Understanding Vorticity and Propagation of Ring Vortex

[skywo1f]

my question relates to the axisymmetrical ring vortex.
i know that vorticity must remain constant within a tube, (helmholtz vortex theorem 2)
so does that mean that the vortex lines on the outside of the ring are longer (spinning faster)
than the ones on the inside?

also is that what makes vortex rings propagate?
like, does the ring draw energy from its translational speed and put it into maintaining its vorticity, or is it the other way around?
or am i completely off?

 

[Terry Day]

skywolf, the particles must all move at the same speed as the speed is determined by the pressure. So particles close to the centre or periphery are at the same speed and so have different RPM. That means they shear which helps the vortex to decay. The ring vortex swims by entrainment in front and ejection aft, almost propulsion by negative drag. There are two kinds of vorticity, convection as in a smokers ring and diffusion as in airfoil lift. See my PDF through the website www.newfluidtechnology.com[/URL] called "lift and the Coanda Effect"

 

[sir-pinski]

Yes, you are correct that the vorticity must remain constant within a tube, as stated by the Helmholtz vortex theorem. This means that the vorticity, which is a measure of the local rotation of fluid particles, is conserved along the vortex lines.

In the case of an axisymmetrical ring vortex, the vorticity is highest at the center and decreases towards the edges of the ring. This is because the fluid particles at the center have a smaller radius to travel around and therefore spin faster than those on the outer edges.

As for the propagation of vortex rings, it is a result of the interaction between the vorticity and the translational speed of the ring. The vorticity creates a self-induced velocity, which helps to maintain the ring's structure and keep it moving. At the same time, the translational speed of the ring also affects the vorticity, causing it to stretch and change shape as the ring moves through the fluid.

So, it is a combination of both factors that contribute to the propagation of vortex rings. The ring draws energy from its translational speed to maintain its vorticity, while the vorticity also plays a role in keeping the ring moving and intact. Therefore, you are not completely off in your understanding.

I hope this helps to clarify your understanding of the axisymmetrical ring vortex and its propagation. Keep exploring and learning about vorticity and fluid dynamics, as it is a fascinating subject with many real-world applications.