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Derivation of Three-Dimensional Radiation Stress Based on Lagrangian Solutions of Progressive Waves

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  • 1 State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin, China
  • | 2 Marine Ecosystem Section, Ocean Ecosystem Sciences Division, Fisheries and Oceans Canada, Bedford Institute of Oceanography, Dartmouth, Nova Scotia, Canada
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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.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Qinghe Zhang, qhzhang@tju.edu.cn

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.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Qinghe Zhang, qhzhang@tju.edu.cn
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