depth integration of the expressions agree well with the theory of Longuet-Higgins and Stewart. In the case involving a sloping bottom, the radiation stress expressions from this study provide a better balance of the net momentum compared to those from previous studies.

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Yuefeng Wu, Qinghe Zhang, Yongsheng Wu, and Chao Ji

Abstract

We commented on the empirical adjustment term recently introduced by Mellor. The purpose of the adjustment term is to include the effect of concentrating momentum at the surface, and the adjustment significantly improves the comparisons between modeled and measured velocity profiles. We found that the concentrating momentum from the adjustment term is largely overestimated relative to the commonly used parameterization approaches of concentrating momentum. The overestimated concentrating momentum leads to stronger velocity shear at the surface, which is partially canceled out by the vertical mixing caused by wave breaking. The model results also agree well with the measured velocity profiles if the fractions of the adjustment and the vertical mixing are simultaneously reduced. We also discussed an alternative method that includes the vertical radiation stress gradient term. The method exhibits no empiricism or uncertainty under the given wave conditions.

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