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首页> 外文会议>IUTAM(International Union of Theoretical and Applied Mechanics) Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions and Symposium on Non-Uniqueness of Solutions to the Navier-Stokes Equations and Their Connection with Laminar-Turbule >THE KARHUNEN-LOEVE DECOMPOSITION OF THE AUTONOMOUS MINIMAL FLOW UNIT
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THE KARHUNEN-LOEVE DECOMPOSITION OF THE AUTONOMOUS MINIMAL FLOW UNIT

机译：自治最小流动单元的卡鲁因-爱分解

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摘要

We propose to examine the effects of restricting the interaction between near-wall turbulence and the outer flow on the structure and dynamics of the empirical eigenfunctions functions determined using the proper orthogonal decomposition (POD). This research is motivated by the fact that standard POD-based low-dimensional models for the near-wall region have been derived for empirical eigenfunctions computed for an unbiased channel flow. However, under the present truncation of the flow dynamics, the POD basis may be significantly affected so that the common assumption that effective reduced-order models can be constructed from the POD basis of an unaltered flow may be suspect. This issue is explored for plane, incompressible, turbulent channel flow at Reynolds number, Re_τ = 180. Based on direct numerical simulations, POD basis functions are constructed for an unbiased and four truncated minimal channel flows. The POD eigenfunctions which characterize these modified flows are associated to a travelling-wave solution which undergoes a series of bifurcation until settling into a turbulent regime. A POD-based two-mode model is also derived for the near-wall layer and is evaluated. It is shown that travelling-wave solutions appear as a backbone to the low-dimensional dynamics of the autonomous near-wall region.
机译：我们建议检查限制近壁湍流和外流之间的相互作用对使用适当的正交分解（POD）确定的经验本征函数的结构和动力学的影响。这项研究是受以下事实启发的：已经为针对无偏通道流计算的经验本征函数推导了近壁区域基于标准POD的低维模型。但是，在当前截断的流体动力学中，POD基础可能会受到重大影响，因此可以怀疑可以从不变的POD基础构建有效的降阶模型的一般假设。研究了雷诺数为Re_τ= 180的平面，不可压缩湍流通道的问题。基于直接数值模拟，为无偏和四个截断的最小通道流构造了POD基函数。表征这些修正流的POD本征函数与行波解相关联，行列解经历了一系列分叉直到沉降为湍流状态。还为近壁层导出了基于POD的两模模型并进行了评估。结果表明，行波解似乎是自主近壁区域低维动力学的主干。

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