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arXiv 2005.05303physics.flu-dyn
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支撑壁turbulence的线性机制的因果关系

Cause-and-effect of linear mechanisms sustaining wall turbulence

Adrián Lozano-Durán, Navid C. Constantinou, Marios-Andreas Nikolaidis, Michael Karp

发表信息：
J. Fluid Mech., vol. 914, A8, 2021
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摘要：

尽管湍流的非线性性质，有证据表明，部分能量传递机制维持壁湍流可以归因于线性过程。不同的情况源于线性稳定性理论，包括指数不稳定性，中性模式，非正常运营商的瞬态增长，以及时间平均流量变化的参数不稳定性，等等。这些机制，每一个潜在的能够导致观察到的湍流结构，植根于理论和概念的争论。流动是否遵循其中任何一个或组合仍然是难以捉摸的。在这里，我们评估的线性机制负责的能量传递从流向平均的平均流量（$\bf U$）的脉动速度（$\bf u'$）。我们使用基于干预措施的因果分析。这是通过在低雷诺数下直接数值模拟湍流槽道流来实现的，其中从$\bf U$到$\bf u'$的能量传递被约束以排除目标线性机制。我们表明，瞬态增长是足以维持现实的壁湍流。当平均流的指数不稳定性、中性模式和参数不稳定性被抑制时，自持湍流持续存在。我们进一步表明，瞬态增长的一个关键组成部分是奥尔/推过机制引起的展向变化的基流。最后，我们证明了各种冻结的时间$\bf U$安排，以便只有瞬态增长是活跃的模拟合奏，可以忠实地代表能量转移从$\bf U$到$\bf u'$在现实的湍流。我们的方法提供了直接的因果关系评估的线性能量压射机构，从$\bf U$到$\bf u'$在完全非线性系统和简化的概念模型的自持壁湍流。

英文摘要：

Despite the nonlinear nature of turbulence, there is evidence that part of the energy-transfer mechanisms sustaining wall turbulence can be ascribed to linear processes. The different scenarios stem from linear stability theory and comprise exponential instabilities, neutral modes, transient growth from non-normal operators, and parametric instabilities from temporal mean-flow variations, among others. These mechanisms, each potentially capable of leading to the observed turbulence structure, are rooted in theoretical and conceptual arguments. Whether the flow follows any or a combination of them remains elusive. Here, we evaluate the linear mechanisms responsible for the energy transfer from the streamwise-averaged mean-flow ($\bf U$) to the fluctuating velocities ($\bf u'$). We use cause-and-effect analysis based on interventions. This is achieved by direct numerical simulation of turbulent channel flows at low Reynolds number, in which the energy transfer from $\bf U$ to $\bf u'$ is constrained to preclude a targeted linear mechanism. We show that transient growth is sufficient for sustaining realistic wall turbulence. Self-sustaining turbulence persists when exponential instabilities, neutral modes, and parametric instabilities of the mean flow are suppressed. We further show that a key component of transient growth is the Orr/push-over mechanism induced by spanwise variations of the base flow. Finally, we demonstrate that an ensemble of simulations with various frozen-in-time $\bf U$ arranged so that only transient growth is active, can faithfully represent the energy transfer from $\bf U$ to $\bf u'$ as in realistic turbulence. Our approach provides direct cause-and-effect evaluation of the linear energy-injection mechanisms from $\bf U$ to $\bf u'$ in the fully nonlinear system and simplifies the conceptual model of self-sustaining wall turbulence.

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