Isotropic turbulence means that there is no mean shear, rotation or buoyancy effects in the flow as this can lead to anisotropy.
Homogeneous turbulence means that there are no mean flow gradients.
In another way isotropy deals with invariance in rotation and homogeneity deals with invariance in translation.
Isotropic flows can have a homogeneous or non-homogeneous microscopic structures.
In many cases, the flow can be homogeneous and anisotropic . The Homogeneous Anisotropic Turbulence (HAT) is observed in many problems, such atmospheric flows…
Isotropic turbulence means that there is no mean shear, rotation or buoyancy effects in the flow as this can lead to anisotropy.
Homogeneous turbulence means that there are no mean flow gradients.
In another way isotropy deals with invariance in rotation and homogeneity deals with invariance in translation.
Isotropic flows can have a homogeneous or non-homogeneous microscopic structures.
In many cases, the flow can be homogeneous and anisotropic . The Homogeneous Anisotropic Turbulence (HAT) is observed in many problems, such atmospheric flows…
For the isotropic-nonhomogeneous flow, the explosion of a bomb is an example. The surrounding air expands in the same rate in all the direction, but is certainly not homogeneous.
For the homogeneous-anisotropic flow, turbulent channel flow, or uniformly sheared turbulence. For the latter example, it is anisotropic, and homogeneous in all three directions. The uniformly sheared turbulence has been extensively studied, e.g., Cambon JFM, 1997, 303–332.