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

Join

Sign In

Sign Up

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

748

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!

Kobe球鞋經典重現：Nike Kobe系列全面解析

在籃球場上，Kobe Bryant 的傳奇影響力不僅來自他無可挑剔的技術與精神，更延伸至鞋款文化。kobe 球鞋系列由 Nike...

By 2025-09-02 05:53:09 0 2K

Nike跑鞋全攻略：SNKRS搶購技巧與經典款解析

在運動鞋市場中，Nike始終以創新科技與潮流設計佔據領先地位。從經典板鞋到專業跑鞋，Nike旗下多款鞋型成為鞋迷必收單品。本文將聚焦Nike SNKRS搶購平台、經典Nike Air...

By 2025-07-21 07:01:58 0 2K

Sacai聯名鞋解密｜紅藍雙層美學台灣搶購攻略

當解構主義遇上復古跑鞋，Nike x Sacai LDWaffle 便成為鞋圈核彈級藏品！這雙由阿部千登勢操刀的Sacai神作，以「雙重靈魂」設計血洗潮流圈。nike x sacai...

By 2025-07-04 01:18:18 0 2K

Philippines factory, fast assembly container homes, fast construction homes, Philippines modular homes, Philippines prefabricated homes, container homes, luxury prefabricated homes, custom prefabricated homes, off-grid living, resort development, vacation

Looking for quick-to-build vacation rentals for your resort development? Our luxury prefab...

By 2025-10-17 10:02:04 0 943

潮流與舒適兼具：YEEZY拖鞋的時尚新主張

在追求舒適與時尚並重的當代穿搭中，yeezy拖鞋無疑已成為眾多潮流人士的日常首選。由潮流教父 Kanye West 與 adidas...

By 2025-06-18 01:39:34 1 2K