A multifaceted isoneutral eddy transport diagnostic framework and its application in the Southern Ocean -- code

We propose a multifaceted 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 a generalized form of eddy flux. A local sampling method is employed and validated to estimate the transport tensor. We introduce Leonard’s decomposition and stationary-transient decomposition to diagnose the role of multiscale interactions. The non-Reynolds term under Leonard’s decomposition and the stationary effect perform prominently in determining the transport property. 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 total eddy flux and the transport eigenvalues is controlled by the non-Reynolds term. We further investigate the eigenvalues in terms of the potential enstrophy budget 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. The results urge future diagnostic works to examine the generalized eddy flux form in a spatiotemporal sense.