Some Consequences of the Three-Dimensional Current and Surface Wave Equations

George Mellor Princeton University, Princeton, New Jersey

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Abstract

Three-dimensional, interacting current and surface gravity wave equations have recently been derived and compared with their counterpart vertically integrated equations; they are in the form of sigma-coordinate equations. The purpose of this paper is to examine some of the consequences of these equations including energy transfer between mean energy, wave energy, and turbulence energy, to frame some outstanding research issues, to provide a Cartesian version of the sigma-coordinate equations, and to compare with other formulations of wave–current interaction. In general, the paper is intended to set the stage for the development of numerical coupled surface wave and three-dimensional general circulation models. These models often include a flow-dependent turbulence-based viscosity.

Corresponding author address: George Mellor, AOS Program, Sayre Hall, Forrestal Campus, Princeton University, Princeton, NJ 08540-0710. Email: glm@splash.princeton.edu

Abstract

Three-dimensional, interacting current and surface gravity wave equations have recently been derived and compared with their counterpart vertically integrated equations; they are in the form of sigma-coordinate equations. The purpose of this paper is to examine some of the consequences of these equations including energy transfer between mean energy, wave energy, and turbulence energy, to frame some outstanding research issues, to provide a Cartesian version of the sigma-coordinate equations, and to compare with other formulations of wave–current interaction. In general, the paper is intended to set the stage for the development of numerical coupled surface wave and three-dimensional general circulation models. These models often include a flow-dependent turbulence-based viscosity.

Corresponding author address: George Mellor, AOS Program, Sayre Hall, Forrestal Campus, Princeton University, Princeton, NJ 08540-0710. Email: glm@splash.princeton.edu

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