A Vorticity-Selective Dissipative Model for Incompressible Flows: Global Well-Posedness and Subgrid-Scale Dynamics

This work introduces a modified incompressible Navier-Stokes system, designated as NS-TZT, incorporating a rotational selective dissipation operator and a Leray-projected first-order gyroscopic alignment term on the three-dimensional periodic flat torus. At any fixed positive filter scale, the effective eddy viscosity is governed by a smooth threshold switch, which activates non-linear dissipation exclusively within localized coherent vortex structures while strictly preserving laminar kinematics. The global existence, uniqueness, and regularity of strong solutions are proven for arbitrary divergence-free Sobolev H-one initial data and square-integrable external forcing. The regularity mechanism relies on a natural cubic scaling balance: the cubic vortex stretching term is analytically bounded by the Calderon-Zygmund inequality and absorbed by the cubic dissipation naturally generated by the convex potential structure of the rotational dissipation operator, guaranteeing finite global enstrophy for all forward time without finite-time singularities. Furthermore, direct numerical simulations of the Taylor-Green vortex at Reynolds number 1600 demonstrate that while the classical Smagorinsky model suffers from severe unphysical over-damping during the early laminar stage (prior to non-dimensional time 0.4, dissipating at 2.33 times 10 to the minus 4), the proposed model suppresses artificial dissipation by over 80 percent (0.45 times 10 to the minus 4), transitioning into active selective dissipation only during turbulence peak breakdown. All mathematical statements in this work concern the regularized system at a fixed positive filter scale and do not assert claims regarding the classical vanishing-filter Navier-Stokes Millennium problem.