Three-regime turbulent pair-separation model

For positive initial separation below the Kolmogorov length scale, a phenomenological pair-dispersion model has smooth-flow exponential stretching, inertial-range Richardson pair dispersion, and diffusive large-scale pair dispersion beyond the integral scale of turbulence. A positive Lyapunov exponent is needed for the first regime, scale locality and initial-memory loss for the second, and integrable relative-velocity autocorrelation for the third. The inertial-range crossing time is of order $L^{2/3}{ϵ}^{-1/3}$, one outer eddy turnover time.