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

Δημοσιευμένα 2025-10-29 01:30:19

741

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

Παρακαλούμε συνδέσου στην Κοινότητά μας για να δηλώσεις τι σου αρέσει, να σχολιάσεις και να μοιραστείς με τους φίλους σου!

Sacai x Nike價錢攻略——VaporWaffle穿搭聖經

當解構主義遇上經典運動鞋，sacai x nike 聯名系列便誕生了讓鞋頭瘋狂的藝術品！從初代雙鞋舌設計轟動潮流圈，到最新sacai vapor...

από 2025-06-17 01:24:14 0 2χλμ.

Flash Stripping Machine | Metal Shielding Mesh | Thermocouple Wires | New Energy Cable Harnesses

Thermocouple Plant Equipment Manufacture

από 2025-10-16 03:41:24 0 791

รีวิว relx ทุกรุ่น ฟีลสูบสุดฟินที่คุณห้ามพลาด

บุหรี่ไฟฟ้า Relx ตัวจริงเสียงจริงของสายควัน หากพูดถึง บุหรี่ไฟฟ้า...

από 2025-09-27 01:17:16 0 1χλμ.

The Growing Demand for Ethernet Cable in a Connected World

The Ethernet Cable Market has been experiencing rapid growth in recent years, driven by...

από 2025-09-24 09:20:06 0 1χλμ.

Κεντρική Σελίδα

橡胶输送带硫化接头机

我公司专业制造电热式橡胶带硫化接头机。所制造的硫化接头机与同类产品相比：...

από 2025-08-15 03:44:15 0 2χλμ.