Vortex Filament Dynamics
Biot-Savart induced velocity field — vortex ring, leapfrogging, trefoil knot
Configuration
Single Vortex Ring
Leapfrogging Rings
Counter-rotating Pair
Trefoil Knot
Vortex Dipole Array
Circulation Γ:
1.0
Core radius δ:
0.15
Speed:
1.0
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Biot-Savart Law
dv = (Γ/4π) dl × r̂ / r²
v(x) = Γ/4π ∮ (dl×(x−x')) / |x−x'|³
Vortex ring self-velocity:
V = (Γ/4πR)[ln(8R/δ) − ½]
Kelvin impulse: P = ρΓπR²ẑ
Vorticity ω = ∇×v
Helicity: H = ∫v·ω dV
(topological invariant!)
Select a configuration