Dear Sir

Your question is not clear enough: it is known that for flows in tube with triangular cross section the transversal circulation occurs at the angles (two vortexes in each angle). This process demands additional energy, so Darcy coefficient for such flows increases till 15% in comparison with tubes of round cross section. It is not clear what are "oscillating bluff bodies" ?

Dear Ms Dolgopolova,

Thank you for your reply. I would like to tell you the context in which I asked the question.

There has been quite a number of research on streamline topology induced by three vortices. Vortices generally occurs in pairs when we consider flow past bluff bodies ( cylinders or cube). But when oscillating bluff bodies are considered there can be more than three vortices can be shed in the fluid during one oscillation cycle. But the net circulation of all these vortices will be zero and therefore they move along the flow.

When we consider flow in bent tubes we find a pair of two vortices, and they are of opposite signs. Also the wing tip vortices are of opposite signs. The pair of like signed vortices occours in the wake of bluff bodies.

But I did not find any physical examples where three vortices rotating in the same sense (clockwise or otherwise) are found.

Regards,

Ananth

Dear Ananth,

Yes, I agree with you.  I also have not heard of tree vortices of the same same sign. May be you will find something useful in this book:

G.K. Batchelor "The theory of homogenious turbulence",  Cambridge Science Press 1982.

Thank you Dr. Dogopolova.

Greetings Ananth,

I discovered that you had an interesting question:

" But I did not find any physical examples where three vortices rotating in the same sense (clockwise or otherwise) are found. "

I may have such an example. Not three vortices, but for sure two vortices ... and highly likely sometimes four vortices - rotating in the same sense.

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Tornado research discovered multi-vortex tornadoes showing up on film 20 years ago or so. You can see several good examples on You Tube.

Dr Fugita, also noted back 40 or so years ago, that some tornadoes left 'J' shaped tracks, or debris trails, within the width of the main damage trace ... again indicating that there were sub-vortices within the main cyclonic storm.

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The answer to this problem appears to have something to do with the very top of the supercell, specifically the interaction of the 'Anvil' with that river of air known as a 'Jet Stream'.

The theory that is developing is that the largest storms in size can contain either 2 or 4 rotating sub-vortices - about the central axis of the storm.

To visualize this, an analogous situation would be similar to how a hand gun called a revolver works. Specifically a revolver chambered for four bullets.

All four revolving sub-vortices must exhaust upwards ... and then have their four exhaust bent 90-degrees outwards at 90, 180, 270 and 360-degrees compass bearings ... to form the Anvil.

With a powerful jet stream present, only but one of the sub-vortices will revolve into position - where the Jet Stream directly 'aspirates it' ... thus transferring 'the power' of the Jet Stream to just this sub-vortex.

As this vortex revolves (off center) about the central axis of the storm, it moves 90-degrees out of phase ... where now the exhaust of the sub-tornado is 90-degrees out of phase to that flow of the jet stream... thus it now is neutral, receives no help.

When the storm rotates the sub-vortex a further 90-degrees, the exhaust of the sub-tornado is now directed 'directly into the oncoming Jet Stream's flow'. The sub-tornado 'chokes', loses a great deal of power - and so weakens that it lifts off the ground.

The next 90-degree rotation results in a neutral position again, but a further 90-degree rotation now starts allining the exhaust of the sub-tornado - to that of the jet stream. The tornado powers up, drops down onto the ground. Power-On!

Thus, underneath the storm, one sees 'J' tracks of maximum debris damage.

Watch for further developments.

Thank you Mr. Bruce Zerr.

Greetings Mr Ananth Pai S,

I had a chance to look at my answer above. I then realized that my following statement below, about aspiration, 'is unclear' - and needs some clarification.

" With a powerful jet stream present, only but one of the

sub-vortices will revolve into position - where the Jet

Stream directly 'aspirates it".

Theoretically, looking downward - as if viewed from above the tornadic storm ...such a system would be revolving. The four subvorticies would all be some distance outward from the central spin axis of the main storm. Thus, the upward directed 'exhaust' of each of these four sub-vortexes, is being directed outward (by the Anvil) ... flowing away from the central spin axis of rotation.

Thus there is only one quadrant(out of four), where the wind vector-angle(direction) of the sub-vortexe's exhaust, now also aline's with the the same vector-angle(direction) of the Jet Stream. Thus the two flows aline. Thus the concept of the Jet Stream 'aspirating' the sub-vortex.

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An interesting prediction results from this theory - that the max velocity going to be discovered for Tornadoes, will closely match the max velocity of the strongest Jet Streams ... caused by this superposition.

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If you're interested, check out the resulting calculations for the Thermodynamics of the Forced Vortex, when the author takes one of the best gas mixtures possible, and then max's out the tip speed of one just past Mach-6.

The vortex can and does centrifuge huge quantities of Heat- outward, from the central core axis of rotation.

It operates on a totally different thermodynamic principle than the Heat Pump does ...i.e., Kinetic Energy.

https://www.google.com/patents/US4612646

-Bruce Zerr