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Description
During the core-collapse of a massive star, the phase of stalled accretion shock following the birth of a proto-neutron star can be directly observed with gravitational waves and neutrinos. Hydrodynamical instabilities responsible for the asymmetric character of this phase, such as the Standing Accretion Shock Instability, produce characteristic oscillation frequencies that can be identified in the multi-messenger analysis of numerical models of the explosion. A perturbative analysis is used to improve the accuracy of the relation between the time evolution of the oscillation frequencies and the stellar parameters, including turbulence and stellar rotation. The results can be tested on numerical simulations and on the shallow water analogue of SASI in the turbulent regime.