The isotropy definition in Wikipedia is uniformity in all orientations; it is derived from the Greek isos (ἴσος, "equal") and tropos (τρόπος, "way"). Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix an, hence anisotropy. Anisotropy is also used to describe situations where properties vary systematically, dependent on direction. Based on that definition can you please define in the context of fluid mechanics field the isotropic and anisotropic fluid flow. What is the difference between them?


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A flow is isotopic if the three principal components of the rate of strain tensor are all equal. This would correspond to a purely volumetric expansion or compression of the fluid.


Imagine you are sitting at a point in a flow and everything is frozen around you. You look forward, then to your left, then to your right. If the flow looks the same in each direction*, it is isotropic.

On the other hand, if you look left and it is very different from what you see when you look ahead, it is anisotropic.

* What does it mean for a flow to "look the same?" Well, it depends. But for a turbulent flow, it usually means that it has the same statistics in space when you consider all the points along the direction you are looking.

It is sometimes more obvious when you think about what is not isotropic -- imagine you are standing on a channel wall (within the boundary layer) as the flow moves past you. If you look parallel to the wall, it's probably statistically similar in all directions parallel to the wall. But, if you look up (normal to the wall), it's obviously not the same as the parallel directions. There's a velocity gradient and a big change in vorticity. In this case, the flow is anisotropic -- statistics normal to the wall do not look the same as parallel to the wall.


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