| Summary: | Abstract We propose an isoneutral eddy transport diagnostic framework and apply it in the Southern Ocean to analyze eddy potential vorticity (PV) transport dynamics. We leverage a thickness‐weighted spatiotemporal scale separation to define the generalized eddy flux. A local sampling method is employed and validated to estimate the transport tensor. We introduce Leonard's decomposition in Large Eddy Simulations (LES) to split the process into the Reynolds and non‐Reynolds parts. We also use the stationary‐transient decomposition. The non‐Reynolds term and the stationary effect contribute significantly to the transport properties. The Reynolds and transient parts have distinctions, that show oceanic mesoscale dynamics are not synergistic in time and spatial scales. We investigate the spatial scale dependence of each part and find that the transient and stationary components of the Reynolds (non‐Reynolds) term have consistent (dissimilar) scale dependence. The scale dependence of the generalized eddy flux and the transport eigenvalues is controlled by the non‐Reynolds term. We further investigate the eigenvalues in terms of the potential enstrophy and anisotropy. The potential enstrophy in the Southern Ocean holistically has a forward cascade on the researched scales. The Reynolds and transient effects efficiently promote the forward enstrophy cascade. The non‐Reynolds and stationary effects stimulate drastically anisotropic eddy transport. The PV gradient barrier mechanism dominates the drastic anisotropic case. When the anisotropy is weak, a special anisotropic case with a locally balanced potential enstrophy budget overwhelms the case of real isotropy. We also introduce several LES concepts, hoping to enlighten any potential ocean modeling and parameterization.
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