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

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

Vă rugăm să vă autentificați pentru a vă dori, partaja și comenta!

ทำความรู้จัก RELX บุหรี่ไฟฟ้า รุ่นใหม่ คุณภาพดี ราคาคุ้มค่า

ในปัจจุบัน บุหรี่ไฟฟ้า relx ได้รับความนิยมอย่างกว้างขวางในประเทศไทย...

By 2025-09-05 02:27:47 0 2K

我家的明星产品

Tuodianda focuses on producing vacuum battery valves, IPR valves, turbocharger relief valves,...

By 2025-06-23 01:18:47 6 4K

เจาะลึกทุกเรื่องที่ควรรู้เกี่ยวกับผลิตภัณฑ์จาก RELX

ในตลาดอุปกรณ์สูบไฟฟ้า relx ถือเป็นแบรนด์ชั้นนำที่ครองใจผู้ใช้จำนวนมากด้วยคุณภาพและนวัตก...

By 2025-09-25 01:43:30 0 1K

悅刻煙彈口味全攻略｜RELX 蘋果口味、老冰棍六代煙彈通用4/5代推薦

在電子菸市場中，悅刻（RELX）已成為許多用戶的首選品牌。無論是設計質感、霧化技術還是多樣的口味選擇，悅刻始終在行業中保持領先地位。尤其在悅刻煙彈口味...

By 2025-08-29 02:49:16 0 2K

谷仓门滑轨

谷仓门滑轨承受门的重量，确保门在轨道上顺畅滑动。选择合适的滑轨材质和设计，以确保长期使用的稳定性和耐用性。...

By 2025-09-03 12:51:10 0 2K