Passivity of plane Poiseuille flow
Passivity of plane Poiseuille flow
复制标题
平面泊肃叶流的无源性
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
S. Duncan
中科院分区：
文献类型：
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作者：
Shi Zhao;S. Duncan
本文讨论了平面Poiseuille流动的无源性，平面Poiseuille流动是在两个平行平板之间观察到的不可压缩流动，假定它们的范围是无穷大的。该模型将流量视为线性时不变系统和静态、无记忆非线性系统之间的反馈连接。众所周知，平面Poiseuille流的非线性不仅是被动的，而且是无损的，这意味着它不产生或消耗能量，其唯一的影响是将能量从一种流动模式转移到另一种流动模式。然而，关于整个流动系统的被动性的论述很少。本文的主要目的是找到一个亚临界雷诺数，使线性化流动总是严格无源的，这意味着当雷诺数不超过亚临界数时，整个非线性系统的原点是全局渐近稳定的。我们的结果表明，用无源方法得到的亚临界雷诺数等于用经典能量方法得到的能量雷诺数。这一结果表明，被动方法与能量方法密切相关，是研究流体流动稳定性的一种有价值的工具。
This paper considers the passivity of plane Poiseuille flow, which is the incompressible flow observed between two parallel plates that are assumed to be of infinite extent. A model in which the flow is considered as the feedback connection between a linear time-invariant system and a static, memoryless nonlinear system is used. It is well known that the nonlinearity of plane Poiseuille flow is not only passive but lossless, which means that it does not generate or consume energy and the only effect of the nonlinearity is to move energy from one flow mode to another. However, little has been addressed about the passivity of the entire flow system. The primary aim of this paper is to find a subcritical Reynolds number below which the linearized flow is always strictly passive, which means that the origin of the full nonlinear system is globally asymptotically stable when the Reynolds number does not exceed the subcritical number. Our results show that the subcritical Reynolds number obtained by the passivity approach is equal to the energy Reynolds number, which is derived by the classical energy approach. This result indicates that the passivity approach is closely related to the energy approach and is a valuable tool to study the stability of fluid flows.