[CFD_USER_]

How do you prove that boundary layer has Vorticity?

[FMDenaro]

Originally Posted by CFD_USER_

How do you prove that boundary layer has Vorticity?

the x-component of the velocity depends on the normal direction, therefore du/dy does not vanish and that is a component of the vorticity

[adrin]

To be careful/precise - and food for thought - it is not sufficient to suggest that du/dy is part of vorticity and hence there is vorticity in the boundary layer. The other component of vorticity is dv/dx. How do you know that the two components don't cancel each other out?

So, a more rigorous response based on math or physics is necessary!

Assume the wall is stationary, so the wall velocity is zero everywhere. This means dv/dx is zero _at_ the wall. Since there is free stream velocity, u_inf, and u_wall = 0, we have (only) du/dy _at_ the wall (assuming 2D). So, there is vorticity (generation) _at_ the wall, which then diffuses away from the wall and convects in the boundary layer. If the flow is incompressible, the wall is the only source of vorticity generation.

adrin

[FMDenaro]

Originally Posted by adrin

To be careful/precise - and food for thought - it is not sufficient to suggest that du/dy is part of vorticity and hence there is vorticity in the boundary layer. The other component of vorticity is dv/dx. How do you know that the two components don't cancel each other out?

So, a more rigorous response based on math or physics is necessary!

Assume the wall is stationary, so the wall velocity is zero everywhere. This means dv/dx is zero _at_ the wall. Since there is free stream velocity, u_inf, and u_wall = 0, we have (only) du/dy _at_ the wall (assuming 2D). So, there is vorticity (generation) _at_ the wall, which then diffuses away from the wall and convects in the boundary layer. If the flow is incompressible, the wall is the only source of vorticity generation.

adrin

But in the BL, v=O(Delta) and does not vary on x

[adrin]

My explanation was based on the origin of vorticity (at the wall) and its evolution due to diffusion and convection, and it leaves no room for "what if" - except if the wall moves or there's flow through. One can also provide order-of-magnitude justification.

Having said that, v does vary with x in the boundary layer (when it's not fully developed yet, though very small)

adrin

adrin