A dissipative-signed subgrid-scale flux decomposition for local enstrophy transfer in two-dimensional decaying turbulence

Filtered two-dimensional vorticity transport contains both forward and local reverse subgrid-scale (SGS) enstrophy transfer, which a positive scalar diffusivity cannot represent simultaneously. We develop a neural flux decomposition that retains an explicitly dissipative tensor-diffusive component and adds a bounded sign-indefinite correction supported by resolved gradients. The dissipative component has non-negative local enstrophy transfer, while the correction supplies signed and non-collinear transport. Physical SGS labels are constructed by applying a periodic Gaussian filter to a grid-refined numerical reference. A three-seed 2×2 factorial identifies the signed correction as the dominant reproducible contribution: for the isotropic model, mean a priori transfer correlation increases from 0.483 to 0.933 on the training realization and from 0.465 to 0.934 on an independently phased initial condition. Learned symmetric positive-definite anisotropy provides a smaller, interaction-sensitive increment. Classical and neural closures exhibit distinct local and dynamical rankings. Clark gives the smallest instantaneous SGS-source error, whereas the signed isotropic neural model has the lowest mean free-running vorticity error among the original comparators; substantial late-time drift and a high-error Full realization remain. Fixed 4% sparse observations further constrain drift in extended-time reconstruction to 10 s. Frozen evaluations at two unseen filter widths, two viscosity settings, and one periodically forced flow retain Clark's local transfer advantage but reveal greater wide-filter trajectory sensitivity for Clark and Mixed, alongside a material increase in neural trajectory error. These results establish the role of the signed correction and distinguish local SGS fidelity from closed-loop performance in the tested two-dimensional flows.