Localized Enstrophy Growth in an Explicit Forced Two-Tube Navier–Stokes Model on \mathbb T^3

This technical note studies an explicit forced two-tube periodic Navier–Stokes model on the three-dimensional torus. The paper develops a localized core/shell framework, derives a conditional short-time core-growth proposition, and organizes the mechanism into explicit geometric, forcing, and regularity components. The note does not claim a solution of the Clay Navier–Stokes problem. Its purpose is to present a concrete model, a structured reduction, and a set of sanity-checked intermediate results that may be useful for further mathematical analysis.