Instability of P-waves just below the transition region in a global solar wind simulation

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.