Geometric Frustration in a Vector Shell Model with Angular Dependence and the Approach to the Navier–Stokes Equations

This paper introduces a vector shell model with angular dependence (VSMAM) that interpolates between discrete shell models and the full three‑dimensional Navier–Stokes equations. As stated in the abstract, “each shell carries a complex vector depending on a continuous angular variable, and the nonlinearity is the cross product extended to the angular modes,” and “the enstrophy remains bounded and the maximum vorticity oscillates without blow-up.” The results show that geometric frustration continues to suppress coherent forward cascades even when an additional angular degree of freedom is introduced. This suggests that weakening of frustration observed in axisymmetric geometries requires a fully continuous spatial dimension.