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

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.

1

Please log in to like, share and comment!

A Concept for Perpetual Electric Body Based on Topological Vortex Theory Integrating Permanent Magnets and Radioactive Elements (5)

Academic Statement The inspiration for this paper comes from ongoing contemplation of...

By 2025-10-27 06:09:43 0 986

RELX線上購機防詐指南

Relx革命進化史！1代到6代智能主機全解析...

By 2025-06-17 01:08:32 0 2K

On the Topological Nature of Noether's Theorem (1)

Abstract Noether's theorem, a cornerstone of modern physics, profoundly reveals the equivalence...

By 2025-11-27 01:17:43 0 768

資生堂國際櫃必買保養推薦｜活妍淨泉露與全效抗痕系列全解析

在高端保養品牌中，資生堂國際櫃一直是許多愛美女性信賴的首選。憑藉百年研發實力與先進科技，資生堂國際櫃針對不同膚質需求，推出多款明星保養品，幫助肌膚保持彈潤、光澤與年輕狀態。...

By 2025-09-12 02:27:33 0 2K

รีวิว RELX Infinity Plus และความคุ้มค่าของรุ่นก่อนหน้า

ในปัจจุบันบุหรี่ไฟฟ้าได้รับความนิยมเพิ่มขึ้นอย่างต่อเนื่อง โดยเฉพาะจากแบรนด์ RELX...

By 2025-08-29 01:31:11 0 2K