By tracking the divergence of two initially close trajectories in phase space in an Eulerian approach to forced turbulence, the relation between the maximal Lyapunov exponent $\lambda$ and the Reynolds number Re is measured using direct numerical simulations, performed on up to $2048^3$ collocation points. The Lyapunov exponent is found to solely depend on the Reynolds number with $\lambda \propto {\mathrm{Re}}^{0.53}$ and that after a transient period the divergence of trajectories grows at the same rate at all scales. Finally a linear divergence is seen that is dependent on the energy forcing rate. Links are made with other chaotic systems.

中文翻译：

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各向同性湍流流体的混沌特性

通过在欧拉强迫湍流方法中跟踪相空间中两个初始接近的轨迹的发散，最大李雅普诺夫指数之间的关系 $\lambda$ 雷诺数Re是使用直接数值模拟测量的，该模拟最多可进行 $2048^3$搭配点。发现李雅普诺夫指数仅取决于雷诺数$\lambda \propto {\mathrm{关于}}^{0.53}$在过渡期之后，轨迹的散度在所有尺度上都以相同的速率增长。最后，可以看到线性发散，该发散取决于能量强迫率。链接是与其他混沌系统建立的。