Smoke and a mirror

Etna jellyfish pairGrammie always grimaced when Grampie lit up one of his cigars inside the house.  We kids grinned though because he’d soon be blowing smoke rings for us.  Great fun to try poking a finger into the center, but we quickly learned that the ring itself vanished if we touched it.

My grandfather can’t take credit for the smoke ring on the left — it was “blown” by Mt Etna.  Looks very like the jellyfish on the right, doesn’t it?  When I see two such similar structures, I always wonder if the resemblance comes from the same physics phenomenon.

This one does — the physics area is Fluid Dynamics, and the phenomenon is a vortex ring. We need to get a little technical and abstract here: to a physicist a fluid is anything that’s composed of particles that don’t have a fixed spatial relationship to each other. Liquid water is a fluid, of course (its molecules can slide past each other) and so is air.  The sun’s ionized protons and electrons comprise a fluid, and so can a mob of people and so can vehicle traffic (if it’s moving at all).  You can use Fluid Dynamics to analyze motion when the individual particles are numerous and small relative to the volume in question.

Ring x-section

Adapted from a NOAA page

You get a vortex whenever you have two distinct fluids in contact but moving at sufficiently different velocities.  (Remember that “velocity” includes both speed and direction.)  When Grampie let out that little puff of air (with some smoke in it), his fast-moving breath collided with the still air around him.  When the still air didn’t get out of the way, his breath curled back toward him.  The smoke collected in the dark gray areas in this diagram.

That curl is the essence of vorticity and turbulence.  The general underlying rule is “faster curls toward slower,” just like that skater video in my previous post.  Suppose fluid is flowing through a pipe.  Layers next to the outside surface move slowly whereas the bulk material near the center moves quickly.  If the bulk is going fast enough, the speed difference will generate many little whorls against the circumference, converting pump energy to turbulence and heat.  The plant operator might complain about “back pressure” because the fluid isn’t flowing as rapidly as expected from the applied pressure.

But Grampie didn’t puff into a pipe (he’s a cigar man, right?), he puffed into the open air.  Those curls weren’t just at the top and bottom of his breath, they formed a complete circle all around his mouth.  If his puff didn’t come out perfectly straight, the smoke had a twist to it and circulated along that circle, the way Etna’s ring seems to be doing (note the words In and Out buried in the diagram’s gray blobs).  When a vortex closes its loop like that, you’ve got a vortex ring.

A vortex ring is a peculiar beast because it seems to have a life of its own, independent of the surrounding medium.  Grampie’s little puff of vortical air usually retained its integrity and carried its smoke particles for several feet before energy loss or little fingers broke up the circulation.

To show just how special vortex rings are, consider the jellyfish.  Until I ran across this article, I’d thought that jellyfish used jet propulsion like octopuses and squids do — squirt water out one way to move the other way.  Not the case.  Jellyfish do something much more sophisticated, something that makes them possibly “the most energy-efficient animals in the world.”

jellyfish vortices

Thanks to a very nice piece of biophysics detective work (read the paper, it’s cool, no equations), we now know that a jellyfish doesn’t just squirt.  Rather, it relaxes its single ring of muscle tissue to open wide.  That motion pulls in a pre-existing vortex ring that pushes against the bell.  On the power stroke, the jellyfish contracts its bell to push water out (OK, that’s a squirt) and create another vortex ring rolling in the opposite direction.  In effect, the jellyfish continually builds and climbs a ladder of vortex rings.

Vortex rings are encapsulated angular momentum, potentially in play at any size in any medium.

~~ Rich Olcott


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