Two-time energy spectrum of weak magnetohydrodynamic turbulence
In this work a weak-turbulence closure is used to determine the structure of the two-time power spectrum of weak magnetohydrodynamic (MHD) turbulence from the nonlinear equations describing the dynamics. The two-time energy spectrum is a fundamental quantity in turbulence theory from which most stat...
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| Format: | Article |
| Language: | English |
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American Physical Society
2020-05-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.023189 |
| _version_ | 1797211509398437888 |
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| author | Jean C. Perez Augustus A. Azelis Sofiane Bourouaine |
| author_facet | Jean C. Perez Augustus A. Azelis Sofiane Bourouaine |
| author_sort | Jean C. Perez |
| collection | DOAJ |
| description | In this work a weak-turbulence closure is used to determine the structure of the two-time power spectrum of weak magnetohydrodynamic (MHD) turbulence from the nonlinear equations describing the dynamics. The two-time energy spectrum is a fundamental quantity in turbulence theory from which most statistical properties of a homogeneous turbulent system can be derived. A closely related quantity, obtained via a spatial Fourier transform, is the two-point two-time correlation function describing the space-time correlations arising from the underlying dynamics of the turbulent fluctuations. Both quantities are central in fundamental turbulence theories as well as in the analysis of turbulence experiments and simulations. However, a first-principles derivation of these quantities has remained elusive due to the statistical closure problem, in which dynamical equations for correlations at order n depend on correlations of order n+1. The recent launch of the Parker Solar Probe (PSP), which will explore the near-Sun region where the solar wind is born, has renewed the interest in the heliophysics community to understand the structure and possible universal properties of space-time correlations. The weak MHD turbulence regime that we consider in this work allows for a natural asymptotic closure of the two-time spectrum, which may be applicable to other weak turbulence regimes found in fluids and plasmas. An integro-differential equation for the scale-dependent temporal correlation function is derived for incompressible Alfvénic fluctuations whose nonlinear dynamics is described by the reduced MHD equations. |
| first_indexed | 2024-04-24T10:27:37Z |
| format | Article |
| id | doaj.art-f6e0bb4d433a4d16bb6776feea34e29c |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:27:37Z |
| publishDate | 2020-05-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-f6e0bb4d433a4d16bb6776feea34e29c2024-04-12T16:54:08ZengAmerican Physical SocietyPhysical Review Research2643-15642020-05-012202318910.1103/PhysRevResearch.2.023189Two-time energy spectrum of weak magnetohydrodynamic turbulenceJean C. PerezAugustus A. AzelisSofiane BourouaineIn this work a weak-turbulence closure is used to determine the structure of the two-time power spectrum of weak magnetohydrodynamic (MHD) turbulence from the nonlinear equations describing the dynamics. The two-time energy spectrum is a fundamental quantity in turbulence theory from which most statistical properties of a homogeneous turbulent system can be derived. A closely related quantity, obtained via a spatial Fourier transform, is the two-point two-time correlation function describing the space-time correlations arising from the underlying dynamics of the turbulent fluctuations. Both quantities are central in fundamental turbulence theories as well as in the analysis of turbulence experiments and simulations. However, a first-principles derivation of these quantities has remained elusive due to the statistical closure problem, in which dynamical equations for correlations at order n depend on correlations of order n+1. The recent launch of the Parker Solar Probe (PSP), which will explore the near-Sun region where the solar wind is born, has renewed the interest in the heliophysics community to understand the structure and possible universal properties of space-time correlations. The weak MHD turbulence regime that we consider in this work allows for a natural asymptotic closure of the two-time spectrum, which may be applicable to other weak turbulence regimes found in fluids and plasmas. An integro-differential equation for the scale-dependent temporal correlation function is derived for incompressible Alfvénic fluctuations whose nonlinear dynamics is described by the reduced MHD equations.http://doi.org/10.1103/PhysRevResearch.2.023189 |
| spellingShingle | Jean C. Perez Augustus A. Azelis Sofiane Bourouaine Two-time energy spectrum of weak magnetohydrodynamic turbulence Physical Review Research |
| title | Two-time energy spectrum of weak magnetohydrodynamic turbulence |
| title_full | Two-time energy spectrum of weak magnetohydrodynamic turbulence |
| title_fullStr | Two-time energy spectrum of weak magnetohydrodynamic turbulence |
| title_full_unstemmed | Two-time energy spectrum of weak magnetohydrodynamic turbulence |
| title_short | Two-time energy spectrum of weak magnetohydrodynamic turbulence |
| title_sort | two time energy spectrum of weak magnetohydrodynamic turbulence |
| url | http://doi.org/10.1103/PhysRevResearch.2.023189 |
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