  We investigate how wave propagation is modified by the presence of heat
sources and sinks, in the simple 1D, hydrodynamical case, including
chromosphere and solar wind. We integrate the time-dependent hydrodynamic
equations of the solar wind with spherical symmetry, including conduction,
radiative cooling and a prescribed mechanical heat flux. Once a
quasi-stationary wind is established, we study the response of the system to
pressure oscillations at the photospheric boundary. We use transparent boundary
conditions. We find that wavepackets with high enough amplitude propagating
upward from the photosphere implode just below the transition region. This
implosion is due to the radiative cooling term generating pressure holes close
to the wave crests of the wave, which make the wave collapse. In the case where
heat sources and sinks are not present in the equations, the wave remains
stable whatever the initial wave amplitude, which is compatible with published
work. Instability should be observable when and where the TR is high enough
above the optically thick regions.
