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I am currently taking a fluids mechanics class and during the lecture the Prof. explained the following: when dealing with a 2D incompressible newtonian flow without external forces (gravity), vorticity is produced at a wall only when there is a pressure gradient.

When I think of pressure gradient I think of changes in pressure along the wall, and when I think of vorticity I think of fluid particles rotating about their own axis (e.g regions of flow were if you drop a pencil the pencil will start rotating). So I am trying to imagine a fluid with zero vorticity (irrotational flow) "flowing" on a flat plate. I see how the shear due to the contact with the plate can make the fluid particles at the wall spin therefore generating vorticity but I don't see how a pressure gradient comes into the picture.

Prof. also mentions and I quote: A pressure gradient along the wall is necessary to sustain a flux of vorticity from the surface to the fluid. I would appreciate if someone can clarify this definitions/concepts for me.

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    $\begingroup$ Perhaps he meant that pressure gradient along the wall is necessary to sustain viscous flow over a wall, which in turn produces viscosity? Flux of vorticity can be achieved by viscous diffusion of vorticity as well, but I think he was alluding to transport of vorticity. For transport you will need some body force to carry fluid elements from surface into fluid interior, a pressure gradient normal to wall (leaving out hydrostatic contribution) and not just along the wall. $\endgroup$
    – Deep
    Commented Oct 23, 2017 at 7:17

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