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 *k*_{i} is the circulation of the fluid around the *i*th 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 *k*_{i} is the linear charge density of the *i*th 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.

## See also

## 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.