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

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

Please log in to like, share and comment!

#Directly operated by the factory in the Philippines

1. The first choice for emergency response after a typhoon. A safe house that can be assembled in...

By 2025-08-18 10:15:03 1 2K

Underwater Fishing Camera

Underwater Fishing Camera (水下可视钓鱼器) Calling all outdoor fishing enthusiasts ! I use a...

By 2025-08-20 07:49:50 0 2K

รีวิว RELX รุ่นห้าและรุ่น 6 พร้อมหัวพอดยอดนิยมในปีนี้

ในยุคที่บุหรี่ไฟฟ้ากลายเป็นทางเลือกยอดนิยมสำหรับผู้ที่ต้องการเลิกบุหรี่แบบเดิม relx ได้...

By 2025-07-19 01:37:43 1 2K

Fully Automatic Plastic Cup Forming, Mineral Water Filling, Sealing and Cutting Machine

Fully Automatic Plastic Cup Forming, Mineral Water Filling, Sealing and Cutting Machine Click to...

By 2025-06-20 02:12:58 1 3K

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

Thermocouple Plant Equipment Manufacture

By 2025-10-16 03:41:24 0 791