Order parameter in laminar-turbulent patterns

Abstract

Over a century, and thousands of articles, after Reynolds' description of the transition to turbulence in pipe flow, a predictive theory of transition is still unavailable. One of the most intriguing phenomena observed near transition ishe coexistence of well-defined and long-lived laminar and turbulent regions, first observed in counter-rotating Taylor-Couette flow in the 1960s [1]. In the 2000s, Prigent & Dauchot [2] showed that these coexisting regions were part of a regular pattern of stripes, whose wavelength and orientation are Reynolds-number-dependent and reproducible. Analogous phenomena have been observed experimentally [2] and numerically [3] in plane Couette flow, in stator-rotor experiments (the flow between a stationary and a rotating disk) [4], in plane Poiseuille simulations [5], and, most recently, in simulations of pipe flow [6].