An Objective Method for Determining the Generalized Transport Tensor for Two-Dimensional Eulerian Models

Edwin F. Danielsen NASA-Ames Research Center, Moffett Field, CA 94035

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Abstract

An objective method for deriving the components of a generalized transport tensor for a two-dimensional model is presented. The method uses representative meridional and vertical velocities and thermodynamic scalars at a uniform grid to reduce the problem to solving two flux equations for two unknowns. One unknown is the streamfunction, coefficient of an antisymmetric tensor, which corrects the Eulerian mean motions for Stokes drift. The other is a time constant, which converts the deviatory velocity tensor (Reynold's stress tensor for temporal averaging) to a symmetric transport tensor. The complete asymmetric tensor is called a transport rather than a diffusion tensor because its divergence yields both advection and diffusion by the deviatory velocities. Advantages and disadvantages of Lagrangian and Eulerian averages are also discussed.

Abstract

An objective method for deriving the components of a generalized transport tensor for a two-dimensional model is presented. The method uses representative meridional and vertical velocities and thermodynamic scalars at a uniform grid to reduce the problem to solving two flux equations for two unknowns. One unknown is the streamfunction, coefficient of an antisymmetric tensor, which corrects the Eulerian mean motions for Stokes drift. The other is a time constant, which converts the deviatory velocity tensor (Reynold's stress tensor for temporal averaging) to a symmetric transport tensor. The complete asymmetric tensor is called a transport rather than a diffusion tensor because its divergence yields both advection and diffusion by the deviatory velocities. Advantages and disadvantages of Lagrangian and Eulerian averages are also discussed.

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