The dynamical behavior of propagating structures, determined from a Karhunen-Lo`eve decomposition, in turbulent pipe flow undergoing reverse transition to laminar flow is investigated. The turbulent flow data is generated by a direct numerical simulation started at a fully turbulent Reynolds number of Re_τ=150, which is slowly decreased until Re_τ=95. At this low Reynolds number the high frequency modes decay first, leaving only the decaying streamwise vortices. The flow undergoes a chugging phenomena, where it begins to relaminarize and the mean velocity increases. The remaining propagating modes then destabilize the streamwise vortices, rebuild the energy spectra, and eventually the flow regains its turbulent state. Our results capture three chugging cycles before the flow completely relaminarizes. The high frequency modes present in the outer layer decay first, establishing the importance of the outer region in the self-sustaining mechanism of wall bound turbulence.
A traveling wave bifurcation analysis of turbulent pipe flow
使用来自动力系统理论的各种技术，我们严格地研究了[Barkley et al.，Nature，526：550-553，2015]，其描述了经由复杂性降低的PDE系统的湍流管流的上升。湍流的快速发展是由反应扩散动力学耦合到中心线速度，这与伯格斯型平流和缓慢的再层化项。应用空间动力学分析和几何奇异摄动理论，我们证明了在湍流和层流定态之间存在异宿环，并建立了一个由各种行波组成的分叉级联。最复杂的行为可以发现在中间雷诺数制度，其中的行波表现出任意长的类似于混沌的动态指示的发病。我们的分析提供了一个系统的数学方法来确定过渡到时空湍流结构，也可能适用于其他模型中产生的流体动力学。
Drag reduction and subcritical turbulence in controlled pipe flows
Politecnico di Milano（米兰理工大学）；Univ. Lille, CNRS, ONERA, Arts et Metiers Institute of Technology, Centrale Lille（里尔大学、法国国家科学研究中心、法国航空发展局、巴黎国立高等工艺学院、里尔中央理工学院）；Massachusetts Institute of Technology（麻省理工学院）
Hydroacoustic Absorption and Amplification by Turbulence
Ningbo University（宁波大学）；Zhejiang Provincial Engineering Research Center for the Safety of Pressure Vessel and Pipeline, Ningbo University（宁波大学压力容器与管道安全浙江省工程研究中心）；Key Laboratory of Impact and Safety Engineering (Ningbo University), Ministry of Education（教育部冲击与安全工程重点实验室（宁波大学））；Ningbo Jiangbei District People's Government（宁波市江北区人民政府）
