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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.

二维湍流的理论与数值研究在查尼-长谷川-美马湍流中，湍流发展过程中能量会流入波数空间中的小波数区域。我们观察到，在这种逆级联过程中形成了准晶体结构，并且涡量场的结构函数服从动态标度定律。在衰变湍流中，我们证明了总能量是渐近守恒的，并且存在涡度谱的动力学标度定律，并发展了唯象理论。进一步利用涡系系的哈密顿动力学特性，唯象地确定了表征涡系系衰减过程的指数。大自由度非线性动力系统提出了一种新的高波数动力学强耗散非线性介质模型，并对包括该模型在内的三个混沌元模型进行了数值求解。当系统尺寸小于临界尺寸Lc时，空间均匀混沌振荡是稳定的。另一方面，当系统规模大于Lc时，系统变得不稳定。在后一种情况下，我们观察到一种间歇性，其统计数据与开关间歇性的统计数据相同。此外，我们发现了开关间歇性的以下新特征：（1）我们发现了通过开关间歇性产生的新扩散。这被称为开关扩散。 (2)提出了一种新的开关变量傅立叶谱动态标度律。 (3)发现了开关间歇发生前暂态过程的新统计规律。