Lagrangian Coherent Structures

FTLE (finite-time Lyapunov exponent) field for the double-gyre flow — reveals transport barriers and mixing

Double Gyre Flow

Amplitude ε: 0.25 Frequency ω: 3.14 Integration time T: 10.0 Grid resolution: 80

Computation

Color map:

u = -πA·sin(πf(x,t))cos(πy) v = πA·cos(πf(x,t))sin(πy)·f'(x,t) f(x,t) = ε·sin(ωt)x² + (1-2ε·sin(ωt))x FTLE = (1/T)·log(√λ_max(C)) C = (∂Φ_T/∂x)ᵀ(∂Φ_T/∂x)

Ridges in FTLE field = LCS = material barriers to transport. High FTLE (bright) = strong separation of nearby particles.