3.10 Shocks

Occasional supersonic flows and shocks occur in both the horizontal flows at the intergranular lane boundaries and in the vertical flows below the surface, which results in weak shocks where these downflows collide with the upflows (Stein and Nordlund, 1998Jump To The Next Citation Point). The maximum Mach numbers are about 1.5 for horizontal flows and 1.8 for vertical flows. The maximum Mach numbers occur at the surface for the horizontal flows and half a megameter below the surface for the vertical flows (Figure 19View Image). The largest Mach numbers for both vertical and horizontal flows occur at the boundaries of the granules that overlie the boundaries of the larger scale subsurface flows (Figure 20View Image). It is at these locations that the downdrafts are strongest because they do not have to push against upflowing fluid and it is also here where these strong downflows are the strongest sinks for the diverging horizontal flows in the granules. Observational evidence for shocks waves in the solar photosphere were presented by (Rybák et al., 2004).

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, 1991Stein and Nordlund, 1998Jump To The Next Citation PointWedemeyer et al., 2003Jump To The Next Citation Point2004Schaffenberger et al., 2006Jump To The Next Citation PointHansteen, 2008).

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