# Why does the gas cloud of an underwater gunshot pulse?

I have been watching some slow motion video and I was intrigued by the slow motion underwater gunshot. The first moments of the video go as expected. The gun fires and a cloud forms in front of the gun. Then the bullet rips through the water, leaving an open space (which I assume is a cavitation vacuum.) Soon after, the rip closes, and the gas bubble shrinks (I'm assuming this is due to the cooling and/or compression of the hot high pressure gasses.) Then something funny happens. The bubble pulses a few times and almost appears to emit light. Each pulse is accompanied by a noise.

The video can be seen here from start, or just showing the bubbles .

What is this pulse effect and/or what causes it?

EDIT: Here is another great video for a possible explanation:

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The overall effect (in particular with regard to this light emission, which really happens – it's not just apparent) is mostly investigated under the name sonoluminescence.

Though the process of this luminescence itself remains unsettled, it is for sure that extremely high temperatures are produced at a bubble collapse (in fact, it was conjectured they might be hot enough to build a nuclear fusion reactor!), and this high temperature obviously causes another steam bubble to form very quickly, so that would explain the pulse-oscillation effect.

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Thanks! This leads to another question, Where does all of that heat come from? – Hoytman Mar 29 '14 at 19:13
Not really: there's not that much heat in fact, only, a round obviously contains quite a lot of energy in its explosive! The interesting thing is that this heat gets concertrated in such a small space, that's what causes the temperature to rise so remarkably high. – leftaroundabout Mar 29 '14 at 19:17
@Hoytman: Adiabatic compression of the gas cloud generates heating. When the gas cloud initially forms in the explosion, the water is flung away and the gas bubble expands. At equilibrium pressure, the gas is no longer exerting pressure on the surrounding water, but the water is still moving, so the gas gets "stretched out", causing the water to get sucked back in again like a spring. This collapse compresses the gas adiabatically to generate high temperatures again, and the process repeats, albeit with damping (so that the oscillations die out after a couple pulses). – DumpsterDoofus Mar 29 '14 at 19:19
another observation: the water is moving very quickly both in and out. If the bubbles were perfectly round, the walls of the water would slam back into each other at a very small point. All that energy would be focused into another explosion. Is this focusing effect the potential cause of nuclear fusion? – Hoytman Mar 29 '14 at 20:25

There are many things in nature that lead to periodic phenomena. The governing equation behind all such phenomena with small amplitude is something like $\ddot{x}(t)=-x(t)$. $x$ is the displacement from equilibrium, and $\ddot{x}$ is the acceleration of that parameter. If $x$ is negative, this equation tells us that $x$ is accelerating and trying to become positive. If $x$ is positive, the equation tells us that $x$ is accelerating in the opposite direction trying to become negative. The result is that $x$ oscillates back and forth perfectly between minimum (very negative) and maximum (very positive) values.

One of the reasons that this effect might seem weird is because we're looking at a gas, not at a liquid. Water is not very springy at all. It takes a lot of force to compress it, and even worse, for each pound of force applied, compressed water barely stores any energy! Gasses are a different story. Think of it this way: If you had a scuba tank pressurized to a certain PSI, you should be much more afraid of a fully pressurized tank of oxygen exploding, than of a fully pressurized tank with 95% liquid water and 5% gaseous oxygen (in different phases, not mixed in). The former stores much more energy than the latter. So, the uncompressed gas is pushed in by the water, the gas builds up a lot of energy in a small space and acts like a spring, then explodes outwards again.

leftroundabout's answer may explain the light emission. On that wikipedia page is a perfectly clear and relevant video: http://en.wikipedia.org/wiki/File:Sonoluminescence_of_Synthetic_Ordnance_Gel.ogv

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Where do you you see a small amplitude here? I think this is in fact quite a good example of an oscillation that's totally unrelated to the usual 2nd-order differential equation. I know little about the processes involved in cavity collapse, but pretty sure it's very much more complicated. For one thing, a prediction of a $\ddot x \propto - x$ model would be that the frequency is constant, but pretty clearly big bubbles oscillate slower than small ones. – leftaroundabout Mar 29 '14 at 23:28
@leftaroundabout Okay, I'm not doing pulsing bubbles justice at all, but this page en.wikipedia.org/wiki/Liquid_bubble#Pulsation seems to imply that the amplitude is independent of initial displacement from equilibrium [in that specific case] (I say nothing about the bubble radius). I'm not familiar with much about nonlinear ODEs but this seems fine to me. (if I was familiar I'd try to do things more formally to see whether I'm right or wrong, but at the moment I'd probably spend way too long on it before I got anywhere) – NeuroFuzzy Mar 30 '14 at 1:01
Well, that wiki article is about "ordinary" gas bubbles, the ones that are permanently stable under their own inner pressure. Those behave in many ways quite different from cavitation vapour bubbles. – leftaroundabout Mar 30 '14 at 1:26
@leftaroundabout What can I say - I think that gross oversimplification is fine for non-technical questions, and I think that discussion of oscillatory phenomena in general adds to an understanding of this. Overshoot/undershoot from equilibrium, even though there may be no equilibrium, among other problems. – NeuroFuzzy Mar 30 '14 at 1:51
you said " for each pound of force applied, compressed water barely stores any energy" - although it is hard to get water to store energy via compression, it does appear to store it quite well in the video. Otherwise, the pulse would only happen once and the pulse resonance would die away very quickly. In the video, the pulse reoccurs (resonates?) and dissipates over the course of several pulses. This demonstrated that both the gas and the water are storing and emitting energy. Is this true or is there something else going on here (I have no training in this field so I may be way off.) – Hoytman Mar 31 '14 at 12:54