
The transfer of energy from larger scales of motion to smaller scales, as in turbulent flows.An energy cascade is the process by which energy in a turbulent fluid flows from large scales of motion down to smaller scales, until it is dissipated as heat at the smallest scales. This concept is central to understanding turbulence, which appears in everything from ocean currents and atmospheric flows to blood flow and star-forming clouds. The cascade explains why turbulence looks similar across vastly different systems: energy is injected at a large scale, then transferred stepwise through a hierarchy of eddies.
The concept was formalized by Lewis Fry Richardson in the 1920s, who described the cascade in a famous rhyme: 'Big whorls have little whorls, which feed on their velocity; and little whorls have lesser whorls, and so on to viscosity.' Kolmogorov's 1941 theory gave it a rigorous mathematical foundation.
In a turbulent flow, large eddies (whirls) are unstable and break into smaller eddies, which themselves break into even smaller ones. This continues until the eddies are so small that molecular viscosity becomes important, and their kinetic energy is converted into heat. The Russian mathematician Andrey Kolmogorov showed in 1941 that, in the 'inertial range' between the injection and dissipation scales, the energy spectrum follows a universal power law, independent of the fluid's details.
Understanding energy cascades helps improve weather prediction models, design more efficient aircraft wings, and even optimize industrial mixing processes.
The same cascade physics applies to quantum fluids like superfluid helium, where energy flows through quantized vortices instead of classical eddies.
















