Diagnosing the thickness-weighted averaged eddy-mean flow interaction in an eddying North Atlantic ensemble
Résumé
The thickness-weighted average (TWA) framework, which treats the residual-mean flow as the prognostic variable, has provided us with a clear theoretical understanding of the eddy feedback onto the residual-mean flow. The averaging operator involved in the TWA framework, although in theory being an ensemble mean, in practice has often been approximated by a temporal mean, which conflates the temporal variability with the eddies. Here, we analyze an ensemble of North Atlantic simulations at mesoscale resolving resolution (1/12{degree sign}). We therefore recognize means and eddies in terms of ensemble means and fluctuations about those means, in keeping with the TWA formalism proposed by Young (2012). Eddy-mean flow feedbacks are encapsulated in the Eliassen-Palm (E-P) flux tensor and its divergence indicates that the eddies contribute to the zonal meandering of the Gulf Stream and its deceleration in the meridional direction. We also show that the eddy Ertel potential vorticity (PV) flux can be parametrized as an isopycnic local-gradient flux of the residual-mean Ertel PV via an anisotropic eddy diffusivity tensor. As the E-P flux divergence and eddy Ertel PV flux are directly related to one another, this provides a new pathway forward for a unified mesoscale eddy closure scheme.