On eddy transport in the ocean. Part II: The advection tensor

Abstract

This study considers the isopycnal eddy transport of mass and passive tracers in eddy-resolving double-gyre quasigeostrophic oceanic circulation. Here we focus on advective transport, whereas a companion paper focuses on eddy-induced diffusive tracer transport. To work towards parameterising eddy tracer transport we quantify the eddy tracer flux using a transport tensor with eddies defined using a spatial filter, which leads to results distinct from those obtained via a temporal Reynolds eddy decomposition. The advection tensor is the antisymmetric part of the transport tensor, and is so named since the associated tracer transport can be expressed as advection of the large-scale tracer field by a rotational eddy-induced velocity (EIV) u∗c with streamfunction A. The EIV u∗c is fastest (∼1 m s−1) where eddy activity is strongest, e.g., in the upper layer, near the eastward jet and western boundary current. Our results suggest that a stochastic closure for the eddy transport would be most suitable since A exhibits a probabilistic distribution when conditioned on, for example, the large-scale relative vorticity. Consistent with closures in ocean circulation models, we quantify eddy mass (isopycnal layer thickness) fluxes as eddy-induced advection by the thickness EIV u∗h. The divergent part of u∗h – the only part relevant for mass transport in the quasigeostrophic limit – tends to be oriented down the thickness gradient suggesting it quantifies some baroclinic eddy effects similar to those parameterised by the Gent & McWilliams (GM90) EIV. Although u∗h has some qualitative similarities to u∗c, our results suggest that eddy-induced tracer advection is driven by more than just the thickness-determined EIV and, in turn, more than just the GM90 EIV.