Low-order representation of turbulent pipe flow

A simple model of pipe flow turbulence based on a forcing-response analysis of the Navier-Stokes equations (McKeon \textit{et al.} 2010) is presented and used to investigate the dynamics of the large-scale structures. The model is validated against pipe flow DNS data and naturally leads to a low-order representation of the flow as a sum of traveling waves corresponding to the response modes predicted by the model. The low-order flow representation captures a significant fraction of the turbulence intensity and Reynolds stress in the core of the pipe and is highly correlated to the large-scale structures observed in the DNS data. Furthermore, by considering the forcing modes associated with each response mode in the low-order flow representation the amplification mechanisms sustaining the large-scale structures can be identified.