Symmetry breaking and Hamiltonian bifurcation theory for three-dimensional instability of a vortex tube

涡流管三维不稳定性的对称破缺和哈密顿分岔理论

基本信息

批准号：
14540379
负责人：
FUKUMOTO Yasuhide
金额：
$ 1.41万
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：
2002
资助国家：
日本
起止时间：
2002 至 2003
项目状态：
已结题

项目摘要

1.Three-dimensional instability of an elliptic vortex and a vortex ring was investigated from the viewpoint of the Hamiltonian spectral theory.(1)A pure shear breaks the SO(2)xO(2)-symmetry of the Rankine vortex and deforms the circular core into an ellipse.We have succeeded in explicitly writing down the infinitesimal disturbances in terms of the Bessel functions.The relation with the elliptical instability is clarified.(2)For a vortex ring, symmetry-bresking perturbation is the curvature effect. The infinitesimal disturbances on Kelvin's vortex ring are written out in a closed form.We have found a possibility of parametric resonance between pairs of Kelvin waves whose azimuthal wavenumbers are separated by two.A local stability analysis is also made, using the WKB method It is clarified that the structure of unstable modes on a Gaussian core is very different from that on Kelvin's vortex ring.(3)We have derived weakly nonlinear evolution equations of amplitudes of several unstable mo … More des on a vortex tube subjected to a pure shear, with the aid of equivariant vector fields associated with Z2xO(2) symmetry.2.When a pulse of excimer laser of a few ten nanoseconds is irradiated on a Co-coated substrate, vortex filaments are created, quenched and frozen at once.By estimating the time scales from a stability analysis in the localized induction approximation, we have extracted a dynamical picture from the micrographs of the frozen pictures.(2)By repeating the irradiation, of pulses several times, unstable vortex rings are obtained.3.For the side-band instability of a plane wave, it is proven that, near the linear critical point, the methods based on envelope equations, on amplitude equations and on a secondary-instability analysis are all equivalent.4.For the Rayleigh-Benard convection, the fifth-order amplitude equations are derived, using the center-manifold reduction, and their bifurcation analysis is made near the degeneracy point with quadratic dependence on temperature of the density being an unfolding parameter It is clarified that right-hexagonal, right-triangle and patch-work quilt patterns are unstable as a primary bifurcation solution of the generic normal form equations. Less

1。从哈米尔顿语光谱理论的角度研究了椭圆涡流和涡旋环的三维不稳定。（1）纯剪切破坏了so（2）xo（2）xo（2） - 兰金涡流的 - 对称性，并将圆形核心变形为e椭圆形，使explients explactients teclesitions tequestients condients.cline nistimity instains intallimit.cline in and and secter.cline in and and intains in and sectity in and and intains.complys in and and in consect.natime intalsim ins and and and in and and and。（2）对于涡旋环，对称性打扰是曲率效应。开尔文涡流环上的无限惊喜以封闭形式写出。我们发现，在开尔文波之间有参数共振的可能性，其空调的波浪人通过两种局部稳定性分析。在WKB方面，也可以澄清的是，与Quussian的结构相差很大。（3）我们已经在几个不稳定的mo的振幅中得出了弱的非线性进化方程……在涡旋管上更属于纯剪切的涡流管，借助Z2XO（2）对称性相关的纯态矢量场。2。通过在局部归纳近似中的稳定性分析中估算时间尺度，我们已经从冷冻图片的显微照片中提取了动态图片。（2）通过重复几次脉冲，几次脉冲，几次获得不稳定的涡旋环。方程，放大器方程式和二次不稳定性分析都是等效的。4。对于雷利 - 贝纳德的转换，使用中心序列降低得出了五阶放大器方程，其分支分析是在重点依赖的二次依赖和依赖的范围的依赖性和依赖的依赖性的情况下，并依赖于二次依赖的依赖，并将其分支分析构成。被子图案是通用正常形式方程的主要分叉解决方案不稳定的。较少的