A General Intensity-Structure Separation Principle:Persistent Response-Mode Locking under Spatiotemporal Forcing

We report numerical evidence for a more general forcing-response principle emerging from a study that began with the Weak-Response Spatiotemporal Enstrophy Law. The central finding is not merely near-quadratic enstrophy scaling. Across acoustic and non-acoustic forcing families, response intensity and response structure behaved as distinct dynamical coordinates: forcing amplitude strongly controlled peak enstrophy, whereas the effective vortex scale and dominant wavenumber remained comparatively insensitive to amplitude. In a 240-run generalization set, six non-acoustic forcing families yielded a mean peak-enstrophy amplitude exponent of 1.9951 (range 1.9758-1.9998; minimum R² 0.999954), while acoustic forcing yielded a mean exponent of 1.9781 (range 1.9302-1.9990; minimum R² 0.999652). The maximum absolute scale exponent was only 0.00374 for non-acoustic forcing and 0.00686 for acoustic forcing. A dedicated 2,048-fold amplitude sweep across 16 forcing/mapping/viscosity conditions detected no >5% abrupt jump in either effective vortex scale or energy-weighted dominant wavenumber. A separate smaller-time-step extension to amplitude 1638.4 retained near-quadratic behavior, with a median fitted exponent of 2.026 and no numerical blow-up. We therefore propose a General Intensity-Structure Separation Principle: scalar forcing amplitude primarily sets response intensity, while normalized spatiotemporal forcing geometry together with fluid parameters primarily selects response structure. The persistence of the selected structure over large amplitude changes is termed Persistent Response-Mode Locking. These results elevate the earlier weak-response observation into a broader, falsifiable numerical theory. Because absolute vortex-scale estimates remain resolution dependent, the present claim is a general numerical principle within the tested model class, not yet a universal physical law of turbulence.