Point Vortex Gas — 2D Euler Flow

Point vortices in 2D Euler flow are an exactly solvable Hamiltonian system. Each vortex induces velocity v = Γ/(2πr) on others, tangential to the separation vector. Onsager (1949) predicted negative-temperature clustering of same-sign vortices.

Parameters

Num vortices 20 dt (step size) 0.5 Softening ε 5

Conserved

H (energy): —

Px: —

Py: —

L (angular): —

Red = +Γ, Blue = −Γ
H = −Σᵢ<ⱼ ΓᵢΓⱼ ln|rᵢⱼ| / 2π
Negative T: same-sign vortices cluster