Last time I promised you a flame that will not hold still. Light a single candle and it will.
It burns steady. Tape two together and you get an occasional twitch, nothing you could set a watch by. Tape three together and the flame breaks into a clean beat — ten to twelve times a second, holding amplitude and rate for as long as the wax lasts. Three is the threshold, and the threshold is the whole story.
The beat is old news. Chamberlin and Rose reported it at the first Combustion Symposium in 1948: luminous flames flickering about ten times a second, the rate “not greatly affected by the flame conditions.” That last clause is the strange one, and eighty years of measurement have made it stranger.
The rate is not about burning. Pool fires, jet flames, candles and Bunsen burners sit on one line: f ≈ 1.5/√D, with D the width of the fire in metres. There is no fuel term in it. Paraffin, methane, heptane — same line. Written the way it is usually derived, the constant turns out to be gravity: f ≈ 0.48√(g/D). And the reason to trust that version is that experiments run at different gravities land on it too. Change the pull and you change the pitch.
So what is doing the oscillating is not the fire.
Hot gas rises off the flame; the room’s air stands still around it. Between them is a shear layer, and shear layers roll up. What forms is a vortex ring — a smoke ring of hot and cold air encircling the flame, fed from below. And a growing ring cannot grow forever. Past a threshold of circulation — roughly universal across ring-making of every kind — it is too strong to stay attached to the sheet feeding it, and lets go. On the way out it pinches the flame’s waist, a bright bubble breaks off the top and burns out in the air, and a new ring begins at the base.
That is the flicker. The flame is the dye.
Which explains the three-candle rule, and it is worth quoting flat: the vortex “requires a sufficiently large flame to grow to its critical circulation for shedding,” and this “explains why many previous experiments used a bundle of small candles to create a bigger candle flame that can flicker.” One candle is below threshold. The ring starts and never gets strong enough to leave.
No. 102’s vortex street is the near neighbour, and the two differences are clean. A street sheds alternately from the two sides of a body held in a stream — lopsided by construction, and the stream is somebody else’s. This sheds one ring per cycle, symmetric all the way round, into air that was not moving until the fire moved it. No. 102 was called It Always Oscillates. This one doesn’t, until it is wide enough.
It is also the third time this publication has taken the same candle apart. No. 1 read it as a pattern; No. 101 read the wick as the regulator behind it. This is the reading where the candle turns out not to be the object.
Now put two bundles side by side. At about twenty millimetres they flicker in step. At about thirty-five they lock into exact opposition — one at full height as the other necks down. Past fifty-five or so they stop caring. Three bundles in a triangle give four behaviours: all together; two together and one against; a rotation, each flame a third of a cycle behind its neighbour, the beat travelling round the ring; and, strangest, death — the flames stop oscillating and burn steady.
What carries the coupling is genuinely disputed. One camp reads it as radiant heat, the overlap of two temperature profiles setting the coupling strength. The other reads it as the rings: simulations of three methane burners — no wax anywhere — reproduce all four modes, the three rings reconnecting into one trefoil vortex whose single shedding is the in-phase beat, or into a figure-eight that leaves the third flame in antiphase. For two flames, that account collapses the in-phase/antiphase switch onto one dimensionless number built from separation, width, gravity and viscosity. I cannot referee it. Both camps predict the same distances.
No. 8’s fireflies are the obvious comparison and instructively the wrong one. No signal, no receiver, nothing you could call a cue — and no firefly chorus does what these do. Fireflies do not lock into exact opposition, and they do not fall silent from being close.
That last mode is the one I keep turning over. Push the flames near enough and the coupling does not reinforce the beat; it abolishes it. The merged ring never reaches the circulation it needs to shed, and three restless flames go quiet — brighter, taller, and perfectly still.
Buckmaster and Peters, setting up the stability problem in 1988, gave their paper a title I have not stopped enjoying: “The infinite candle and its stability.” A candle of unlimited width — the theorists’ way of asking what the flicker does once the candle stops being the limiting thing.
It never was the limiting thing. One candle holds still not because the wax is calm, but because the fire is too small to build the ring. The ring was doing the beating all along.
≈
One loop I’m watching
Next: a plain metal tube with no moving parts, no refrigerant and nothing that could be called a pump. Compressed air goes in through a hole in the side, and comes out hot from one end and cold from the other — and it will do it all day, as long as you keep feeding it. The arguments about why have outlived nearly everyone who started them. Next time.