Turbulence

Turbulence is a ubiquitous state for many flows in nature and engineering. As the flow velocity is increased, the nonlinear energy transfer generates fluid motion in a broad range of scales forming continuous wave number spectra of the kinetic energy. In isotropic homogeneous incompressible turbulence, energy flux is related to the third‐order velocity structure function via the Kolmogorov 4/5 law. In three‐dimensional turbulence, the energy is transferred from large to smaller scales in the process of the energy cascade. In two‐dimensional turbulence, energy is transferred from smaller to larger scales, the inverse energy cascade. Turbulence greatly increases the rate of mixing in fluids and dispersion. Transport of matter in turbulent flows requires Lagrangian description, in which the observer follows the fluid particles wherever they move. Here, we review the approaches to turbulence description in two and three dimensions.