Isotropic turbulence

Short definition of Isotropic turbulence
Turbulence properties are independent of direction

This is the common definition for Isotropic turbulence, but other definitions maybe discussed within the wiki.

A state whereby the velocity components and their derivatives are independent of direction. If this is not the case the turbulence is said to be anisotropic.

The largest scale eddies of a turbulent flow contain the bulk of the turbulence kinetic energy of the flow. These eddies tend to be somewhat organized, and their shape and size reflect the physical boundaries and other characteristics of the flow. The large eddies break down into smaller eddies through flow interactions and they eventually reach a size at which they tend to be isotropic – they do not have a preferred orientation and appear similar from all points of view. For isotropic turbulence, the irreversible rate of dissipation of the turbulence kinetic energy through viscous friction, ϵ, is related to the variance of any component of the (rate of) strain or the (rate of) shear, by
[math]\displaystyle{ \begin{equation} \varepsilon =15\nu \overline{\left(\frac{\partial u}{\partial x} \right)^2} = \frac{15}{2} \nu \overline{\left(\frac{\partial u}{\partial z} \right)^2} \label{eq:epsilon_1} \end{equation} }[/math]
where [math]\displaystyle{ \partial u/\partial x }[/math] is any one of the three-components of strain, [math]\displaystyle{ \partial u/\partial z }[/math] is any one of the six components of shear, [math]\displaystyle{ \nu }[/math] is the kinematic viscosity, and the overline denotes a spatial average .