Vortex stretching is the primary mechanism by which turbulence sustains itself in 3D flows. When a vortex tube is stretched along its axis (by the strain field of surrounding fluid), conservation of angular momentum causes the vorticity ω to intensify: Dω/Dt = (ω·∇)u + ν∇²ω. The term (ω·∇)u is the stretching term — absent in 2D flows, it drives the energy cascade to small scales. This mechanism has no counterpart in 2D, explaining why 2D turbulence behaves so differently (inverse energy cascade).
Vortex tube cross-section — color = vorticity magnitude
ω(t) — vorticity growth
ω₀ = —
ω(t) = —
r(t) = —
Amplification = —