Experiments on the subcritical transition to spiral turbulence in Taylor-Couette flow by parametric modulation and chaos control

解开湍流的复杂性是物理科学的基本问题之一，与许多应用有很大的关系。虽然层流是线性稳定的，但在许多剪切流（如库埃特流和泊泽维尔流）中，向湍流的过渡是突然发生的。虽然现在人们普遍认为，有限振幅的非连通流动状态可以存在于Navier-Stokes方程中，但关于这些状态在剪切流动中所谓的亚临界过渡到湍流中的作用仍存在争议。本项目的目的是为线性稳定剪切流有限振幅解的存在性提供一个明确的实验证据。实验将在逆旋转泰勒-库埃特流的螺旋湍流状态下进行，该状态也存在于系统的“经典”离心不稳定性之下。在这个封闭流动实验中，通过雷诺数的时间变化（如突然变化和周期调制）来破坏线性稳定状态下层流的不稳定，以及通过时滞反馈混沌控制来稳定无序流动，将允许研究这种有限振幅断开状态的渐近解和分岔结构。这项研究将阐明它们在剪切流的亚临界过渡到湍流中的作用。

Disentangling the complexity in turbulent flows is one of the fundamental problems in physical science with a large relevance to many applications. The transition to turbulence occurs abruptly in many shear flows, such as Couette and Poiseuille flows, even though the laminar flow is linearly stable. Though it is now well accepted that disconnected flow states of finite-amplitude can exist in Navier-Stokes equation there is an ongoing debate on the role of these states for this so-called subcritical transition to turbulence in shear flows. The aim of this project is to provide a definite experimental evidence for the existence of finite-amplitude solutions in a linearly stable shear flow. The experiments will be performed in the spiral turbulence regime of counter-rotating Taylor-Couette flow which exists also below the 'classical' centrifugal instability of the system. Destabilisation of the laminar flow in the linearly stable regime by temporal variations of Reynolds numbers, such as sudden changes and period modulations, as well as stabilisation of disordered flow by means of time-delayed feedback chaos control in this closed flow experiment will allow an investigation of the asymptotic solution and bifurcation structure of such disconnected states of finite amplitude. This study will shed light on their role in the subcritical transition to turbulence in shear flows.