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.)
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 equations of motion reflect the guiding center drift of the charge filaments, hence the name.