Role of the sonic scale in the growth of magnetic field in compressible turbulence. (arXiv:1906.11065v1 [physics.flu-dyn])

Role of the sonic scale in the growth of magnetic field in compressible turbulence. (arXiv:1906.11065v1 [physics.flu-dyn])
<a href="http://arxiv.org/find/physics/1/au:+Fouxon_I/0/1/0/all/0/1">Itzhak Fouxon</a>, <a href="http://arxiv.org/find/physics/1/au:+Mond_M/0/1/0/all/0/1">Michael Mond</a>

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.

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.

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