Paper detail

Role of the sonic scale in the growth of magnetic field in compressible turbulence

We study the growth of small fluctuations of magnetic field in supersonic turbulence, the small-scale dynamo. The growth is due to the fastest turbulent eddies above the resistive scale. We observe that for supersonic turbulence these eddies are effectively incompressible which creates a robust structure of the growth. The eddies are localised below the sonic scale $l_s$ defined as the scale where the typical velocity of the turbulent eddies equals the speed of sound. Thus the flow below $l_s$ is effectively incompressible and the field growth proceeds as in incompressible flow. At large Mach numbers $l_s$ is much smaller than the integral scale of turbulence so the fastest growing mode of the magnetic field belongs to small-scale turbulence. We derive this mode and the associated growth rate numerically in a white noise in time model of turbulence. The relevance of this model relies on considering evolution time larger than the correlation time of turbulence.