# Do superfluids lack inertia and/or don't exist with a finite speed of sound?

I've been reading a few things on other sources about superfluids and what kind of propulsion would work in them. Supposedly a propeller won't work in a superfluid, but I'm having a hard time understanding why.

As the propeller spins, it pushes against the fluid which should have an equal and opposite affect on the propeller, no? Is it that there is also fluid on the other side pushing the propeller in the other direction?

If so, this can only work when the speed of sound in the superfluid is >> than the speed of rotation of the propeller, right? If I somehow had a propeller that could spin an appreciable fraction of the speed of sound, would it be able to cause cavitation in the fluid and actually accelerate forward?

And why is a propeller, which can be seen as being a truncated corkscrew with less than a full rotation, unable to work in a superfluid, but a corkscrew with several rotations can work in a superfluid?

• "this can only work when the speed of sound in the superfluid is >> than the speed of rotation of the propeller, right" Yes, I believe so. If the propeller is spinning faster than the critical angular velocity of the superfluid, I would expect that the motion would create vortices and ultimately destroy the superfluidity. What is certain is that none of this has anything to do with the speed of light, which is normally many orders of magnitude above the relevant speeds. Feb 10, 2017 at 19:51
• Fixed the typos by replacing "light" with "sound".
– Pirx
Feb 10, 2017 at 20:20
• @Pirx It wasn't a typo. I was just thinking about things in terms of the speed of light being a complete upper bound on the speed of sound of something. And thinking about it in terms of if you're going fast enough, at some point the propeller is kicking bits of fluid backwards so quickly that it doesn't have time to flow around to the other side of the propeller. Feb 10, 2017 at 21:19
• But the edits probably work just as well to answer my question. Feb 10, 2017 at 21:19
• Well, I'd strongly recommend you call it a typo and leave it at that...
– Pirx
Feb 10, 2017 at 21:22

I am not convinced that your corkscrew will work. Do you have a reference for where you got that idea?

Notice that the superfluidity case is completely different from the ultra-low Reynolds number situation of swimming microorganisms. It's virtually the opposite: In the latter case you are in fact dealing with a fluid at a nondimensionally very high viscosity, which means the differential equations of fluid flow become (approximately) linear and spatio-temporally symmetric as you go from the Navier-Stokes to the Stokes equations. See Purcell's classic "Life at Low Reynolds Number". Thus reciprocating motion cannot be used for swimming propulsion, and amoebas and such use e.g. corkscrew designs or various kind of flagellar motion.

As for the supersonic flow case, well, sure, in that case you can in theory generate (singular) vorticity sheets through the development of discontinuity surfaces. I don't know enough to tell you off the top of my head whether or not you could use this for propulsion purposes. I'm not planning to spend time thinking about this, since it's fairly clear that this is not a very realistic scenario that anyone is likely to ever contemplate seriously.

• I just bought a superfluid yacht and I'm trying to figure out if I have to rely on the sails! It's a pretty common scenario.
– JMac
Feb 10, 2017 at 20:37
• Yeah, everyone is buying these "superfluid yachts" these days... ;-) You better hope you don't have to rely on the winds of a superfluid to fill those sails!
– Pirx
Feb 10, 2017 at 20:39
• It's really chilly out on the superfluid lake. I really don't want to have to take out the sail.
– JMac
Feb 10, 2017 at 20:40