2014 Fiscal Year Final Research Report
Theory of vortex-wave interaction by deepening the topological vorticity dynamics
| Project/Area Number |
24540407
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Kyushu University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | トポロジカル不変量 / クロスヘリシティ / ネータ―の定理 / 弱非線形安定性 / 波のエネルギー / 等磁気循環摂動 / 磁気回転不安定性 / ケプラー型回転流 |
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| Outline of Final Research Achievements |
By invoking the Noether theory associated with the particle-relabeling symmetry, we revealed that the topological integral invariants for barotropic and baroclinic flows, magnetohydrodynamics (MHD) and a relativistic flow are all represented in the form of the cross-helicity. By restricting disturbances to isovortical ones that keep the topology of the vorticity, we succeeded in calculating the weakly nonlinear stability of a rotating flow with elliptic streamlines. By restricting to the isomagnetovortical perturbations, we derived a general formula for waves on MHD flows. Using the Lagrangian treatment that realizes this class of perturbations, we made the three-dimensional short-wave stability analysis of the azimuthal magnetorotational instability, and showed that the Keplerian rotational flow is unstable.
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| Free Research Field |
流体力学
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