On the Energy Spectrum of Strong Magnetohydrodynamic Turbulence
The energy spectrum of magnetohydrodynamic turbulence attracts interest due to its fundamental importance and its relevance for interpreting astrophysical data. Here we present measurements of the energy spectra from a series of high-resolution direct numerical simulations of magnetohydrodynamics tu...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2012-10-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.2.041005 |
| _version_ | 1819140757691301888 |
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| author | Jean Carlos Perez Joanne Mason Stanislav Boldyrev Fausto Cattaneo |
| author_facet | Jean Carlos Perez Joanne Mason Stanislav Boldyrev Fausto Cattaneo |
| author_sort | Jean Carlos Perez |
| collection | DOAJ |
| description | The energy spectrum of magnetohydrodynamic turbulence attracts interest due to its fundamental importance and its relevance for interpreting astrophysical data. Here we present measurements of the energy spectra from a series of high-resolution direct numerical simulations of magnetohydrodynamics turbulence with a strong guide field and for increasing Reynolds number. The presented simulations, with numerical resolutions up to 2048^{3} mesh points and statistics accumulated over 30 to 150 eddy turnover times, constitute, to the best of our knowledge, the largest statistical sample of steady state magnetohydrodynamics turbulence to date. We study both the balanced case, where the energies associated with Alfvén modes propagating in opposite directions along the guide field, E^{+}(k_{⊥}) and E^{-}(k_{⊥}), are equal, and the imbalanced case where the energies are different. In the balanced case, we find that the energy spectrum converges to a power law with exponent -3/2 as the Reynolds number is increased, which is consistent with phenomenological models that include scale-dependent dynamic alignment. For the imbalanced case, with E^{+}>E^{-}, the simulations show that E^{-}∝k_{⊥}^{-3/2} for all Reynolds numbers considered, while E^{+} has a slightly steeper spectrum at small Re. As the Reynolds number increases, E^{+} flattens. Since E^{±} are pinned at the dissipation scale and anchored at the driving scales, we postulate that at sufficiently high Re the spectra will become parallel in the inertial range and scale as E^{+}∝E^{-}∝k_{⊥}^{-3/2}. Questions regarding the universality of the spectrum and the value of the “Kolmogorov constant” are discussed. |
| first_indexed | 2024-12-22T11:43:38Z |
| format | Article |
| id | doaj.art-0c7ebdd77afe432eab2841f057f9d6aa |
| institution | Directory Open Access Journal |
| issn | 2160-3308 |
| language | English |
| last_indexed | 2024-12-22T11:43:38Z |
| publishDate | 2012-10-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj.art-0c7ebdd77afe432eab2841f057f9d6aa2022-12-21T18:27:13ZengAmerican Physical SocietyPhysical Review X2160-33082012-10-012404100510.1103/PhysRevX.2.041005On the Energy Spectrum of Strong Magnetohydrodynamic TurbulenceJean Carlos PerezJoanne MasonStanislav BoldyrevFausto CattaneoThe energy spectrum of magnetohydrodynamic turbulence attracts interest due to its fundamental importance and its relevance for interpreting astrophysical data. Here we present measurements of the energy spectra from a series of high-resolution direct numerical simulations of magnetohydrodynamics turbulence with a strong guide field and for increasing Reynolds number. The presented simulations, with numerical resolutions up to 2048^{3} mesh points and statistics accumulated over 30 to 150 eddy turnover times, constitute, to the best of our knowledge, the largest statistical sample of steady state magnetohydrodynamics turbulence to date. We study both the balanced case, where the energies associated with Alfvén modes propagating in opposite directions along the guide field, E^{+}(k_{⊥}) and E^{-}(k_{⊥}), are equal, and the imbalanced case where the energies are different. In the balanced case, we find that the energy spectrum converges to a power law with exponent -3/2 as the Reynolds number is increased, which is consistent with phenomenological models that include scale-dependent dynamic alignment. For the imbalanced case, with E^{+}>E^{-}, the simulations show that E^{-}∝k_{⊥}^{-3/2} for all Reynolds numbers considered, while E^{+} has a slightly steeper spectrum at small Re. As the Reynolds number increases, E^{+} flattens. Since E^{±} are pinned at the dissipation scale and anchored at the driving scales, we postulate that at sufficiently high Re the spectra will become parallel in the inertial range and scale as E^{+}∝E^{-}∝k_{⊥}^{-3/2}. Questions regarding the universality of the spectrum and the value of the “Kolmogorov constant” are discussed.http://doi.org/10.1103/PhysRevX.2.041005 |
| spellingShingle | Jean Carlos Perez Joanne Mason Stanislav Boldyrev Fausto Cattaneo On the Energy Spectrum of Strong Magnetohydrodynamic Turbulence Physical Review X |
| title | On the Energy Spectrum of Strong Magnetohydrodynamic Turbulence |
| title_full | On the Energy Spectrum of Strong Magnetohydrodynamic Turbulence |
| title_fullStr | On the Energy Spectrum of Strong Magnetohydrodynamic Turbulence |
| title_full_unstemmed | On the Energy Spectrum of Strong Magnetohydrodynamic Turbulence |
| title_short | On the Energy Spectrum of Strong Magnetohydrodynamic Turbulence |
| title_sort | on the energy spectrum of strong magnetohydrodynamic turbulence |
| url | http://doi.org/10.1103/PhysRevX.2.041005 |
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