Robustness of Geometric Frustration in a Vector Shell Model with Angular Dependence Across Resolutions

This paper investigates whether geometric frustration persists when the angular resolution of the vector shell model with angular dependence (VSMAM) is increased. As stated in the abstract, “in all cases the enstrophy remains bounded and slowly decays,” and “the frustration mechanism is insensitive to the angular resolution.” Simulations with N_θ=16,32,64 show nearly identical enstrophy evolution curves, confirming that adding more angular modes does not open new channels for coherent nonlinear amplification. The results reinforce the hypothesis that geometric frustration is a universal barrier against finite-time blow-up in shell models and may extend to the full Navier–Stokes equations.