Compressible two-dimensional turbulence: cascade reversal and sensitivity to imposed magnetic field

Abstract: We study the impact of compressibility on two-dimensional turbulent flows, such as those modeling astrophysical disks. We demonstrate that the direction of cascade undergoes continuous transition as the Mach number Ma increases, from inverse at zero Ma, to direct at infinite Ma. Thus, at Ma of order one comparable amounts of energy flow from the scale of the pumping to large and small scales, in accord with previous data. For supersonic turbulence with large Ma, the cascade is direct, as in three dimensions, which results in multifractal density field. For compressible flows of conducting fluids, imposing external magnetic field allows to manipulate the flow producing possibly large changes even at small Mach number. Thus Zeldovich antidynamo theorem, by which at zero Ma the magnetic field is zero in the steady state, must be used with caution. Real flows have finite Ma and, however small it is, for large magnetic flux through the disk, the magnetic field changes the flow appreciably, or rearranges it completely. For large Ma, relevant for astrophysical disks, the magnetic field energy is enhanced by a large factor as compared to estimates based on the mean field. We propose to use two-dimensional Burgers turbulence, whose three-dimensional counterpart is used for studies of the large-scale structure of the Universe, as a model for supersonic thin accretion disks.