Residual Energy and Broken Symmetry in Reduced Magnetohydrodynamics
Alfvénic interactions that transfer energy from large to small spatial scales lie at the heart of magnetohydrodynamic turbulence. An important feature of the turbulence is the generation of negative residual energy—excess energy in magnetic fluctuations compared to velocity fluctuations. By contrast...
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2025-01-01
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| Series: | The Astrophysical Journal |
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| Online Access: | https://doi.org/10.3847/1538-4357/ad9012 |
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| author | S. Dorfman M. Abler S. Boldyrev C. H. K. Chen S. Greess |
| author_facet | S. Dorfman M. Abler S. Boldyrev C. H. K. Chen S. Greess |
| author_sort | S. Dorfman |
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| description | Alfvénic interactions that transfer energy from large to small spatial scales lie at the heart of magnetohydrodynamic turbulence. An important feature of the turbulence is the generation of negative residual energy—excess energy in magnetic fluctuations compared to velocity fluctuations. By contrast, an MHD Alfvén wave has equal amounts of energy in fluctuations of each type. Alfvénic quasi-modes that do not satisfy the Alfvén wave dispersion relation and exist only in the presence of a nonlinear term can contain either positive or negative residual energy, but until now, an intuitive physical explanation for why negative residual energy is preferred has remained elusive. This paper shows that the equations of reduced MHD are symmetric in that they have no intrinsic preference for one sign of the residual energy over the other. An initial state that is not an exact solution to the equations can break this symmetry in a way that leads to net-negative residual energy generation. Such a state leads to a solution with three distinct parts: nonresonant Alfvénic quasi-modes, normal modes produced to satisfy initial conditions, and resonant normal modes that grow in time. The latter two parts strongly depend on initial conditions; the resulting symmetry breaking leads to net-negative residual energy both in Alfvénic quasi-modes and ω = k _∥ V _A = 0 modes. These modes have net-positive residual energy in the equivalent boundary value problem, suggesting that the initial value setup is a better match for solar wind turbulence. |
| format | Article |
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| institution | Kabale University |
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| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
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| spelling | doaj-art-cf48d3dd0fe64188bfe17e01abede43b2025-01-31T15:23:32ZengIOP PublishingThe Astrophysical Journal1538-43572025-01-01979216310.3847/1538-4357/ad9012Residual Energy and Broken Symmetry in Reduced MagnetohydrodynamicsS. Dorfman0https://orcid.org/0000-0001-5955-9552M. Abler1https://orcid.org/0000-0003-2528-8752S. Boldyrev2https://orcid.org/0000-0001-6252-5169C. H. K. Chen3https://orcid.org/0000-0003-4529-3620S. Greess4https://orcid.org/0000-0002-3107-258XSpace Science Institute , Boulder, CO, USA ; sethd@SpaceScience.org; Department of Physics and Astronomy, University of California , Los Angeles, CA, USASpace Science Institute , Boulder, CO, USA ; sethd@SpaceScience.org; Department of Physics and Astronomy, University of California , Los Angeles, CA, USASpace Science Institute , Boulder, CO, USA ; sethd@SpaceScience.org; Department of Physics, University of Wisconsin-Madison , Madison, WI, USADepartment of Physics and Astronomy, Queen Mary University of London , London, UKDepartment of Physics and Astronomy, Queen Mary University of London , London, UKAlfvénic interactions that transfer energy from large to small spatial scales lie at the heart of magnetohydrodynamic turbulence. An important feature of the turbulence is the generation of negative residual energy—excess energy in magnetic fluctuations compared to velocity fluctuations. By contrast, an MHD Alfvén wave has equal amounts of energy in fluctuations of each type. Alfvénic quasi-modes that do not satisfy the Alfvén wave dispersion relation and exist only in the presence of a nonlinear term can contain either positive or negative residual energy, but until now, an intuitive physical explanation for why negative residual energy is preferred has remained elusive. This paper shows that the equations of reduced MHD are symmetric in that they have no intrinsic preference for one sign of the residual energy over the other. An initial state that is not an exact solution to the equations can break this symmetry in a way that leads to net-negative residual energy generation. Such a state leads to a solution with three distinct parts: nonresonant Alfvénic quasi-modes, normal modes produced to satisfy initial conditions, and resonant normal modes that grow in time. The latter two parts strongly depend on initial conditions; the resulting symmetry breaking leads to net-negative residual energy both in Alfvénic quasi-modes and ω = k _∥ V _A = 0 modes. These modes have net-positive residual energy in the equivalent boundary value problem, suggesting that the initial value setup is a better match for solar wind turbulence.https://doi.org/10.3847/1538-4357/ad9012MagnetohydrodynamicsInterplanetary turbulenceAlfvén wavesSolar wind |
| spellingShingle | S. Dorfman M. Abler S. Boldyrev C. H. K. Chen S. Greess Residual Energy and Broken Symmetry in Reduced Magnetohydrodynamics The Astrophysical Journal Magnetohydrodynamics Interplanetary turbulence Alfvén waves Solar wind |
| title | Residual Energy and Broken Symmetry in Reduced Magnetohydrodynamics |
| title_full | Residual Energy and Broken Symmetry in Reduced Magnetohydrodynamics |
| title_fullStr | Residual Energy and Broken Symmetry in Reduced Magnetohydrodynamics |
| title_full_unstemmed | Residual Energy and Broken Symmetry in Reduced Magnetohydrodynamics |
| title_short | Residual Energy and Broken Symmetry in Reduced Magnetohydrodynamics |
| title_sort | residual energy and broken symmetry in reduced magnetohydrodynamics |
| topic | Magnetohydrodynamics Interplanetary turbulence Alfvén waves Solar wind |
| url | https://doi.org/10.3847/1538-4357/ad9012 |
| work_keys_str_mv | AT sdorfman residualenergyandbrokensymmetryinreducedmagnetohydrodynamics AT mabler residualenergyandbrokensymmetryinreducedmagnetohydrodynamics AT sboldyrev residualenergyandbrokensymmetryinreducedmagnetohydrodynamics AT chkchen residualenergyandbrokensymmetryinreducedmagnetohydrodynamics AT sgreess residualenergyandbrokensymmetryinreducedmagnetohydrodynamics |