Transition Problem and Localized Turbulent Structures in Pipes

Abstract

In the classical experiments of O. Reynolds made in 1883 the critical value of a dimensionless parameter, named now the Reynolds number, $${\text{R}}{{{\text{e}}}_{c}} \approx 2000$$ , was determined. As this value is exceeded in a pipe of circular cross-section, a turbulent flow regime can occur. The attempts to define this value more exactly undertaken during the twentieth century have not met with success. In this study, we present a review of theoretical, experimental, and numerical investigations of flows in a round pipe at the stage of transition to turbulence performed in recent years, which make it possible to formulate a new view on the nature of laminar-turbulent transition in these flows.