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)

Статьи пользователей Literature

Сообщение 2025-10-29 01:30:19

1Кб

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

Войдите, чтобы отмечать, делиться и комментировать!

The Global Evolution of the Crowdfunding Market: Empowering Modern Financing Models

The digital economy has redefined how entrepreneurs, startups, and individuals access funding,...

От 2025-10-16 03:12:32 0 1Кб

Competitive Landscape in the Insulin Delivery Market: Innovations, Key Players, and Strategic Moves

According to the most recent analysis by Emergen Research, the size of the global insulin...

От 2025-10-31 07:43:52 0 1Кб

เจาะลึกทุกเรื่องที่ควรรู้เกี่ยวกับผลิตภัณฑ์จาก RELX

ในตลาดอุปกรณ์สูบไฟฟ้า relx ถือเป็นแบรนด์ชั้นนำที่ครองใจผู้ใช้จำนวนมากด้วยคุณภาพและนวัตก...

От 2025-09-25 01:43:30 0 2Кб

RELX電子菸選購與口味指南

談到入門與進階並重的電子菸 relx，多數使用者看重其主機穩定、煙彈口味多樣與售後方便。無論是剛從紙菸轉換，或追求更精緻風味的老手，RELX的設計與體驗都易於上手，日常通勤、聚會使用皆得體。...

От 2025-10-27 01:55:33 0 1Кб

Polycrystalline Diamond Compact Drill Bit Market Revenue, Trends, Analysis, Demand and Forecast to 2032

The Polycrystalline Diamond Compact Drill Bit Market was valued at USD 1.2 billion in 2024 and is...

От 2025-12-22 08:27:56 0 1Кб