Local axisymmetric diffusive stability of weakly magnetized, differentially rotating, stratified fluids
We study the local stability of stratified, differentially rotating fluids to axisymmetric perturbations in the presence of a weak magnetic field and of finite resistivity, viscosity, and heat conductivity. This is a generalization of the Goldreich-Schubert-Fricke (GSF) double-diffusive analysis to...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Institute of Physics Publishing
2004
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| _version_ | 1797080258910879744 |
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| author | Menou, K Balbus, S Spruit, H |
| author_facet | Menou, K Balbus, S Spruit, H |
| author_sort | Menou, K |
| collection | OXFORD |
| description | We study the local stability of stratified, differentially rotating fluids to axisymmetric perturbations in the presence of a weak magnetic field and of finite resistivity, viscosity, and heat conductivity. This is a generalization of the Goldreich-Schubert-Fricke (GSF) double-diffusive analysis to the magnetized and resistive, triple-diffusive case. Our fifth-order dispersion relation admits a novel branch that describes a magnetized version of multi-diffusive modes. We derive necessary conditions for axisymmetric stability in the inviscid and perfect-conductor (double-diffusive) limits. In each case, rotation must be constant on cylinders and angular velocity must not decrease with distance from the rotation axis for stability, irrespective of the relative strength of viscous, resistive, and heat diffusion. Therefore, in both double-diffusive limits, solid-body rotation marginally satisfies our stability criteria. The role of weak magnetic fields is essential to reach these conclusions. The triple-diffusive situation is more complex, and its stability criteria are not easily stated. Numerical analysis of our general dispersion relation confirms our analytic double-diffusive criteria but also shows that an unstable double-diffusive situation can be significantly stabilized by the addition of a third, ostensibly weaker, diffusion process. We describe a numerical application to the Sun's upper radiative zone and establish that it would be subject to unstable multidiffusive modes if moderate or strong radial gradients of angular velocity were present. |
| first_indexed | 2024-03-07T00:57:27Z |
| format | Journal article |
| id | oxford-uuid:88908467-36c9-4dd2-85b7-f92ec0f00854 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:57:27Z |
| publishDate | 2004 |
| publisher | Institute of Physics Publishing |
| record_format | dspace |
| spelling | oxford-uuid:88908467-36c9-4dd2-85b7-f92ec0f008542022-03-26T22:18:11ZLocal axisymmetric diffusive stability of weakly magnetized, differentially rotating, stratified fluidsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:88908467-36c9-4dd2-85b7-f92ec0f00854EnglishSymplectic Elements at OxfordInstitute of Physics Publishing2004Menou, KBalbus, SSpruit, HWe study the local stability of stratified, differentially rotating fluids to axisymmetric perturbations in the presence of a weak magnetic field and of finite resistivity, viscosity, and heat conductivity. This is a generalization of the Goldreich-Schubert-Fricke (GSF) double-diffusive analysis to the magnetized and resistive, triple-diffusive case. Our fifth-order dispersion relation admits a novel branch that describes a magnetized version of multi-diffusive modes. We derive necessary conditions for axisymmetric stability in the inviscid and perfect-conductor (double-diffusive) limits. In each case, rotation must be constant on cylinders and angular velocity must not decrease with distance from the rotation axis for stability, irrespective of the relative strength of viscous, resistive, and heat diffusion. Therefore, in both double-diffusive limits, solid-body rotation marginally satisfies our stability criteria. The role of weak magnetic fields is essential to reach these conclusions. The triple-diffusive situation is more complex, and its stability criteria are not easily stated. Numerical analysis of our general dispersion relation confirms our analytic double-diffusive criteria but also shows that an unstable double-diffusive situation can be significantly stabilized by the addition of a third, ostensibly weaker, diffusion process. We describe a numerical application to the Sun's upper radiative zone and establish that it would be subject to unstable multidiffusive modes if moderate or strong radial gradients of angular velocity were present. |
| spellingShingle | Menou, K Balbus, S Spruit, H Local axisymmetric diffusive stability of weakly magnetized, differentially rotating, stratified fluids |
| title | Local axisymmetric diffusive stability of weakly magnetized, differentially rotating, stratified fluids |
| title_full | Local axisymmetric diffusive stability of weakly magnetized, differentially rotating, stratified fluids |
| title_fullStr | Local axisymmetric diffusive stability of weakly magnetized, differentially rotating, stratified fluids |
| title_full_unstemmed | Local axisymmetric diffusive stability of weakly magnetized, differentially rotating, stratified fluids |
| title_short | Local axisymmetric diffusive stability of weakly magnetized, differentially rotating, stratified fluids |
| title_sort | local axisymmetric diffusive stability of weakly magnetized differentially rotating stratified fluids |
| work_keys_str_mv | AT menouk localaxisymmetricdiffusivestabilityofweaklymagnetizeddifferentiallyrotatingstratifiedfluids AT balbuss localaxisymmetricdiffusivestabilityofweaklymagnetizeddifferentiallyrotatingstratifiedfluids AT spruith localaxisymmetricdiffusivestabilityofweaklymagnetizeddifferentiallyrotatingstratifiedfluids |