Can Inviscid Flows Be Rotational?

[jason.bourne]

viscous flows are always rotational because of shear stress that is exerted on the fluid element due to viscosity.

what about the inviscid flows? can they be rotational ? if yes then what are the factors which makes the inviscid flows rotational?

 

[minger]

By rotational do you mean have vorticity? If so then yes, in fact the fundamental equations can be written in terms of vorticity rather than velocity by taking the curl of the equations.

http://en.wikipedia.org/wiki/Vorticity][/PLAIN]
For any flow, you can write the equations of the flow in terms of vorticity rather than velocity by simply taking the curl of the flow equations that are framed in terms of velocity (may have to apply the 2nd Fundamental Theorem of Calculus to do this rigorously). In such a case you get the vorticity transport equation which is as follows in the case of incompressible (i.e. low mach number) fluids, with conservative body forces

$$\frac{D\omega}{Dt} = \omega \cdot \nabla u + \nu \nabla^2 \omega$$

 

[jason.bourne]

okay fine but what is it that is making it to rotate?
like in viscous flows its the shear stress that causes the rotation of the fluid element.

 

[minger]

Anything. Don't think of vorticity as a whirlpool in your bathtub; any time the flow turns even a little bit, it has vorticity.

 

[jason.bourne]

viscous flows are always rotational because of the shear stress exerts a rotational moment about the center of the element .

what about the inviscid flows? what causes rotation in an inviscid flows?
shear stress is absent. The only forces acting on the fluid element are pressure force and weight. Weight acts through COG, pressure acts normal to the element surface, neither can cause rotation , then what is causing rotation in inviscid flows?

i don't think it can just rotate at its own wish. There has to be something right?

 

[FireBones]

You may want to look up Helmholtz's third theorem.

 

[boneh3ad]

When using inviscid flow, usually a point vortex is added to the model to simulate the vorticity present in an actual viscous flow (for example, the trailing edge of an airfoil). Vorticity is conserved in potential flow, so you have to introduce it somewhere in order for the flow to make sense in real problems. That sort of highlights the problem with potential flow; you can't fully model viscous phenomena with inviscid flow, and the real world is viscous.

 

[Nick RT]

Hey Jason,

I don't know know whether you've figured out your answer by now or not but I'll give you mine. This is a good question and here's how it works.

Consider solid body rotation of a fluid. Viscous forces are negligible but what causes the fluid particles to rotate is the pressure gradiant in the normal direction to the streamlines. There is no moment acting on the particles but each fluid particle rotates as it moves along the streamlines. I hope it makes sense if you need more help send me an email nikan4now@yahoo.com