Evaluation of a scalar eddy transport coefficient based on geometric constraints

- Residual-mean theory can be used to constrain the magnitude of an eddy transport coefficient.
- The dimensional terms in this coefficient are specified, and the only free parameter is dimensionless.
- The skill of any scaling for this coefficient can be evaluated using a multiple-tracers inversion method.
- A set of idealized baroclinic channel models is used to evaluate the skill of several proposed scalings.
- The scaling from residual-mean theory exhibits greater skill in all phases of baroclinic spindown.

A suite of idealized models is used to evaluate and compare several previously proposed scalings for the eddy transport coefficient in downgradient mesoscale eddy closures. Of special interest in this comparison is a scaling introduced as part of the eddy parameterization framework of Marshall et al. (2012), which is derived using the inherent geometry of the Eliassen-Palm eddy flux tensor. The primary advantage of using this coefficient in a downgradient closure is that all dimensional terms are explicitly specified and the only uncertainty is a nondimensional parameter, α, which is bounded by one in magnitude.In each model a set of passive tracers is initialized, whose flux statistics are used to invert for the eddy-induced tracer transport. Unlike previous work, where this technique has been employed to diagnose the tensor coefficient of a linear flux-gradient relationship, the idealization of these models allows the lateral eddy transport to be described by a scalar coefficient. The skill of the extant scalings is then measured by comparing their predicted values against the coefficients diagnosed using this method. The Marshall et al. (2012), scaling is shown to scale most closely with the diagnosed coefficients across all simulations. It is shown that the skill of this scaling is due to its functional dependence on the total eddy energy, and that this scaling provides an excellent match to the diagnosed fluxes even in the limit of constant α. Possible extensions to this work, including how to incorporate the resultant transport coefficient into the Gent and McWilliams parameterization, are discussed.