Covariant Lyapunov analysis of solutions of the Navier-Stokes equations

纳维-斯托克斯方程解的协变李雅普诺夫分析

• 批准号: 22654014
• 负责人: YAMADA Michio
• 金额: $ 1.93万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Challenging Exploratory Research
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22654014/
• 关键词: 応用数学; 流体; カオス; ナビエ・ストークス方程式; コルモゴロフ流; リヤプノフ解析; 共変リヤプノフ解析; 力学系; 双曲性; 相関関数

We studied chaotic states of Kolmogorov flows on a 2D flat torus (R/2πZ)2governed by the Navier-Stokes equations of incompressible fluids, by using the covariant Lyapunov analysis. Obtaining the bifurcation diagram of solutions, we performed the traditional Lyapunov analysis, and found that the first Lyapunov number becomes positive at Re/Rc～18, and the second one does at Re/Rc～23. Based on these data, we calculated the covariant Lyapunov vectors by the method of Ginelli et al. (2007), and found that the solution orbit is hyperbolic just after the chaotic transition, but becomes nonhyperbolic at Re/Rc～23, by observing the distribution of the angle between the stable/unstabletangent spaces of the orbit. At the hyperbolic/nonhyperbolic transition point, we found that the fuctional form of the time correlation function of the vorticity changes from oscillatory to non-oscillatory.

采用协变Lyapunov分析方法，研究了不可压缩流体Navier-Stokes方程下二维平面环面（R/2πZ）2上Kolmogorov流动的混沌态。得到了解的分岔图，进行了传统的Lyapunov分析，发现第一个Lyapunov数在Re/Rc~18处变为正，第二个Lyapunov数在Re/Rc~23处变为正。基于这些数据，我们采用Ginelli et al.（2007）的方法计算了协变Lyapunov向量，通过观察轨道稳定/不稳定空间之间夹角的分布，发现解轨道在混沌跃变后是双曲的，但在Re/Rc~23处变为非双曲的。在双曲/非双曲过渡点，涡度时间相关函数的函数形式由振荡型变为非振荡型。

项目成果

Triaxial rotation of the inner and outer spheres driven by Boussinesq thermal convection in a rotating spherical shell.

由旋转球壳中的 Boussinesq 热对流驱动的内球和外球的三轴旋转。

• 发表时间: 2012
• 作者: K. Obuse;S. Takehiro;M. Yamada;平岡裕章;A.C.Chian;平岡裕章;K..Obuse;平岡裕章;斉木吉隆;M.Inubushi;佐々木英一;犬伏正信;佐々木英一;Masanobu Inubushi;Eiichi Sasaki;Keiji Kimura;M.Yamada;S.Takehiro;K.Kimura;M.Yamada;Michio Yamada;Michio Yamada;Shin-ichi Takehiro;Keiji Kimura
• 通讯作者: Keiji Kimura

Covariant Lyapunov analysis of chaotic Kolmogorov flows

混沌 Kolmogorov 流的协变 Lyapunov 分析

• DOI: 10.1103/physreve.85.016331
• 发表时间: 2012
• 期刊: Physical Review E
• 影响因子: 2.4
• 作者: Masanobu Inubushi;Miki U. Kobayashi;Shin-ichi Takehiro;Michio Yamada
• 通讯作者: Michio Yamada

Orbital instability of a minimal wall turbulence

最小壁湍流的轨道不稳定性

• 发表时间: 2012
• 作者: K. Obuse;S. Takehiro;M. Yamada;平岡裕章;A.C.Chian;平岡裕章;K..Obuse;平岡裕章;斉木吉隆;M.Inubushi;佐々木英一;犬伏正信;佐々木英一;Masanobu Inubushi;Eiichi Sasaki;Keiji Kimura;M.Yamada
• 通讯作者: M.Yamada

Kolmogorov流の共変Lyapunov解析

柯尔莫哥洛夫型协变李雅普诺夫分析

• 发表时间: 2010
• 作者: K. Obuse;S. Takehiro;M. Yamada;平岡裕章;A.C.Chian;平岡裕章;K..Obuse;平岡裕章;斉木吉隆;M.Inubushi;佐々木英一;犬伏正信;佐々木英一;Masanobu Inubushi;Eiichi Sasaki;Keiji Kimura;M.Yamada;S.Takehiro;K.Kimura;M.Yamada;Michio Yamada;Michio Yamada;Shin-ichi Takehiro;Keiji Kimura;犬伏正信;佐々木英一;佐々木英一;佐々木英一;犬伏正信;犬伏正信;M.Yamada;Michio Yamada;Masanobu Inubushi;M.Inubushi;山田道夫;山田道夫;小布施祈織;Y.Saiki;Y.Saiki;M.U.Kobayashi;Y.Saiki;Y.Saiki;佐々木英一;犬伏正信
• 通讯作者: 犬伏正信

Covariant Lyapunov Analysis of a Minimal Wall Turbulence.

最小壁湍流的协变李雅普诺夫分析。

• 发表时间: 2013
• 作者: 太田克弘;江川嘉美;藤田慎也;佐久間雅;Osamu Iyama;S. Kamada;Hiroya Hashimoto and Takahiro Tsuchiya;Ken'ichi Ohshika;M. Nakamura;M. Inubushi
• 通讯作者: M. Inubushi