We study the splitting dynamics of a triply quantized vortex (TQV) confined in a ring-shaped Bose-Einstein condensate under a weakly elliptical harmonic trap. Using full 3D simulations in cylindrical coordinates, combined with a semi-analytical energy analysis, we show that the vortex preferentially splits along the long axis of the trap, a direction that minimizes the kinetic-energy cost relative to the initial TQV state. Systematic parameter scans reveal that initial quantum fluctuations increase the splitting time and suppress the transient three-core pattern observed in noise-free simulations, whereas stronger nonlinear interactions accelerate the splitting. When the trap is nearly isotropic, the unstable Bogoliubov modes are dominated by both azimuthal quantum number $l_q=3$ and $l_q=2$; this leads to a dynamical sequence where three daughter vortices first form a triangular arrangement, later evolving into a linear chain. For stronger anisotropy, geometric coupling selectively enhances the $l_q=2$ mode, making it the sole dominant channel and resulting directly in linear vortex alignment -- a clear signature of geometry-induced mode competition explained through combined energy-based and Bogoliubov stability analysis. Our results provide a quantitative picture of how trap geometry can steer the instability pathway, splitting time, and final pattern of a multiply quantized vortex, offering a route toward geometry-controlled vortex engineering.
Los Alamos National Laboratories（洛斯阿拉莫斯国家实验室）；Technology Innovation Institute（技术创新研究所）；Università di Catania（卡塔尼亚大学）；INFN-Sezione di Catania（意大利国家核物理研究所卡塔尼亚分部）；Nanyang Technological University Singapore (NTU)（新加坡南洋理工大学）
Realization of a Synthetic Hall Torus with a Topological Charge Pump in a Spinor Bose-Einstein Condensate
Institute of Atomic and Molecular Sciences, Academia Sinica（中央研究院原子与分子科学研究所）；Department of Physics, University of Mumbai（孟买大学物理系）；Department of Physics and Astronomy, Purdue University（普渡大学物理与天文学系）；Department of Physics, National Tsing Hua University（国立清华大学物理系）
Emergence of giant vortices under nonlinear rotation with attractive interactions in a toroidal condensate
Indian Institute of Technology, Guwahati（印度理工学院古瓦哈提分校）；Indian Institute of Technology Kharagpur（印度理工学院卡拉格普尔分校）；Hiroshima University（广岛大学）；Keio University（庆应义塾大学）；Bharathidasan University（巴拉蒂达桑大学）
