Changes in the flow due to moving bodies (Batchelor))

[nik2011]

Please help me make sure I understand the following right. Or correct me in case of misunderstanding.

...explanation of the formation of the standing eddies...
we may say that, as R increases and the convection of vorticity becomes more effective than diffusion of vorticity, more and more vorticity is carried round to the rear of the cylinder, the vorticity being of negative sign (or clockwise rotation) near the upper surface and of positive sign near the lower surface. Ultimately there is more vorticity of each sign at the rear of the cylinder than is needed for the satisfaction of the no-slip condition there, and a backward-moving fluid is induced near the surface...
(Batchelor's "An introduction to fluid dynamics" 4.12. Changes in the flow due to moving bodies as R increases from 1 to about 100)

1. Because of vorticity the boundary layer separates and this separated part of the boundary layer is reversed in direction because of adverse pressure gradient? (This question is the most important)

2. Equation for amount of vorticity needed to satisfy the no-slip condition doesn't exist, correct?
3. Beyond the boundary layer the flow is irrotational (at least, until separation occurs)?
4. What do terms vorticity diffusion and vorticity convection mean? Do they have a strict definition? (If so, could you please give me a link to the definitions)

Thank you!

 

[Valerie Park]

1. No, the boundary layer separates because of adverse pressure gradient and the vorticity helps to sustain the separation by providing additional momentum to the separated flow.2. Correct.3. Yes.4. Vorticity diffusion refers to the process in which vorticity is mixed by the flow's turbulent eddies. Vorticity convection refers to the process in which the vorticity is advected by the flow.