Hi,
Stemming from the conservation of angular momentum, we associated the amplification/attenuation of vorticity with the stretching/compressing of a single vortex filament. But this conservative identity seems to me indicate nothing about the proliferation/conservation of the number of vortex filaments.
Let us consider a flow domain away from the boundary so that the vortex filaments are self-closed into vortex loops and let us assume the distribution of vortex loops are diluted without mutual interactions. Could anyone point me out whether the total number of such vortex loops is conserved in the flow domain?
Thanks in advance.
Wang Zhe
The conservation of angular momentum (a continuous quantity in classical mechanics) would not lead to the conservation of the number of vortex loops (a discrete, integer quantity). A different situation occurs in quantum mechanics, though; but this is not your question.
In optics, the number of optical vortices can change, but the total angular momentum per photon is conserved.
Dear all,
Thank you so very much for the answers!
The question stems from the seminal paper by Kosterlitz and Thouless (1973). They said, see attached, the first paragraph on pp.1198, "the system can change from one such state to another by the creation and separation of a pair of vortices..." in the context of the superfluid.
Please, could you point me out what mechanism causes the proliferation of vortex pairs in superfluid? During a discussion on Monday, Prof. Haldane told me that in the XY model the total number of vortex pairs are conserved. Is this considered to me a contradiction?
Thank you.
Very kind wishes,
Wang Zhe
It can be very dangerous to understand the real physics from model. Instead model should be constructed from real physics.
Topologically the total number of vortex loops can not be conserved. Turbulence is just a good example. You see when transit from laminar (with zero vortex loop) to turbulence (numerous vortex loops).
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