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

77

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!

On the Dialectical Unity of Absolute Space and Relative Space (5)

6. Warning Physics should be vigilant: True progress lies in inclusion and synthesis, not in...

By 2025-10-22 06:03:02 0 349

MK斜背包熱度與選購指南

想入手當季熱門與經典耐看款，建議先從 michael kors 官網台灣...

By 2025-10-27 02:11:12 0 120

法國直流接觸器市場：產品類型、市場趨勢與未來機遇

法國直流接觸器市場正在快速增長，主要受到電動車（EV）普及、再生能源整合以及工業自動化發展的推動。隨著法國積極推進能源轉型與碳減排政策，直流接觸器已成為確保高壓系統安全與效率的關鍵組件。...

By 2025-08-24 08:24:47 0 1K

The quantum is not a cat that is both dead and alive (1)

Abstract This paper aims to propose and elucidate a quantum theoretical framework based on...

By 2025-10-15 01:29:44 0 376

山系機能革命！Nike ACG巔峰解密

當玉山雲海漫過稜線，Nike ACG Mountain Fly 2 米黑橙色的鋸齒大底正撕裂碎石坡！這雙被山友封為「移動安全艙」的巔峰戰靴，以軍規級nike acg gore...

By 2025-06-17 01:12:34 0 2K