Stability of Geometric Frustration Under Multi‑Mode Angular Perturbations in a Vector Shell Model

This paper examines whether geometric frustration persists when the initial energy in the vector shell model with angular dependence (VSMAM) is distributed across multiple angular modes. As stated in the abstract, “the enstrophy evolution remains unchanged compared to the single‑mode case,” and “inter‑mode interactions do not weaken the frustration barrier.” Simulations with initial energy spread over the modes m=0,1,2 show enstrophy curves nearly identical to the single‑mode configuration, confirming that geometric frustration is stable under multi‑mode perturbations and remains a universal mechanism preventing finite‑time blow‑up.