论文标题
完全发育的二维湍流中的确切相干结构
Exact Coherent Structures in Fully Developed Two-Dimensional Turbulence
论文作者
论文摘要
本文报告了具有周期性边界条件的正方形域上2+1维欧拉方程的几类新类别的弱不稳定的复发解决方案。这些解决方案具有许多引人注目的特性，可将它们与描述过渡流的Navier-Stokes方程的类似解决方案区分开。首先，它们有高维的连续家庭。其次，连接了不同类型的溶液，例如，平衡可以平稳地继续到行动波或时间周期状态。第三，也是最重要的是，其中许多解决方案在高雷诺数下与湍流动态相关。具体而言，我们发现数值模拟中的湍流表现出大规模连贯的结构，类似于我们的某些时间周期性解决方案，既经常又超过较长的时间间隔。这种溶液类似于最初在过渡流中引入的确切相干结构。
This paper reports several new classes of weakly unstable recurrent solutions of the 2+1-dimensional Euler equation on a square domain with periodic boundary conditions. These solutions have a number of remarkable properties which distinguish them from analogous solutions of the Navier-Stokes equation describing transitional flows. First of all, they come in high-dimensional continuous families. Second, solutions of different types are connected, e.g., an equilibrium can be smoothly continued to a traveling wave or a time-periodic state. Third, and most important, many of these solutions are dynamically relevant for turbulent flow at high Reynolds numbers. Specifically, we find that turbulence in numerical simulations exhibits large-scale coherent structures resembling some of our time-periodic solutions both frequently and over long temporal intervals. Such solutions are analogous to exact coherent structures originally introduced in the context of transitional flows.
