Large volume limit of the distribution of characteristic exponents in turbulence
Large volume limit of the distribution of characteristic exponents in turbulence
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DOI：
10.1007/bf01218566
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发表时间：
1982-06
影响因子：
2.4
通讯作者：
D. Ruelle
中科院分区：
文献类型：
--
作者：
D. Ruelle
对于空间扩展的保守或耗散物理系统，当体积趋于无穷大时，每单位体积的特征指数密度应该存在，这似乎是很自然的。然而，在湍流粘性流体的情况下，这个简单的想法由于不稳定性现象而变得复杂。在本文中，我们得到严格的上界的分布的特征指数的耗散。这些边界具有合理的大体积行为。对于二维流体，得到了一个特别惊人的结果：总信息的产生是由总能量耗散的固定倍数（在固定粘度下）限制的。在间歇湍流模型中估计了特征指数的分布（见[7]），发现在自相似维数D =2.6处发生行为变化。
For spatially extended conservative or dissipative physical systems, it appears natural that a density of characteristic exponents per unit volume should exist when the volume tends to infinity. In the case of a turbulent viscous fluid, however, this simple idea is complicated by the phenomenon of intermittency. In the present paper we obtain rigorous upper bounds on the distribution of characteristic exponents in terms of dissipation. These bounds have a reasonable large volume behavior. For two-dimensional fluids a particularly striking result is obtained: the total information creation is bounded above by a fixed multiple of the total energy dissipation (at fixed viscosity). The distribution of characteristic exponents is estimated in an intermittent model of turbulence (see [7]), and it is found that a change of behavior occurs at the valueD=2.6 of the self-similarity dimension.