Time-periodic flow, stretch and fold, Poincaré sections
Particles
Poincaré Section
Stretch Map
A (amplitude): 1.0
ω (frequency): 1.0
Particles: 500
Passive tracers in the double-gyre flow (Shadden 2005): ψ(x,y,t) = A·sin(πf(x,t))·sin(πy), with f(x,t) = ε·sin(ωt)·x² + (1−2ε·sin(ωt))·x. Even though the velocity field is smooth, chaotic advection creates exponential stretching of material blobs — a key mechanism for mixing in the ocean. Poincaré sections reveal KAM tori (ordered regions) and chaotic seas.