Isotropic turbulence

The isotropic turbulence belongs together with the homogeneous turbulence to the simplest idealized flow forms, through which turbulent flows can be described in a simplified manner .

In isotropic turbulence, all statistical properties of the flow (mean speed fluctuations) are independent of direction:

${\displaystyle {\overline {u'^{2}}}={\overline {w'^{2}}}={\overline {v'^{2}}}}$

This goes hand in hand with the fact that the statistical properties are also invariant (rotationally invariant ) when the coordinate system is rotated and mirrored on any surface .

The Reynolds' stresses are thus the same in all spatial directions:

The following applies to normal stresses :

${\displaystyle \tau _{ii}=-\rho {\overline {u'^{2}}}=-\rho {\overline {w'^{2}}}=-\rho {\overline {v'^{2}}}=konstant}$

The following applies to the shear stresses :

${\displaystyle \tau _{ij}=-\rho {\overline {u'v'}}=-\rho {\overline {u'w'}}=-\rho {\overline {v'w'}}=0}$

The isotropic turbulence can be approximately realized in the experiment, the flow behind a turbulence grid is approximately isotropic.