The two-dimensional point vortex gas is a discrete particle model used to
study turbulence in two-dimensional
ideal fluid
In physics, a perfect fluid is a fluid that can be completely characterized by its rest frame mass density \rho_m and ''isotropic'' pressure ''p''. Real fluids are "sticky" and contain (and conduct) heat. Perfect fluids are idealized models in whi ...
s. The two-dimensional guiding-center plasma is a completely equivalent model used in plasma physics.
General setup
The model is a
Hamiltonian system
A Hamiltonian system is a dynamical system governed by Hamilton's equations. In physics, this dynamical system describes the evolution of a physical system such as a planetary system or an electron in an electromagnetic field. These systems can ...
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 fluid dynamics, a vortex ( : vortices or vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in th ...
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
In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in ...
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
In physics, the motion of an electrically charged particle such as an electron or ion in a plasma in a magnetic field can be treated as the superposition of a relatively fast circular motion around a point called the guiding center and a relativ ...
drift
Drift or Drifts may refer to:
Geography
* Drift or ford (crossing) of a river
* Drift, Kentucky, unincorporated community in the United States
* In Cornwall, England:
** Drift, Cornwall, village
** Drift Reservoir, associated with the village
...
of the charge filaments, hence the name.
See also
*
List of plasma (physics) articles
Notes
References
*{{cite journal , author=Eyink, Gregory , author2=Katepalli Sreenivasan , name-list-style=amp , title=Onsager and the theory of hydrodynamic turbulence , journal=Reviews of Modern Physics , volume=78 , issue=1 , date=January 2006 , pages=87–135 , doi=10.1103/RevModPhys.78.87 , bibcode=2006RvMP...78...87E, citeseerx=10.1.1.516.6219
Turbulence models
Plasma physics