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.
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.)
Interpretationsedit
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 centerdrift of the charge filaments, hence the name.
Notesedit
Referencesedit
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. CiteSeerX10.1.1.516.6219. doi:10.1103/RevModPhys.78.87.
January 01, 1970
dimensional, point, vortex, dimensional, point, vortex, discrete, particle, model, used, study, turbulence, dimensional, ideal, fluids, dimensional, guiding, center, plasma, completely, equivalent, model, used, plasma, physics, contents, general, setup, interp. 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 Contents 1 General setup 2 Interpretations 3 Notes 4 ReferencesGeneral setup editThe model is a Hamiltonian system of N points in the two dimensional plane executing the motion k i d x i d t H y i k i d y i d t H x i displaystyle k i frac dx i dt frac partial H partial y i qquad k i frac dy i dt frac partial H partial x i nbsp In the confined version of the problem the logarithmic potential is modified Interpretations editIn 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 Notes editReferences editEyink Gregory amp 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 Retrieved from https en wikipedia org w index php title Two dimensional point vortex gas amp oldid 1187111431, wikipedia, wiki, book, books, library,