  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.
