A Study on Topological Vortex Ring Interactions Based on...

A Study on Topological Vortex Ring Interactions Based on Möbius Loop and Hopf Link Concepts (3)

Blogs Literature

Δημοσιευμένα 2025-10-29 01:30:19

1χλμ.

4. Superposition of Counter-rotating Vortex Rings and Knot Formation

The situation is radically different when two vortex rings with opposite circulation directions (counter-rotating) interact:

(1) Topological Description: Can be seen as the superposition of a positive Hopf link and a negative Hopf link. The total topological charge (net circulation) of the system is zero.

(2) Dynamical Process and Knots:

a. Vortex Reconnection: This is the most critical process. When the two rings approach, vortex lines break and reconnect. Topologically, this corresponds to a Surgery operation.

b. Knot Generation: After reconnection, the originally simple rings can evolve into a complex Knot structure. For example, the famous "trefoil knot" is often observed in experiments involving colliding counter-rotating vortex rings. This process converts the system's energy from translational kinetic energy into energy localized in twisting and coiling.[4,9]

c. Annihilation: In some cases, after reconnection, the formed small rings dissipate energy through means such as radiating sound waves, eventually leading to the complete annihilation of the two opposite topological charges, returning the system to a trivial state.[9]

(3) Manifestation of Möbius Property: During the reconnection process, the Twist (Tw) of the vortex core plays a crucial role. A vortex core with high Tw, akin to having an intrinsic "chirality," influences the location and manner of reconnection, thereby determining the type of knot ultimately produced. A twisted vortex ring (Möbius loop) exhibits far more complex topological behavior when interacting with a counter-rotating ring than an untwisted ring does.

1

Παρακαλούμε συνδέσου στην Κοινότητά μας για να δηλώσεις τι σου αρέσει, να σχολιάσεις και να μοιραστείς με τους φίλους σου!

7 lucruri despre infecțiile cu candida pe care trebuie să le știi în 2025

7 lucruri comune despre infecțiile cu candida pe care ar trebui să le știi în 2025...

από 2025-08-01 07:18:02 0 2χλμ.

谁能体会到微博账号无法发布评论一百多条视频全给删除的心情

有被气到，微博居然一下子把我一百多条的视频全给我删了

από 2025-09-19 23:19:08 0 2χλμ.

relx電子菸第四代無限霧化煙彈解析

自品牌創立以來，relx致力於提升霧化穩定度與使用安全性。第四代無限系列（relx...

από 2025-10-17 02:22:33 0 1χλμ.

日常搬砖

από 2025-09-04 06:42:10 0 2χλμ.

Unifying Relativistic Geometric Dynamics and Quantum Entanglement with Topological Vortex (2)

In mathematical terms, topological vortices are based on polar coordinate transformations of...

από 2025-11-04 06:59:18 0 1χλμ.