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

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 numberMaincreases, from inverse atMa = 0, to direct atMa=. Thus, atMa1comparable amounts of energy flow from the pumping scale to large and small scales, in accord with previous data. For supersonic turbulence withMa1the cascade is direct, as in three dimensions, which results in multifractal density field. For that regime (Ma1) we derive a Kolmogorov-type law for potential forcing and obtain an explicit expression for the third order correlation tensor of the velocity. We further show that all third order structure functions are zero up to first order in the inertial range scales, which is in sharp contrast with incompressible turbulence where the third order structure function, that describes the energy flux associated with the energy cascade is non-zero. The properties of compressible turbulence have significant implications on the amplification of magnetic fields in conducting fluids. We thus demonstrate that imposing external magnetic field on compressible flows of conducting fluids allows to manipulate the flow producing possibly large changes even at small Mach numbers. Thus Zeldovich’s antidynamo theorem, by which atMa = 0 the magnetic field is zero in the steady state, must be used with caution. Real flows have finiteMaand, however small it is, for large enough values ofI, the magnetic flux through the disk, the magnetic field changes the flow appreciably, or rearranges it completely. This renders the limitMa → 0 singular for non-zero values ofI. Of particular interest is the effect of the density multifractality, atMa1which is relevant for astrophysical disks. We demonstrate that in that regime, in the presence of non-zeroIthe magnetic field energy is enhanced by a large factor as compared to its estimates based on the mean field. Finally, based on the insights described above, we propose a novel 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 two-dimensional magnetohydrodynamic flows.

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Author(s) / Creator(s):
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Publisher / Repository:
IOP Publishing
Date Published:
Journal Name:
New Journal of Physics
Medium: X Size: Article No. 113005
["Article No. 113005"]
Sponsoring Org:
National Science Foundation
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