The convection that takes place in the innermost shells of massive stars plays an important role in the formation of core-collapse supernova explosions .
Upon encountering the supernova shock , additional turbulence is generated , amplifying the explosion .
In this work , we study how the convective perturbations evolve during the stellar collapse .
Our main aim is to establish their physical properties right before they reach the supernova shock .
To this end , we solve the linearized hydrodynamics equations perturbed on a stationary background flow .
The latter is approximated by the spherical transonic Bondi accretion , while the convective perturbations are modeled as a combination of entropy and vorticity waves .
We follow their evolution from large radii , where convective shells are initially located , down to small radii , where they are expected to encounter the accretion shock above the proto-neutron star .
Considering typical vorticity perturbations with a Mach number \sim 0.1 and entropy perturbations with magnitude \sim 0.05 k _ { \mathrm { b } } / \mathrm { baryon } , we find that the advection of these perturbations down to the shock generates acoustic waves with a relative amplitude \delta p / \gamma p \lesssim 10 \% , in agreement with published numerical simulations .
The velocity perturbations consist of contributions from acoustic and vorticity waves with values reaching \sim 10 \% of the sound speed ahead of the shock .
The perturbation amplitudes decrease with increasing \ell and initial radii of the convective shells .