Symmetry breaking of decaying magnetohydrodynamic Taylor-Green flows and consequences for universality
<p style="text-align:justify;"> We investigate the evolution and stability of a decaying magnetohydrodynamic (MHD) Taylor-Green flow. The chosen flow has been shown to result in a steep total energy spectrum with power law behaviour $k^{-2}$. We investigate the symmetry breaking of...
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| Format: | Journal article |
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American Physical Society
2013
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| _version_ | 1826257062704709632 |
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| author | Dallas, V Alexakis, A |
| author_facet | Dallas, V Alexakis, A |
| author_sort | Dallas, V |
| collection | OXFORD |
| description | <p style="text-align:justify;"> We investigate the evolution and stability of a decaying magnetohydrodynamic (MHD) Taylor-Green flow. The chosen flow has been shown to result in a steep total energy spectrum with power law behaviour $k^{-2}$. We investigate the symmetry breaking of this flow by exciting perturbations of different amplitudes. It is shown that for any finite amplitude perturbation there is a high enough Reynolds number for which the perturbation will grow enough at the peak of dissipation rate resulting to a non-linear feedback in the flow and subsequently break the Taylor-Green symmetries. In particular, we show that symmetry breaking at large scales occurs if the amplitude of the perturbation is $\rho_{crit} \sim Re^{-1}$ and at small scales occurs if $\rho_{crit} \sim Re^{-3/2}$. This symmetry breaking modifies the scaling laws of the energy spectra at the peak of dissipation rate away from the $k^{-2}$ scaling and towards the classical $k^{-5/3}$ and $k^{-3/2}$ power laws.</p> |
| first_indexed | 2024-03-06T18:12:10Z |
| format | Journal article |
| id | oxford-uuid:0365210b-2c6e-4aff-b2bf-4b8562ac9301 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:12:10Z |
| publishDate | 2013 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:0365210b-2c6e-4aff-b2bf-4b8562ac93012022-03-26T08:45:53ZSymmetry breaking of decaying magnetohydrodynamic Taylor-Green flows and consequences for universalityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:0365210b-2c6e-4aff-b2bf-4b8562ac9301Symplectic Elements at OxfordAmerican Physical Society2013Dallas, VAlexakis, A <p style="text-align:justify;"> We investigate the evolution and stability of a decaying magnetohydrodynamic (MHD) Taylor-Green flow. The chosen flow has been shown to result in a steep total energy spectrum with power law behaviour $k^{-2}$. We investigate the symmetry breaking of this flow by exciting perturbations of different amplitudes. It is shown that for any finite amplitude perturbation there is a high enough Reynolds number for which the perturbation will grow enough at the peak of dissipation rate resulting to a non-linear feedback in the flow and subsequently break the Taylor-Green symmetries. In particular, we show that symmetry breaking at large scales occurs if the amplitude of the perturbation is $\rho_{crit} \sim Re^{-1}$ and at small scales occurs if $\rho_{crit} \sim Re^{-3/2}$. This symmetry breaking modifies the scaling laws of the energy spectra at the peak of dissipation rate away from the $k^{-2}$ scaling and towards the classical $k^{-5/3}$ and $k^{-3/2}$ power laws.</p> |
| spellingShingle | Dallas, V Alexakis, A Symmetry breaking of decaying magnetohydrodynamic Taylor-Green flows and consequences for universality |
| title | Symmetry breaking of decaying magnetohydrodynamic Taylor-Green flows and consequences for universality |
| title_full | Symmetry breaking of decaying magnetohydrodynamic Taylor-Green flows and consequences for universality |
| title_fullStr | Symmetry breaking of decaying magnetohydrodynamic Taylor-Green flows and consequences for universality |
| title_full_unstemmed | Symmetry breaking of decaying magnetohydrodynamic Taylor-Green flows and consequences for universality |
| title_short | Symmetry breaking of decaying magnetohydrodynamic Taylor-Green flows and consequences for universality |
| title_sort | symmetry breaking of decaying magnetohydrodynamic taylor green flows and consequences for universality |
| work_keys_str_mv | AT dallasv symmetrybreakingofdecayingmagnetohydrodynamictaylorgreenflowsandconsequencesforuniversality AT alexakisa symmetrybreakingofdecayingmagnetohydrodynamictaylorgreenflowsandconsequencesforuniversality |