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

0
939

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.

Like
1
검색
카테고리
더 보기
기타
小冰测颜值
觉得很准,大家去玩玩。 美中不足:会硬夸,但不会虚高。 满分10分。普通人7分,小美小帅8到8点5分,8点5到9花草级别,9以上明星级别  ...
작성자 迷谢の小心晨 蛋蛋营必过版) 2025-08-04 11:12:16 0 2K
Music
Bengals win fifth straight: How Joe Burrow, Cincinnati protection came via vs. Browns
The Bengals 9-4) picked up their fifth straight win Sunday with a 23-10 success versus the AFC...
작성자 Natasha827 Natasha827 2025-10-16 06:49:50 0 1K
Portable Digital Conductivity Meter Market Revenue, Trends, Analysis, Demand and Forecast to 2032
The Portable Digital Conductivity Meter Market was valued at USD 0.5 billion in 2024 and is...
작성자 Vandana Manturgekar 2025-12-22 08:21:43 0 51
Networking
Germany Smartphone Industry: Trends and Market Outlook
The Germany Smartphone Market has emerged as a dynamic and rapidly evolving sector in...
작성자 Kajal Jadhav 2025-09-22 11:18:22 0 1K
기타
Ayome Voice Chat Team – HighEarning Roles Available!
 🚀 Join Ayome Voice Chat Team – HighEarning Roles Available!  Looking for...
작성자 Ada Huang 2025-10-30 02:41:35 0 771