2000 Fiscal Year Final Research Report Summary
Higher-order asymptotic theory and numerical analysis for three-dimensional dynamics of a vortex filament in a flw
| Project/Area Number |
11640398
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
物理学一般
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| Research Institution | KYUSHU UNIVERSITY |
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Principal Investigator |
FUKUMOTO Yasuhide KYUSHU UNIVERSITY Graduate School of Mathematics, Ass.Prof., 大学院・数理学研究院, 助教授 (30192727)
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| Co-Investigator(Kenkyū-buntansha) |
HATTORI Yuji Kyushu Institute of Technology, Faculty of Engineering, Ass.Pof, 工学部, 助教授 (70261469)
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| Project Period (FY) |
1999 – 2000
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| Keywords | vortex ring / three-dimensional motion of a vortex filament / method of matched asymptotic asymptotic expansions / localized induction hierarchy / parametric resonance / vortex-sound interaction / reconnection of quantized vortex filaments / statistical properties of MHD turbulence |
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| Research Abstract |
1. Three-dimensional motion of a vortex filament was investigated theoretically.
i) A general formula for velocity of an axisymmetric vortex ring in a viscous fluid was obtained. Numerical computation was carried through for an infinitely thin core at the initial instant. Expansion of ring radius compares well with an experimental measurement.
ii) Asymptotic development of the Biot-Savart integral and matched asymptotic expansions were extended to a high order, whereby the third-order correction to the speed of a vortex tube was obtained. Its relevance to the localized induction hierarchy was discussed.
2. Three-dimensional instability of a vortex ring was calculated from the viewpoint of Hamiltonian spectrum theory. It was shown that a parametric resonance occurs between axisymmetric and bending modes due to the curvature effect.
3. Direct numerical simulations of the Navier-Stokes equations using a highly accurate finite difference scheme were performed for generation and scattering of sound waves by vortices.
i) An interaction of shock waves with a vortex ring was calculated and mechanism for sound generation was clarified.
ii) Pressure fluctuations of small amplitude in a far region, generated by a head-on collision of vortex rings, was successfully computed.
iii) With a numerical simulation, asymptotic theories for scattering of sound by Hill's spherical vortex were assessed.
iv) A numerical simulation of the Gross-Petaevskii equation was performed for sound generation in the process of reconnection of quantized vortices.
4. Using a model equation for MHD turbulence, the effect of an ordered structure in large-scale magnetic field upon scaling of characteristic time and intermittency was examined.
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Research Products
(24 results)
