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arXiv physics/0607004physics.flu-dynphysics.class-ph
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剪切流中流动不稳定性和湍流转捩的物理学

Physics of Flow Instability and Turbulent Transition in Shear Flows

Hua-Shu Dou

摘要:

本文通过分析底流与扰动相互作用下流体质点的能量变化,研究了剪切流中流动不稳定性和湍流转捩的物理过程。首次提出了一个严格从物理学推导的模型,表明有限振幅扰动下的流动不稳定性导致湍流转捩。该模型被命名为“能量梯度法”。“结果表明,这是横向能量梯度,导致扰动放大,而扰动阻尼的能量损失,由于沿流线的粘性。本文还表明,所得到的扰动幅值阈值与雷诺数成指数-1的比例关系,这正好解释了Hof等人最近的现代管流实验结果。结合分析结果解释了速度拐点和发夹涡形成的机理。由此可以证明,在有壁面的平行流动中,所谓的能量梯度参数Kmax的临界值是一个常数,这一点已被实验所证实,约为370-389。对于圆管Poiffille流(r/R=0.58)和平面Poiffille流(y/h=0.58),流场中的失稳起始位置与实验结果吻合较好。从本文提出的方法还可以推断,横向能量梯度可以作为壁面湍流自持过程的动力。最后讨论了“能量梯度法”与经典的基于瑞利-奥尔方程的“能量法”的关系。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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