Trying to understand how the Vorticity vector is related to the flow

djpailo · November 18, 2014, 15:36

so we know vorticity is given by the curl of a vector field.

But that should give a vector that is perpendicular to the velocity vector u right?

Well from the book I'm reading, its begun to introduce vorticity and briefly touched upon vortex shredding (which I've read on another post here is 3D)

Now they've said that the vorticity is submerged in a potential flow with converging streamlines. Okay that is fine. So the velocity vector must be tangential to the streamlines right?

Then in the picture, how can omega and the velocity vector be pointing in the same direction?

Also, moving onto circulation, can anyone find me a decent diagram showing me the velocity vectors involved? I've looked around but can't find any that really helps me visualize it. As my understanding goes, I know the velocity vector component along the closed boundary (of the integral that we are taking) is multiplied with the incremental length etc. Okay. So am I right in thinking that vorticity would be perpendicular to this closed boundary?

As a final note, from the other thread here, it mentioned that vorticity cannot be destroyed in a 2D flow but it can be in a 3D flow. I don't really understand this, can anyone explain? The book alluded to elements of it but not quite in enough detail for me.

FMDenaro · November 18, 2014, 17:25

what book are you reading?

the vorticity in 2D viscous flows can be dissipated by the molecular diffusion, in inviscid flows you see that the material derivative of the vorticity is zero.

djpailo · November 18, 2014, 20:26

Quote:

Originally Posted by FMDenaro

what book are you reading?

the vorticity in 2D viscous flows can be dissipated by the molecular diffusion, in inviscid flows you see that the material derivative of the vorticity is zero.

P.A.Davidson, Introduction to Turbulence.

Yup, he alluded to this, but then before deriving this equation (showing angular momentum is zero) he said that vorticity cannot be created or destroyed, unlike velocity, within the interior of the fluid and I didn't understand that at all.

FMDenaro · November 19, 2014, 05:26

why don't you read some more fundamental bokk of aerodynamics?

November 18, 2014, 15:36	Trying to understand how the Vorticity vector is related to the flow	#1
djpailo New Member Join Date: Nov 2014 Posts: 8 Rep Power: 12	so we know vorticity is given by the curl of a vector field. But that should give a vector that is perpendicular to the velocity vector u right? Well from the book I'm reading, its begun to introduce vorticity and briefly touched upon vortex shredding (which I've read on another post here is 3D) Now they've said that the vorticity is submerged in a potential flow with converging streamlines. Okay that is fine. So the velocity vector must be tangential to the streamlines right? Then in the picture, how can omega and the velocity vector be pointing in the same direction? Also, moving onto circulation, can anyone find me a decent diagram showing me the velocity vectors involved? I've looked around but can't find any that really helps me visualize it. As my understanding goes, I know the velocity vector component along the closed boundary (of the integral that we are taking) is multiplied with the incremental length etc. Okay. So am I right in thinking that vorticity would be perpendicular to this closed boundary? As a final note, from the other thread here, it mentioned that vorticity cannot be destroyed in a 2D flow but it can be in a 3D flow. I don't really understand this, can anyone explain? The book alluded to elements of it but not quite in enough detail for me.

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November 18, 2014, 17:25		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,896 Rep Power: 73	what book are you reading? the vorticity in 2D viscous flows can be dissipated by the molecular diffusion, in inviscid flows you see that the material derivative of the vorticity is zero.

November 19, 2014, 05:26		#4
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,896 Rep Power: 73	why don't you read some more fundamental bokk of aerodynamics?