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

加入

登录

注册

搜索

主题切换

夜间模式

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

网站博客 Literature

已发布 2025-10-29 01:30:19

1千

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

请登录以点赞、分享和评论！

ประสบการณ์ใหม่ด้วยเครื่อง relx รุ่น 6 และหัวน้ำยาคุณภาพสูง

เยว่เค่อ ถือเป็นบริษัทเทคโนโลยีชั้นนำที่เชี่ยวชาญด้านการวิจัยและพัฒนาบุหรี่ไฟฟ้ามายาวนาน...

通过 2025-08-29 03:20:04 0 3千

RELEX บุหรี่ไฟฟ้าแบรนด์ดังที่ตอบโจทย์คนรุ่นใหม่

ในยุคที่ผู้บริโภคเริ่มหันมาให้ความสำคัญกับสุขภาพมากยิ่งขึ้น บุหรี่ไฟฟ้า...

通过 2025-07-16 01:41:21 0 3千

Driving Innovation in Insurance: Growth of the Telematics-Based Auto Insurance Market

The Telematics Based Auto Insurance Market Share is expanding rapidly as the...

通过 2025-10-31 07:15:49 0 2千

Key Polishing Cleaner Market Trends Shaping Industry Growth

The polishing cleaner market share is distributed among several global and regional...

通过 2025-09-30 23:59:58 0 2千

Paper Sheet Box Gluing Machine Bubble Tea and Yogurt Packing Machine

Paper Sheet Box Gluing Machine Bubble Tea and Yogurt Packing Machine Click to quickly check key...

通过 2025-08-04 00:20:23 3 3千