Higher-order asymptotic theory and numerical analysis for three-dimensional dynamics of a vortex filament in a flw

流场涡丝三维动力学的高阶渐近理论与数值分析

• 批准号: 11640398
• 负责人: FUKUMOTO Yasuhide
• 金额: $ 1.02万
• 依托单位: KYUSHU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640398/
• 关键词: 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 p

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.

1。理论上研究了涡旋细丝的三维运动。I）获得了粘性流体中轴对称涡流环速度的一般公式。在初始瞬间，对无限薄的芯进行了数值计算。环半径的膨胀与实验测量很好地比较。II）生物 - 萨瓦特积分和匹配的渐近扩展的渐近发展扩展到高阶，从而获得了对涡流管的速度的三阶校正。讨论了它与局部归纳层次结构的相关性。2。涡流环的三维不稳定是从哈密顿谱理论的角度计算得出的。结果表明，由于曲率效应，轴对称和弯曲模式之间发生了参数共振3。使用涡流对Navier-Stokes方程进行了直接的数值模拟，以通过涡流进行声波生成和散射。评估了Hill球形涡流散射的渐近理论。IV）在重新连接量化涡旋的过程中，对Gross-Petaevskii方程进行了总petaevskii方程的数值模拟。4。使用模型方程进行MHD湍流，检查了特征时间和间歇性缩放时大规模磁场中有序结构的影响。

项目成果

O.Inoue,Y.Hattori,T.Sasaki: "Sound generation by coaxial collision of vortex rings"Journal of Fluid Mechanics. 424. 327-365 (2000)

O.Inoue，Y.Hattori，T.Sasaki：“涡环同轴碰撞产生声音”流体力学杂志。

Y.Fukumoto: "Motion and expansion of a viscous vortex ring. Part 1.A higher-order asymptotic formula for the velocity"Journal of Fluid Mechanics. (発表予定). (2000)

Y.Fukumoto：“粘性涡环的运动和膨胀。第 1 部分。速度的高阶渐近公式”《流体力学》杂志（即将出版）。

Y.Fukumoto,H.K.Moffatt: "Motion and expansion of a viscous vortex ring : elliptical slowing down and diffusive expansion"Proc.of Symposium on Turbulence Structure and Vortex Dynamics (eds.J.C.R.Hunt and J.C.Vassilicos, Cambridge University Press). 1-22 (2

Y.Fukumoto、H.K.Moffatt：“粘性涡环的运动和膨胀：椭圆减速和扩散膨胀”湍流结构和涡动力学研讨会论文集（J.C.R.Hunt 和 J.C.Vassilicos 编，剑桥大学出版社）。

Y.Hattori,A.Ishizawa: "Characteristic Time Scales and Energy Transfer in MHD Turbulence"Proc.of IUTAM Symposium on Geometry and Statistics of Turbulence (eds.T.Kambe,T.Nakano and T.Miyauchi,Kluwer). 59. 89-94 (2001)

Y.Hattori、A.Ishizawa：“MHD 湍流中的特征时间尺度和能量传递”IUTAM 湍流几何与统计研讨会论文集（编辑 T.Kambe、T.Nakano 和 T.Miyauchi、Kluwer）。

O.Inoue: "Sound generation by shack-vortex interactions"Journal of Fluid Mechanics. 380. 81-116 (1999)

O.Inoue：“通过棚涡相互作用产生声音”流体力学杂志。