权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Three-dimensional nonlinear stability theory of vortices from the view point of Hamiltonian dynamicalsysytems

哈密顿动力系统视角下的涡三维非线性稳定性理论

基本信息

批准号：
16540345
负责人：
FUKUMOTO Yasuhide
金额：
$ 1.47万
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：
2004
资助国家：
日本
起止时间：
2004 至 2005
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540345/
关键词：
Kelvin's vortex ring curvature instability Krein theory weakly nonlinear instability three-wave resonance laser-matter interactions helical vortex tube energy balance of magnetic eddies Dysonの方法ノーマルフォーム振幅方程式らせん渦ハミルトン的スペクトル理論

项目摘要

A new instability mechanism "curvature instability", originating from the curvature of vortex lines, is found for Kelvin's vortex ring. The eigenfunction is explicitly writing out and thereby asymptotic form of the growth rate at large wavelengths is derived. We have elucidated structure of the spectrum from the viewpoint of the Krein theory for Hamiltonian systems. By repeating irradiation of pulses of excimer laser on a Co-coated substrate, unstable vortex rings are created. By analyzing the micrographs of their frozen pictures. we identified four types of instability modes. We made a weakly nonlinear stability analysis of Kelvin's vortex ring. It is found from numerical analysis of the derived amplitude equations that the system exhibits a chaotic behavior. We also conducted a direct numerical simulation of a vortex ring, and clarified a detailed structure of the Widnall instability.We exploited the Hamiltonian normal form, associated with the SO(2) x O(2)-symmetry, to select possib … More le form of the weakly nonlinear evolution equations of amplitude of the bending modes (azimuthal wavenumber m=1,-1) of Kelvin waves on an elliptically strained vortex tube. The coefficient of the amplitude equations are evaluated for non-rotating modes. The nonlinear terms make the elliptical instability saturate. However, it is pointed out that three-wave resonance of modes of m=3,4 and a bending mode derives a secondary instability.By extending Dyson's technique to three dimensions, we developed a method of asymptotic expansions of the Biot-Savart integral, which takes account of the influence of finite core thickness on a vortex tube. This method is applied to calculation of velocity field around a helical vortex tube. In the neighborhood of the core, we cannot ignore the dipoles arranged on the tube center line which reflects the distribution of vorticity in the core.A formulation of contour dynamics is given to the magnetohydrodynamic evolution of axisymmetric magnetic eddies. A family of exact solutions is found. Their significance in energy balance is clarified by both numerical implementation of the contour dynamics and a direct numerical simulation. Less

本文发现了一种新的不稳定性机制“曲率不稳定性”，它起源于涡线的曲率。显式写出本征函数，从而导出了大波长下增长率的渐近形式。我们已经阐明了结构的频谱的观点的克莱因理论的哈密顿系统。通过准分子激光脉冲在镀钴基片上的重复照射，产生了不稳定的涡环。通过分析他们冰冻照片的显微照片。我们确定了四种类型的不稳定模式。对Kelvin涡环进行了弱非线性稳定性分析。通过对所导出的振幅方程进行数值分析，发现系统具有混沌行为。我们还对涡环进行了直接数值模拟，阐明了Widnall不稳定性的详细结构，并利用与SO（2）xO（2）对称性相联系的Hamilton规范形来选择可能的不稳定性。 ...更多信息本文给出了椭圆应变涡管上Kelvin波弯曲模（方位波数m=1，-1）振幅的弱非线性演化方程的形式。非旋转模式的振幅方程的系数进行评估。非线性项使椭圆不稳定性饱和。本文指出，m= 3，4和弯曲模的三波共振会导致二次不稳定性，并将Dyson方法推广到三维空间，发展了一种考虑涡核有限厚度影响的Biot-Savart积分的渐近展开方法。将该方法应用于螺旋涡流管周围速度场的计算。在核附近，不能忽略反映核内涡量分布的偶极子分布。给出了轴对称磁涡磁流体动力学演化的轮廓动力学公式。通过数值模拟和直接数值模拟，阐明了它们在能量平衡中的意义。少