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Old   June 28, 2000, 08:21
Default vorticity
  #1
oliver mulryan
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What are the non-slip boundary conditions in terms of vorticity? Is it that all the vorticity components are equal to zero?
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Old   June 28, 2000, 14:14
Default Re: vorticity
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John C. Chien
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(1). The non-slip boundary condition is, u=0,v=0,w=0 at the wall. (2). You can substitute this condition into the vorticity definition at the wall, using one-sided and central difference schemes to arrive at the vorticity components. (3). I think, only the normal to the wall component of the vorticity will be zero. But you will have to double check on it. (it the wall is not rotating about the axis normal to the wall).
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Old   June 28, 2000, 17:22
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Oliver
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First of all thanks for the insight John.

Vorticity is defined as the curl of the velocity vector and the flow gradient are highest @ the wall,(A bounday layer represented in terms of vorticity is a reflection of a normal velocity boundary layer about the normal axis.) this seems to imply, that @ least one component of Vorticity if not 2 are going to be a Max at the wall in a 3D Boundary layer?. If this is the case, which components are Max? and which are zero?, in a 3D cylindrical Axisymmetric coordinate system, which contains rotating fluid

Thanks again

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Old   June 28, 2000, 17:36
Default Re: vorticity
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Kalyan
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Yes, only the normal component of vorticity needs to zero.
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Old   July 5, 2000, 13:39
Default Re: vorticity
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Adrin Gharakhani
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In what (numerical) context do you need the vorticity boundary condition? In at least one method, it is the velocity boundary condition at the wall that you use!

Physically, as others have already mentioned only the normal component of vorticity is zero (for solid walls) - this is true because the latter is a function of the tangential gradients of the velocities at the wall (which are zero). However, the other two components of vorticity are non-zero since they are equivalent to the normal gradient of the wall velocity (one term is), which is non-zero

Adrin Gharakhani
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