Richardson had it right: large eddies spawn smaller ones, which spawn smaller ones still, until viscosity kills them. What he missed: each generation transfers exactly what it needs to feed the next.
A turbulent flow dissipates its energy by stages. Energy injected at large scales descends toward small scales where viscosity can absorb it. This cascade follows Kolmogorov's law: at each scale ℓ, the energy transfer rate ε remains constant.
$$v(\ell) \sim (\varepsilon \ell)^{1/3}$$
No free parameters. No optimization. Turbulence does not improvise,it executes a strict budget, scale by scale.
Apparent anarchy conceals perfect accounting. No matter the fluid, no matter the geometry,Kolmogorov's -5/3 slope appears wherever the energy cascade establishes itself.
Doctrine
Chaotic systems are not free. They optimize under constraint. Turbulence chooses its scales by necessity, not by chance.
Vecteur ouvert
Kolmogorov's cascade stops at the Kolmogorov scale, where viscosity absorbs everything. Is there an equivalent in systems that do not dissipate energy? A cascade without a floor, where transfer descends indefinitely without ever finding its own terminus?
