[论文解读] Physics of Flow Instability and Turbulent Transition in Shear Flows

Hua-Shu Dou|arXiv (Cornell University)|Jul 2, 2006

Fluid Dynamics and Turbulent Flows参考文献 37被引用 42

一句话总结

本文提出了“能量梯度法”——一种基于物理的模型，通过分析基本流与扰动相互作用下的能量变化，解释剪切流中的流动失稳与湍流转捩现象。该方法识别出横向能量梯度是扰动放大的驱动力，并表明存在一个普遍的临界能量梯度参数 Kmax ≈ 370–389，与管道流和平面Poiseuille流的实验数据高度吻合。

ABSTRACT

In this paper, the physics of flow instability and turbulent transition in shear flows is studied by analyzing the energy variation of fluid particles under the interaction of base flow with a disturbance. For the first time, a model derived strictly from physics is proposed to show that the flow instability under finite amplitude disturbance leads to turbulent transition. The proposed model is named as "energy gradient method." It is demonstrated that it is the transverse energy gradient that leads to the disturbance amplification while the disturbance is damped by the energy loss due to viscosity along the streamline. It is also shown that the threshold of disturbance amplitude obtained is scaled with the Reynolds number by an exponent of -1, which exactly explains the recent modern experimental results by Hof et al. for pipe flow. The mechanism for velocity inflection and hairpin vortex formation are explained with reference to analytical results. Following from this analysis, it can be demonstrated that the critical value of the so called energy gradient parameter Kmax is constant for turbulent transition in wall bounded parallel flows, and this is confirmed by experiments and is about 370-389. The location of instability initiation in the flow field accords well with the experiments for both pipe Poiseuille flow (r/R=0.58) and plane Poiseuille flow (y/h=0.58). It is also inferred from the proposed method that the transverse energy gradient can serve as the power for the self-sustaining process of wall bounded turbulence. Finally, the relation of "energy gradient method" to the classical "energy method" based on Rayleigh-Orr equation is discussed.

研究动机与目标

• 开发一种基于物理的模型，以解释经典线性稳定性理论之外剪切流中湍流起始的机制。
• 解决在有限幅值扰动下预测湍流转捩的长期挑战。
• 识别控制壁面受限流中湍流转捩的普遍参数。
• 利用基于能量的分析解释速度拐点和马蹄涡形成的机制。
• 建立能量梯度法与经典能量方法（如Rayleigh-Orr方程）之间的联系。

提出的方法

• 从基本流与扰动相互作用下的流体能量平衡基本原理出发，推导出一种新模型——“能量梯度法”。
• 分析流体质点的能量变化，区分由横向能量梯度引起的放大与沿流线的粘性耗散引起的衰减。
• 引入能量梯度参数K，定义为横向能量梯度与粘性耗散率的比值。
• 通过解析解证明，Kmax在不同壁面受限流中均保持恒定，约为370–389。
• 将能量梯度法与经典Rayleigh-Orr能量方法进行比较，阐明其物理基础与优势。
• 将预测结果与实验数据进行验证，特别是Hof等人关于管道流转捩的研究结果。

实验结果

研究问题

• RQ1 在有限幅值扰动下，剪切流中扰动放大的物理机制是什么？
• RQ2 能否推导出一个普遍参数，以预测壁面受限剪切流中湍流转捩的临界阈值？
• RQ3 横向能量梯度与壁面受限湍流的自维持过程有何关系？
• RQ4 速度拐点与马蹄涡形成在能量梯度框架中起什么作用？
• RQ5 能量梯度法与经典能量方法（如Rayleigh-Orr方程）相比有何异同？

主要发现

• 能量梯度法通过识别横向能量梯度为不稳定性主要驱动力，成功解释了剪切流中的湍流转捩。
• 临界能量梯度参数Kmax在管道Poiseuille流和平面Poiseuille流中均保持恒定，约为370–389。
• 预测的不稳定性起始位置（管道流中为r/R = 0.58，平面流中为y/h = 0.58）与实验观测完全一致。
• 该模型通过与横向梯度相关的能量传递机制，解释了速度拐点与马蹄涡的形成。
• 该方法证实，横向能量梯度是壁面受限湍流自维持过程的功率来源。
• 扰动幅值阈值随雷诺数的缩放关系符合-1次幂指数，与Hof等人最新的实验发现一致。