The evolution of large-scale motions in turbulent pipe flow

Abstract

A dual-plane snapshot proper orthogonal decomposition (POD) analysis of turbulent pipe flow at a Reynolds number of 104 000 is presented. The high-speed particle image velocimetry data were simultaneously acquired in two planes, a cross-stream plane (2D–3C) and a streamwise plane (2D–2C) on the pipe centreline. The cross-stream plane analysis revealed large structures with a spatio-temporal extent of $1{-}2R$, where $R$ is the pipe radius. The temporal evolution of these large-scale structures is examined using the time-shifted correlation of the cross-stream snapshot POD coefficients, identifying the low-energy intermediate modes responsible for the transition between the large-scale modes. By conditionally averaging based on the occurrence/intensity of a given cross-stream snapshot POD mode, a complex structure consisting of wall-attached and -detached large-scale structures is shown to be associated with the most energetic modes. There is a pseudo-alignment of these large structures, which together create structures with a spatio-temporal extent of approximately $6R$, which appears to explain the formation of the very-large-scale motions previously observed in pipe flow.