Gravitational Enstrophy: Local Geometric Origin and Energy-Cascade Constraints

Two-dimensional fluids conserve energy and enstrophy, driving inverse energy cascades via Fj rtoft's argument. We show General Relativity admits an analogous structure: for linear radiative perturbations of Petrov type D backgrounds (Kerr, Kerr--AdS), the gravitational-wave energy W = sum k W k and magnetic Weyl enstrophy Z = integral B ab B ab sqrt gamma, d 3x about sum k omega k squared W k are approximately conserved in the zero-angular momentum frame, where vorticity coupling vanishes identically and curl exchange cancels mode-by-mode. This yields a gravitational Fj rtoft constraint implying nonlinear energy transfer proceeds preferentially toward lower frequencies. The constraint is dynamically active in near-extremal Kerr (tau damp tau nl) and confined geometries (AdS), but suppressed in generic ringdown. In AdS, Z maps holographically to the boundary fluid enstrophy.