Supersonic convective flows were first studied by Cattaneo et al. (1990) and Malagoli et al. (1990) in simple models with polytropic stratification and no radiative energy transfer. They predicted that supersonic flows are most likely to occur close to the photosphere in the case of convection in real stars; the horizontal pressure fluctuations need to be large, and the radiative (or boundary) cooling needs to be efficient, so the sound speed can be efficiently reduced while the flow is being accelerated. This prediction agrees well with what has later been found in models with detailed radiative transfer and non-ideal equations of state (Nordlund and Stein, 1991; Stein and Nordlund, 1998; Wedemeyer et al., 2003, 2004; Schaffenberger et al., 2006; Hansteen, 2008).
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