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

分离湍流中的复杂性是物理科学中的基本问题之一，与许多应用具有很大的相关性。在许多剪切流中，即使层流是线性稳定的，向湍流的转变也是突然发生的，例如Couette流和Poiseuille流。虽然现在公认的是，在Navier-Stokes方程中可以存在有限幅度的不连通流态，但对于剪切流中这种所谓的亚临界到湍流的转变，这些状态所起的作用仍在争论中。本项目的目的是为线性稳定剪切流中有限幅值解的存在性提供明确的实验证据。实验将在逆旋转Taylor-Couette流的螺旋湍流区域中进行，该区域也存在于系统的“经典”离心力不稳定性之下。在这个封闭流动实验中，通过雷诺数的时间变化，如突变和周期调制，层流流动在线性稳定区域中的失稳，以及通过延迟反馈混沌控制使无序流动稳定，这将使我们能够研究这种有限振幅不连通状态的渐近解和分叉结构。这项研究将阐明它们在剪切流中亚临界向湍流转变中的作用。

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.