Is supersonic movement possible in incompressible media? When reaching the speed of sound in air a shock-wave starts building up in front of the object moving at sonic speeds where the air is compressed.
But what happens, if the medium is not (or almost not) compressible?
In my naive understanding, the pressure would go towards "infinite" and independently of how much power I put into driving the object I'd just increase the force at the front of the object but can't get any faster than the speed of sound.
Can there be anything moving faster than the speed of sound for example in water?
Is there an example of something moving faster than the speed of sound in water?
 A: The incompressibility constraint $\nabla \cdot \mathbf{u} = 0$ is an algebraic constraint in incompressible Navier-Stokes equations. This makes the speed of perturbations (the speed of sound) in the medium to be infinite, since the medium must immediately adapt itself in the whole domain even to a local perturbation, in order to comply with the incompressibility constraint.
That said, pefectly incompressible media do not exist. That is a just a mathematical model for media that behaves (in certain conditions) as a nearly incompressible medium. But in that model, you can find a mathematical justification about the infinite velocity of perturbations.
If a medium is not perfectly incompressible, then it's a compressible medium, and thus you can treat it with the governing equation for compressible media.
In order to find the speed of sound, i.e. to study the propagation of small-amplitude (usually) high frequency perturbations, you usually want to:

*

*find the base-flow;

*linearize the equations around the base-flow: this allows to find the (local) speed of sound, and determine the (local) sonic limit, between subsonic and supersonic conditions.

A: There was some information on a test of a supercavitating torpedo moving under water faster than sound.
