论文标题
部分可观测时空混沌系统的无模型预测
Improved assessment of the statistical stability of turbulent flows using extended Orr-Sommerfeld stability analysis
论文作者
论文摘要
统计稳定性的概念是Malkus 1956年试图预测剪切流湍流中平均轮廓的核心。在这里，我们讨论了他如何通过考虑累积的Navier -Stokes方程的扩展来改善他如何评估这一点的最初尝试（ORR -SOMMERFELD分析）。着眼于最简单的非平地闭合（通常称为CE2），该闭合对应于准线性的Navier-Stokes方程，我们开发了一个扩展的Orr-Sommerfeld分析（EOS），该分析（EOS）还结合了有关波动场的信息。在许多统计稳态，因此统计稳定的湍流通道流量上，对此进行了更实用的版本 - 最小扩展的Orr -Sommerfeld分析（MEOS）。除了统计稳定性的概念之外，这种扩展的稳定性分析还应通过在其预测中包含有关基础流以及其他具有对流等其他物理学的其他流量的信息来改善均值剪切流中平均流线性分析的流行方法。
The concept of statistical stability is central to Malkus's 1956 attempt to predict the mean profile in shear flow turbulence. Here we discuss how his original attempt to assess this - an Orr-Sommerfeld analysis on the mean profile - can be improved by considering a cumulant expansion of the Navier-Stokes equations. Focusing on the simplest non-trivial closure (commonly referred to as CE2) which corresponds to the quasilinearized Navier-Stokes equations, we develop an extended Orr-Sommerfeld analysis (EOS) which also incorporates information about the fluctuation field. A more practical version of this - minimally extended Orr-Sommerfeld analysis (mEOS) - is identified and tested on a number of statistically-steady and therefore statistically stable turbulent channel flows. Beyond the concept of statistical stability, this extended stability analysis should also improve the popular approach of mean-flow linear analysis in time-dependent shear flows by including more information about the underlying flow in its predictions as well as for other flows with additional physics such as convection.
