[Physics] Breaking the sound barrier underwater

Question

Theoretically, if I were to launch something faster than the speed of sound in water (around 5 times that of air), what would happen?

Answer 1

The reason that the speed of sound is a well-defined quantity is that, for small pertubations, the equations which govern the fluid dynamics can be linearised. In that linearised form, the solution boils down to a simple wave ansatz with linear dispersion relation, i.e. constant velocity.
Those are the sound waves.

It so happens that in air, this linear solution holds up pretty well even for rather big pertubations. Only, when something moves faster than the speed of sound, the linear wave mode obviously can't be used anymore to transport away energy, hence any disturbance (which is inevitable when something's trying to move through the air) is “trapped”. The pertubation gets ever stronger, until the dynamics are completely nonlinear and you get a shock wave.
This is the reason the sound barrier is such a crucial limit for aircraft.

In incompressible fluids like water, this doesn't necessarily work out the same way. In water, the dynamics tend to be far more violent, even well below the speed of sound. In particular, you will readily end up with cavitation bubbles. As already said by Acid Jazz, this allows for a rather remarkable mode of underwater motion, which is completely unlike anything you get in air.

tl;dr, the sound barrier isn't really relevant under water, because stranger effects turn up before you ever get close to it.

However, it would still be relevant if you could manage to keep the pressure pertubations small enough even close to the speed of sound. Actually, this is relevant for any supersonic motion under water, if you look at it on a big enough scale. For instance, an asteroid impact into the ocean does no doubt cause a sonic cone quite analogous to the one generated by supersonic aircraft.