TURBULENT MIXING
Batchelor spectrum: E_θ(k) ~ k⁻¹
Richardson dispersion:
⟨r²(t)⟩ ~ εt³ (2-particle)
FSLE (finite-size Lyapunov):
λ(δ) = (1/τ)·ln(δ₁/δ₀)
Kraichnan-Batchelor regime:
smooth velocity field → exponential
separation → Lyapunov exponents
2D turbulence: inverse energy cascade
E(k) ~ k⁻⁵/³