[cvillescas]

Hi to everyone,

I am new in CFD-online. I hope this is the right place to post a theoretical question. Here it goes.

I've heard many times about an "intrinsic" assumption of isotropic turbulence in linear eddy-viscosity-based turbulence models. However, I do not quite understand this assertion. From what I understand, mathematically, isotropic turbulence means that the Reynolds stress is a diagonal matrix where every element is equal. In the eddy viscosity hypothesis for incompressible flows:

The first term in the RHS is isotropic, but the second term it appears to me that is modelling anisotropy, as it has non-zero terms outside the diagonal. Then, what do people mean by "assumption of isotropic turbulence"?

Do they refer to the transport equation for turbulent kinetic energy? Here is stated that turbulent diffusion is what is assumed to be isotropic. (I wouldn't understand anisotropic diffusion, though. What would make diffusion to have a preferential direction?)

Could someone help me with that? Thank you for your time.

Carla