Theory of vortex-wave interaction by deepening the topological vorticity dynamics
Project/Area Number |
24540407
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Mathematical physics/Fundamental condensed matter physics
|
Research Institution | Kyushu University |
Principal Investigator |
|
Project Period (FY) |
2012-04-01 – 2015-03-31
|
Project Status |
Completed (Fiscal Year 2014)
|
Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
|
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 / 方位磁気回転不安定性 / Hain-Lust方程式 / 非理想MHD / WKB法 / Landau-Darrieus不安定性 / 燃焼界面 / トポロジカル積分不変量 / 三波共鳴 / カシミール不変量 / トポロジー的不変量 / バロクリニック流体 / ケルヴィン波 / 渦対 / 運動速度 |
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.
|
Report
(4 results)
Research Products
(45 results)