Turbulence from localized random expansion waves

In an attempt to determine the outer scale of turbulence driven by localized sources, such as supernova explosions in the interstellar medium, we consider a forcing function given by the gradient of Gaussian profiles localized at random positions. Different coherence times of the forcing function are considered. In order to isolate the effects specific to the nature of the forcing function, we consider the case of a polytropic equation of state and restrict ourselves to forcing amplitudes such that the flow remains subsonic. When the coherence time is short, the outer scale agrees with the half-width of the Gaussian. Longer coherence times can cause extra power at large scales, but this would not yield power-law behaviour at scales larger than that of the expansion waves. At scales smaller than the scale of the expansion waves the spectrum is close to power law with a spectral exponent of -2. The resulting flow is virtually free of vorticity. Viscous driving of vorticity turns out to be weak and self-amplification through the non-linear term is found to be insignificant. No evidence for small-scale dynamo action is found in cases where the magnetic induction equation is solved simultaneously with the other equations.