  Context: we study the convection-pulsation coupling that occurs in cold
Cepheids close to the red edge of the classical instability strip. In these
stars, the surface convective zone is supposed to stabilise the radial
oscillations excited by the kappa-mechanism.
  Aims: we study the influence of the convective motions onto the amplitude and
the nonlinear saturation of acoustic modes excited by kappa-mechanism. We are
interested in determining the physical conditions needed to lead to a quenching
of oscillations by convection.
  Methods: we compute two-dimensional nonlinear simulations (DNS) of the
convection-pulsation coupling, in which the oscillations are sustained by a
continuous physical process: the kappa-mechanism. Thanks to both a frequential
analysis and a projection of the physical fields onto an acoustic subspace, we
study how the convective motions affect the unstable radial oscillations.
  Results: depending on the initial physical conditions, two main behaviours
are obtained: (i) either the unstable fundamental acoustic mode has a large
amplitude, carries the bulk of the kinetic energy and shows a nonlinear
saturation similar to the purely radiative case; (ii) or the convective motions
affect significantly the mode amplitude that remains very weak. In this second
case, convection is quenching the acoustic oscillations. We interpret these
discrepancies in terms of the difference in density contrast: larger
stratification leads to smaller convective plumes that do not affect much the
purely radial modes, while large-scale vortices may quench the oscillations.
