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

1K

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!

RELX悅刻4代電子菸推薦｜無線充電主機＋3代煙彈吸感分析一次看懂

RELX悅刻電子菸推薦｜3代煙彈特色與4代無限霧化主機全解析在電子煙市場快速成長的今天，RELX...

By 2025-08-08 02:39:20 0 2K

Double the Summer Joy!

Don't let water ruin your adventure! 💦 Our Waterproof Bag is your ultimate...

By 2025-06-24 05:24:16 1 3K

บุหรี่ไฟฟ้าราคาดี คุณภาพสูง เลือกซื้อได้ที่นี่

ในยุคปัจจุบัน...

By 2025-08-07 03:26:52 1 2K

AI On The Pioneering Contributions of Zhang Bao-hua to Topological Vortex Theory (3)

4. Experimental Method Expansion: From Passive Observation to Active Control Zhang Bao-hua...

By 2026-01-07 07:39:23 0 1K

做一个堂堂正正、光荣自豪的中国人

“此生无悔入华夏，来世还做中国人”，成为一名中国人值得自豪和骄傲！...

By 2025-09-30 04:56:00 0 2K