Energy cascade
Richardson's picture: energy injected at large scales is handed down, eddy by eddy, to smaller scales until viscosity dissipates it as heat.
Definition
In turbulent flow, energy enters at the large scales (driven by pumps, winds, stirrers, boundary conditions) and exits at the small viscous dissipation scale as heat. The intermediate region — the inertial range — is a cascade: large eddies break up into smaller eddies, which break up into still smaller ones, with energy handed down the ladder at a constant rate ε.
The picture was put into verse by Lewis Fry Richardson in 1922 and made quantitative by Kolmogorov in 1941. Kolmogorov's dimensional argument says the spectrum of kinetic energy E(k) in the inertial range must scale as ε^(2/3) k^(−5/3). Experimentally the law holds across many decades of k in everything from wind-tunnel turbulence to the atmospheric boundary layer to astrophysical plasmas.
History
Pictured by Richardson in 1922; quantified by Kolmogorov in 1941.