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 number Ma increases, from inverse at Ma = 0, to direct at $Ma = \infty$ . Thus, at $Ma \sim...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2023-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ad0172 |
| _version_ | 1797639370007642112 |
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| author | Itzhak Fouxon Alexei G Kritsuk Michael Mond |
| author_facet | Itzhak Fouxon Alexei G Kritsuk Michael Mond |
| author_sort | Itzhak Fouxon |
| collection | DOAJ |
| description | 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 Ma = 0, to direct at $Ma = \infty$ . Thus, at $Ma \sim 1$ comparable amounts of energy flow from the pumping scale to large and small scales, in accord with previous data. For supersonic turbulence with $Ma \gg 1$ the cascade is direct, as in three dimensions, which results in multifractal density field. For that regime ( $Ma \gg 1$ ) 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 at Ma = 0 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 enough values of I , the magnetic flux through the disk, the magnetic field changes the flow appreciably, or rearranges it completely. This renders the limit Ma → 0 singular for non-zero values of I . Of particular interest is the effect of the density multifractality, at $Ma\gg 1$ which is relevant for astrophysical disks. We demonstrate that in that regime, in the presence of non-zero I the 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. |
| first_indexed | 2024-03-11T13:16:47Z |
| format | Article |
| id | doaj.art-a85582ab975b49048597b5a760a4c904 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-11T13:16:47Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-a85582ab975b49048597b5a760a4c9042023-11-03T11:48:41ZengIOP PublishingNew Journal of Physics1367-26302023-01-01251111300510.1088/1367-2630/ad0172Compressible two-dimensional turbulence: cascade reversal and sensitivity to imposed magnetic fieldItzhak Fouxon0https://orcid.org/0000-0002-2984-2522Alexei G Kritsuk1Michael Mond2Department of Mechanical Engineering, Ben-Gurion University of the Negev , PO Box 653, Beer-Sheva 84105, Israel; Departments of Chemical Engineering and Mechanical Engineering, Technion , Haifa, 32000, IsraelUniversity of California, San Diego , La Jolla, CA 92093-0424, United States of AmericaDepartment of Mechanical Engineering, Ben-Gurion University of the Negev , PO Box 653, Beer-Sheva 84105, IsraelWe 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 Ma = 0, to direct at $Ma = \infty$ . Thus, at $Ma \sim 1$ comparable amounts of energy flow from the pumping scale to large and small scales, in accord with previous data. For supersonic turbulence with $Ma \gg 1$ the cascade is direct, as in three dimensions, which results in multifractal density field. For that regime ( $Ma \gg 1$ ) 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 at Ma = 0 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 enough values of I , the magnetic flux through the disk, the magnetic field changes the flow appreciably, or rearranges it completely. This renders the limit Ma → 0 singular for non-zero values of I . Of particular interest is the effect of the density multifractality, at $Ma\gg 1$ which is relevant for astrophysical disks. We demonstrate that in that regime, in the presence of non-zero I the 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.https://doi.org/10.1088/1367-2630/ad0172compressibleturbulencetwo dimensionsmagnetic fieldcascademagnetohydrodynamics |
| spellingShingle | Itzhak Fouxon Alexei G Kritsuk Michael Mond Compressible two-dimensional turbulence: cascade reversal and sensitivity to imposed magnetic field New Journal of Physics compressible turbulence two dimensions magnetic field cascade magnetohydrodynamics |
| title | Compressible two-dimensional turbulence: cascade reversal and sensitivity to imposed magnetic field |
| title_full | Compressible two-dimensional turbulence: cascade reversal and sensitivity to imposed magnetic field |
| title_fullStr | Compressible two-dimensional turbulence: cascade reversal and sensitivity to imposed magnetic field |
| title_full_unstemmed | Compressible two-dimensional turbulence: cascade reversal and sensitivity to imposed magnetic field |
| title_short | Compressible two-dimensional turbulence: cascade reversal and sensitivity to imposed magnetic field |
| title_sort | compressible two dimensional turbulence cascade reversal and sensitivity to imposed magnetic field |
| topic | compressible turbulence two dimensions magnetic field cascade magnetohydrodynamics |
| url | https://doi.org/10.1088/1367-2630/ad0172 |
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