Robustness of Geometric Frustration Under Increasing Spectral Depth in a Vector Shell Model with Angular Dependence

This paper investigates whether geometric frustration persists when the spectral depth of the vector shell model with angular dependence (VSMAM) is increased. As stated in the abstract, “in all cases the enstrophy remains bounded and decays slowly,” and “the frustration barrier is independent of the spectral depth of the cascade.” Simulations with N=8,10,12 shells show nearly identical enstrophy decay profiles, confirming that extending the inertial range does not open new channels for coherent nonlinear amplification. The results support the view that geometric frustration is a universal, scale‑invariant mechanism preventing finite‑time blow‑up in vector triad models.