This study considers the isopycnal eddy transport of mass and passive tracers in eddy-resolving doublegyre 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.