Point Vortex Dynamics
Hamiltonian vortex motion in 2D ideal fluid
Controls
Number of vortices
5
Initial config
Random
Symmetric ring
Vortex row
Opposite pairs
Time step
0.10
Trail length
150
Show streamlines
Reset
Pause
H = —
P_x = —
Equations of motion:
ẋᵢ = −Σⱼ Γⱼ(yᵢ−yⱼ)/(2πrᵢⱼ²)
ẏᵢ = +Σⱼ Γⱼ(xᵢ−xⱼ)/(2πrᵢⱼ²)
Hamiltonian: H = −Σᵢ<ⱼ ΓᵢΓⱼ·ln(rᵢⱼ)/2π
Red = positive Γ, Blue = negative Γ. Conservation: H, Px, Py, angular momentum.