The supernova explosion of massive stars is regularly observed in distant galaxies, but the underlying mechanism is still a major challenge to theorists.
This process starts with the gravitational contraction of the stellar core into a proto-neutron star. It is followed by a phase of quasi-stationary accretion where transverse motions and turbulence are induced by hydrodynamical instabilities. 

Numerical simulations of simplified models are used to evaluate their effects on the explosion and on the pulsar kick/spin. Surprisingly, two of these instabilities can be illustrated with a simple hydraulic experiment based on a shallow water analogy. The Standing Accretion Shock Instability and the corotation instability are able to redistribute angular momentum radially even for moderate rotation rates. 
Results are analyzed in view of the constraints set by stellar evolution and by the spin properties of pulsars.
Both instabilities induce oscillations which may be directly observable with current detectors of gravitational waves and neutrinos.