Eddy parameterization challenge suite I: Eady spindown

The first set of results in a suite of eddy-resolving Boussinesq, hydrostatic simulations is presented. Each set member consists of an initially linear stratification and shear as in the Eady problem, but this profile occupies only a limited region of a channel and is allowed to spin-down via baroclinic instability. The diagnostic focus is on the spatial structure and scaling of the eddy transport tensor, which is the array of coefficients in a linear flux–gradient relationship. The advective (antisymmetric) and diffusive (symmetric) components of the tensor are diagnosed using passive tracers, and the resulting diagnosed tensor reproduces the horizontal transport of the active tracer (buoyancy) to within ±7% and the vertical transport to within ±12%. The derived scalings are shown to be close in form to the standard Gent–McWilliams (antisymmetric) and Redi diffusivity (symmetric) tensors with a magnitude that varies in space (concentrated in the horizontal and vertical near the center of the frontal shear) and time as the eddies energize. The Gent–McWilliams eddy coefficient is equal to the Redi isopycnal diffusivity to within ±6%, even as these coefficients vary with depth. The scaling for the magnitude of simulation parameters is determined empirically to within ±28%. To achieve this accuracy, the eddy velocities are diagnosed directly and used in the tensor scalings, rather than assuming a correlation between eddy velocity and the mean flow velocity where ±97% is the best accuracy achievable. Plans for the next set of models in the challenge suite are described.

► The eddy transport tensor is determined by using passive tracers in the flow field.
► Scalings have been derived for the advective and diffusive components of this tensor.
► The vertical structure of the advective and diffusive components has been found.
► The GM coefficient is found to be equal to the Redi coefficient at all depths.
► Parameterization accuracy is improved by using the RMS eddy velocity.