Two-dimensional point vortex gas

The two-dimensional point vortex gas is a discrete particle model used to study turbulence in two-dimensional ideal fluids. The two-dimensional guiding-center plasma is a completely equivalent model used in plasma physics.

General setup

The model is a Hamiltonian system of N points in the two-dimensional plane executing the motion

(In the confined version of the problem, the logarithmic potential is modified.)

Interpretations

In the point-vortex gas interpretation, the particles represent either point vortices in a two-dimensional fluid, or parallel line vortices in a three-dimensional fluid. The constant ki is the circulation of the fluid around the ith vortex. The Hamiltonian H is the interaction term of the fluid's integrated kinetic energy; it may be either positive or negative. The equations of motion simply reflect the drift of each vortex's position in the velocity field of the other vortices.

In the guiding-center plasma interpretation, the particles represent long filaments of charge parallel to some external magnetic field. The constant ki is the linear charge density of the ith filament. The Hamiltonian H is just the two-dimensional Coulomb potential between lines. The equations of motion reflect the guiding center drift of the charge filaments, hence the name.

gollark: I suspect SQLite would lose out somewhat in storage efficiency, but it could plausibly be faster for many things at runtime.
gollark: It's less complex for everyone interacting with it, since they can just... use SQLite, which has bindings for everything, instead of "zimlib". And by "efficiency" do you mean "space efficiency" or "lookup efficiency"? Because, as I said, SQLite would probably only add a few bytes per directory entry row, which is not a significant increase.
gollark: SQLite's overhead is pretty low, and the majority of the filesize is from the binary blobs which would remain the same in each.
gollark: It's less complex for them as the code is already there and written with a nice API, and "less efficient" how? Slightly more space on headers?
gollark: You could easily store the directory entry bits as an SQLite table.

See also
  • List of plasma (physics) articles

Notes

    References
    • Eyink, Gregory & Katepalli Sreenivasan (January 2006). "Onsager and the theory of hydrodynamic turbulence". Reviews of Modern Physics. 78 (1): 87–135. Bibcode:2006RvMP...78...87E. CiteSeerX 10.1.1.516.6219. doi:10.1103/RevModPhys.78.87.
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