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

933

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!

RELX Infinity Plus รุ่นใหม่ ใช้ง่าย รสชาติดี ราคาคุ้ม

ในยุคที่เทคโนโลยีเปลี่ยนไลฟ์สไตล์ของผู้สูบ relx infinity...

От 2025-07-19 01:55:49 1 2Кб

Provide local sales positions for Mo Ge, interested @ me提供墨哥本地销售岗位，有意向@我

Hello, I am Guangzhou Huajin Machinery Manufacturing Co., Ltd. in China, specializing in...

От 2025-07-09 08:27:12 0 2Кб

Hello everyone, welcome to learn about our company! We are located in Jingzhou, Hubei, China—a city steeped in profound historical heritage as a famed Three Kingdoms-era hub and the ancient capital of the Chu State. Here, we specialize in producing c

Hello everyone, welcome to learn about our company! We are located in Jingzhou, Hubei,...

От 2025-09-14 08:08:16 1 2Кб

ช้อปคุ้ม! อัปเกรดประสบการณ์สูบด้วย relx รุ่น 5 และหัวน้ำยารุ่นใหม่

relx บุหรี่อิเล็กทรอนิกส์ ทางเลือกใหม่สำหรับสายควันยุคดิจิทัล ในยุคที่ทุกอย่างต้องสะดวก รวดเร็ว...

От 2025-11-25 01:14:44 0 485

รีวิวบุหรี่ไฟฟ้า RELX และรุ่นยอดนิยมที่ควรรู้จัก

ปัจจุบัน บุหรี่ไฟฟ้า relx ได้กลายเป็นหนึ่งในตัวเลือกที่ได้รับความนิยมสูงในหมู่ผู้สูบยุคใหม่...

От 2025-08-20 01:27:10 0 2Кб