Energy cascade

In continuum mechanics, an energy cascade refers to the transfer of energy from large scales of motion to the small scales (called a direct energy cascade) or a transfer of energy from the small scales to the large scales (called an inverse energy cascade). This transfer of energy between different scales requires that the dynamics of the system is nonlinear. Strictly speaking, a cascade requires the energy transfer to be local in scale (only between fluctuations of nearly the same size), evoking a cascading waterfall from pool to pool without long-range transfers across the scale domain. —Lewis F. Richardson, 1922The largest motions, or eddies, of turbulence contain most of the kinetic energy, whereas the smallest eddies are responsible for the viscous dissipation of turbulence kinetic energy. Kolmogorov hypothesized that when these scales are well separated, the intermediate range of length scales would be statistically isotropic, and that its characteristics in equilibrium would depend only on the rate at which kinetic energy is dissipated at the small scales. Dissipation is the frictional conversion of mechanical energy to thermal energy. The dissipation rate, ε, may be written down in terms of the fluctuating rates of strain in the turbulent flow and the fluid's kinematic viscosity, ν. It has dimensions of energy per unit mass per second. In equilibrium, the production of turbulence kinetic energy at the large scales of motion is equal to the dissipation of this energy at the small scales.