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

Login

Anmelden

Registrieren

Search

Theme Switcher

Night Mode

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

Blogs Literature

Posted 2025-10-29 01:30:19

936

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

Please log in to like, share and comment!

Full-automatic Plastic Cup Forming, Filling and Sealing Machine for Dairy Drinks, Sauces

Full-automatic Plastic Cup Forming, Filling and Sealing Machine for Dairy Drinks, Sauces Click to...

Von 2025-06-18 02:14:58 1 3KB

巴黎世家台灣官網熱門包款全解析｜機車包與沙漏包魅力一次看懂

機車包巴黎世家自 2001 年推出以來，憑藉柔軟的羊皮、標誌性的鉚釘設計與隨性輪廓，迅速成為時尚界的經典之作。其輕盈柔軟的皮革搭配實用容量，讓它既適合日常通勤，也能搭配街頭造型。...

Von 2025-08-15 03:16:41 0 2KB

SP2S電子菸全系列評測：從煙彈到主機的極致體驗

在眾多電子...

Von 2025-07-09 02:14:44 1 2KB

国产用于单导联和六导联的心电算法及API服务

随着心电图应用的逐步推广，智能手表、体脂仪、跑步机等智能设备都逐渐加入心电图功能。心电图作为诊断心脏问题的金标准数据，具备很大的健康监测价值。苹果、欧姆龙等厂商都已经加入。但是心电图的分析算法相...

Von 2025-07-21 12:35:30 0 2KB

On the Dialectical Unity of Absolute Space and Relative Space (4)

4. Dialectical Unity: The Symbiosis of Stage and Actor The crucial argument is: The appearance...

Von 2025-10-22 05:52:11 0 1KB