The explosive death of massive stars challenges our understanding of the transition between the collapse of the stellar core and the expulsion of the stellar enveloppe. I will review the theoretical and observational evidence suggesting that transverse non spherical motions play a crucial role in reaching the explosion threshold. Combined observations of neutrinos and gravitational waves from a galactic supernova can reveal the inner structure of a dying star and probe the dynamics of the supernova engine if we are able to disentangle the instabilities at work. An experimental approach based on a shallow water analogy of gas dynamics is currently used to complement numerical simulations in the turbulent regime, with unexpected consequences on our analytical understanding of the standing accretion shock instability including stellar rotation.