Generalized Transformed Eulerian Mean (GTEM) Description for Boussinesq Fluids

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  • NODA Akira
    Research Institute for Global Change, Japan Agency for Marine-Earth Science and Technology (JAMSTEC), Yokohama, Japan

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Abstract

 The transformed Eulerian mean (TEM) description has been widely used as a standard basic analysis tool for describing wave-mean flow interactions in geophysical fluid dynamics. However, the TEM implicitly assumes that the eddy diffusion tensor is antisymmetric, although the assumption does not hold in general data analyses. To remedy the defect, a generalized transformed Eulerian mean (GTEM) set of equations is derived based on a nonneutral (unstable/dissipative) wave under dissipation and/or diabatic heating conditions in a Boussinesq stratified fluid. All the nine components of the three-dimensional eddy diffusion tensor are derived based on the wave-form. However, the explicit form of the wave frequency and wavenumber of eddies is not referred to so as to apply the GTEM to actual atmospheric and oceanic data analyses. The symmetric part of the eddy diffusion tensor is proportional to the growth rate for the weakly nonneutral wave. It is shown that the Stokes drift velocity defined in the generalized Lagrangian mean (GLM) description agrees to the leading order with the minus sign of the divergence of the transposed eddy diffusion tensor, so that the direction of the transport velocity induced by the symmetric (antisymmetric) part is opposite (identical) to the Stokes drift velocity. An application to the Eady unstable wave is made to illustrate the differences between TEM, GLM, and GTEM.

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