Fluid Chaos

Physics: Lorenz (1963) discovered chaos studying fluid convection. Lyapunov exponent λ > 0 means nearby trajectories diverge as δ(t) ~ δ₀·e^(λt). Predictability horizon T ~ λ⁻¹·ln(ε₀/δ) — doubling measurement precision only extends forecast by ln(2)/λ. Richardson (1926) turbulent pair separation: ⟨|Δr|²⟩ ~ ε t³ (super-diffusive), where ε is energy dissipation rate. The "butterfly effect" (Lorenz): a butterfly flapping wings in Brazil can affect a tornado in Texas weeks later.