Turbulence Cascade — Energy Budget

Richardson cascade: eddies break into smaller eddies, energy flows to dissipation scale

Richardson Cascade

Lewis Fry Richardson (1922): "Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity." Energy injected at scale L cascades self-similarly through an inertial range. At the Kolmogorov scale η, viscosity converts kinetic energy to heat.

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Energy Budget

Each level holds a fraction of total energy. The −5/3 spectrum emerges from self-similar cascade with ε = const through levels.