Numerical simulations of nonlinear dynamical systems with large degree of freedom and turbulence

大自由度和湍流非线性动力系统的数值模拟

基本信息

批准号：
09640487
负责人：
FUJISAKA Hirokazu
金额：
$ 0.32万
依托单位：
KYOTO UNIVERSITY (1998)Kyushu University (1997)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

项目摘要

Theoretical and numerical study of two-dimensional turbulenceIn the Charney-Hasegawa-Mima turbulence, energy flows into a small wavenumber region in the wavenumber space in the process of the development of turbulence. We observed that a quasi-crystal structure is formed in this inverse cascade process, and that the structure function of the vorticity field obeys the dynamic scaling law. In the decaying turbulence we showed that the total energy is asymptotically conserved, and that there exists a dynamical scaling law for the vorticity spectrum and developed a phenomenological theory. Furthermore the exponent characterizing the decaying process of the vortix ensemble is phenomenologically determined by utilizing the Hamiltonian dynamics characteristics of the ensemble of vortices.Nonlinear dynamical systems with large degrees of freedomA new model for nonlinear media with a strong dissipation in high-wavenumber dynamics is proposed, and three models with chaotic elements, including the proposed one were numerically solved. When the systems size is less than the critical size Lc, the spatially uniform chaotic oscillation is stable. On the other hand, when the system size is larger than Lc, it becomes unstable. In the latter case, we observed an intermittency, whose statitics turned out to be identical to those of on-off intermittency. Furthemore, we found the following new characteristics of on-off intermittency : (1) We found a new diffusion generated via on-off intermittency. It was termed as on-off diffusion. (2) A new dynamical scaling law for the Fourier spectrum of on-off variable is proposed. (3) A new statistical law of transient process before the onset of on-off intermittency is found.

在Charney-Hasegawa-Mima湍流中，二维湍流的理论和数值研究在湍流的发展过程中，能量流入波数空间中的小波数区域。我们观察到在这个反级联过程中形成了准晶体结构，并且涡度场的结构函数遵守动态缩放定律。在腐烂的湍流中，我们表明总能量是渐近保守的，并且存在针对涡度光谱的动态缩放定律，并发展了现象学理论。 Furthermore the exponent characterizing the decaying process of the vortix ensemble is phenomenologically determined by utilizing the Hamiltonian dynamics characteristics of the ensemble of vortices.Nonlinear dynamical systems with large degrees of freedomA new model for nonlinear media with a strong dissipation in high-wavenumber dynamics is proposed, and three models with chaotic elements, including the proposed one were numerically solved.当系统尺寸小于临界尺寸LC时，空间均匀的混沌振荡将稳定。另一方面，当系统尺寸大于LC时，它会变得不稳定。在后一种情况下，我们观察到了一个间歇性，其统计与开关间歇性相同。此外，我们发现了以下开关间歇性的新特征：（1）我们发现通过开关间歇性生成的新扩散。它被称为On-Off扩散。（2）提出了针对On-Off变量的傅立叶频谱的新的动力学缩放定律。（3）在开关间歇性发作之前，新的瞬态过程统计定律。