Richardson Pair Dispersion — Turbulent Cascade
⟨r²(t)⟩ ~ ε t³: Richardson's law, Kolmogorov turbulence, pair separation
Parameters
Dissipation ε:
1.0
N pairs:
80
Initial sep r₀:
2.0
Inertial range L:
50
Reset Pairs
Add Pairs
Theory
d/dt⟨r²⟩ = ε r^(4/3) (Kolmogorov)
⟨r²(t)⟩ = g ε t³ (Richardson 1926)
g ≈ 0.5 (Richardson constant)
v_rel ~ ε^(1/3) r^(1/3) (K41 scaling)
η=(ν³/ε)^(1/4): Kolmogorov scale