axisymmetric homogeneous isotropic turbulence
 

If a turbulent velocity field is homogeneous and isotropic does it also mean that it is axisymmetric? Please comment

Re: axisymmetric homogeneous isotropic turbulence
 

Since Isotropic may be understand as : whatever the direction one looks he would see the same field and since Homogeneous may mean : whatever the place one looks from he would see the same field, the turbulent velocity fields you describe should be axisymmetric with repect to any given axis.