标题： 多特征时间尺度系统中的可预测性：湍流情况 显示英文标题

标题： Predictability in Systems with Many Characteristic Times: The Case of Turbulence

摘要： 在混沌动力学系统中，一个无穷小扰动的指数放大率由最大李雅普诺夫指数$\lambda$的倒数决定。 在完全发展的湍流中，$\lambda$的增长与雷诺数的幂次相关。 这一结果似乎与经验性论据相矛盾，后者表明由于“物理”扰动的影响，可预测时间大致由大尺度结构的特征寿命决定，因此与雷诺数无关。 我们证明了这种现象存在于具有多个自由度的通用系统中，因为非无穷小扰动的增长是由许多不同特征时间的累积效应决定的，并且与最大李雅普诺夫指数无关。 我们的结果通过耦合映射链和湍流能量级串的壳模型进行了说明。 显示英文摘要

摘要： In chaotic dynamical systems, an infinitesimal perturbation is exponentially amplified at a time-rate given by the inverse of the maximum Lyapunov exponent $\lambda$. In fully developed turbulence, $\lambda$ grows as a power of the Reynolds number. This result could seem in contrast with phenomenological arguments suggesting that, as a consequence of `physical' perturbations, the predictability time is roughly given by the characteristic life-time of the large scale structures, and hence independent of the Reynolds number. We show that such a situation is present in generic systems with many degrees of freedom, since the growth of a non-infinitesimal perturbation is determined by cumulative effects of many different characteristic times and is unrelated to the maximum Lyapunov exponent. Our results are illustrated in a chain of coupled maps and in a shell model for the energy cascade in turbulence.