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Consider flow over a cylinder. At a high enough Reynold's Number, the strength of the adverse pressure gradient becomes too large for the boundary layer to be able to remain attached to the cylinder. Hence, the fluid is decelerated to rest, and the flow eventually reverses at some point.

The image below shows the behaviour of flow at different Re: Text

At Re = 20, we see that the flow has separated. The separated flow produces two circulation regions just downstream of the cylinder.

I somewhat understand this is due to a velocity gradient between the reverse flow and the forward flow, which I believe is called a shear layer? Also, I have heard that an inflection point in the velocity profile leads to instability in the flow (i.e. the flow is unstable to random disturbances) which leads to the production of vortices at higher Re.

So my question can be split into 2 parts:

1) Why does the velocity gradient lead to vortex formation in the separated flow over a cylinder?

2) More generally, why do velocity gradients lead to formation of vortices in any flow? (Cavity flows, mixing layers, etc.)

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The reason is to keep velocity gradients small. This in turn means that some of the fluid medium which is trapped in a cavity or a region of separated flow will be moved in the direction of the outer flow. To counter this transport of trapped medium, a reverse movement at the opposite side of that region is needed to maintain uniform density.

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  • $\begingroup$ Thanks for your answer. In a compressible flow, does this mean that you would not get vortices? Because there is no need for a uniform density to be maintained anymore. $\endgroup$ Aug 16, 2022 at 12:08
  • $\begingroup$ @MoosaSaghir Please consider first what causes density changes. The speed in vortices puts them firmly in the subsonic range where compressibility has little influence. Besides, if your Re is only 20, your Mach will also be small. $\endgroup$ Aug 16, 2022 at 15:18

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