Hi Dear Friends.

What are the definitions of ISOTROPIC turbulence and HOMOGENEOUS turbulence?

Thanks.

Isotropic turbulence means that the normal components of the Reynolds stress tensor are equal each other. I.e. u'u'=v'v'=w'w'. In other words the turbulent correlations are independent of the direction

Homogeneous turbulence means that spatial gradients of the turbulent correlations are equal zero.

Isotropic homogeneous turbulence is the idealisation which can never be found in the real engineering flows but can be artificially generated in wind tunnel by means of so called turbulent grid

isotropic originally means independent of rotation of coordinates.

homogeneous means independently of translation.

but, when talking about isotropic turbulence, we also imply it's already independent of translation.

look at Batchelor 's book on Homogeneous turbulence.