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. 对涡旋灯丝的三维运动进行了理论研究。i)得到了轴对称涡旋环在粘性流体中速度的一般公式。对无限薄核在初始时刻进行了数值计算。圆环半径扩展与实验测量结果吻合较好。ii)将Biot-Savart积分的渐近展开和匹配的渐近展开式推广到高阶，从而得到涡管速度的三阶修正。讨论了其与局部归纳层次的关系。从哈密顿谱理论的角度计算了涡旋环的三维不稳定性。结果表明，由于曲率效应，轴对称模态和弯曲模态之间发生了参数共振。利用高精度有限差分格式对声波在涡旋中的产生和散射进行了直接数值模拟。i)计算了激波与涡环的相互作用，阐明了声的产生机理。ii)成功计算了涡环正面碰撞产生的远区小幅度压力波动。iii)通过数值模拟，评估了希尔球涡对声音散射的渐近理论。iv)对量子化涡流重连过程中产生声音的Gross-Petaevskii方程进行了数值模拟。利用MHD湍流模型方程，研究了大尺度磁场中有序结构对特征时间和间歇度的影响。

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）。

Y.Fukumoto: "Motion of a curved vortex filament : Higher-order asymptotics"Proc.of IUTAM Symposium on Geometry and Statistics of Turbulence (eds.T.Kambe,T.Nakano and T.Miyauchi, Kluwer). 59. 211-216 (2001)

Y.Fukumoto：“弯曲涡丝的运动：高阶渐进”Proc.of IUTAM 湍流几何与统计研讨会（eds.T.Kambe、T.Nakano 和 T.Miyauchi、Kluwer）。