Fluid Vortex Dynamics
Point vortex system — Hamiltonian mechanics: dxᵢ/dt = -∂H/∂yᵢ, dyᵢ/dt = ∂H/∂xᵢ
Controls
+ Vortex
− Vortex
Dipole
Clear
Preset
Speed:
1.0
x
Vortex strength:
1.0
Trail length:
80
Pause
System State
H = —
Vortices: 0
Physics
H = -1/4π Σᵢ<ⱼ ΓᵢΓⱼ ln|rᵢⱼ|
Conserved quantities:
• Hamiltonian H
• Linear impulse Σ Γᵢxᵢ
• Angular impulse Σ Γᵢrᵢ²
Vortex pairs (Γ>0, Γ<0) → straight propagation. Same-sign → orbit center of vorticity.