Sparse energetically dominant frequencies in direct numerical simulation of turbulent pipe flow: origin and application to reduced-order models

The idea of constructing reduced-order models for canonical wall-bounded turbulent flows based on exploiting the sparse energetically dominant frequencies observed in direct numerical simulation of pipe flow by Bourguignon {\em et al.} (2013, {\em Phys. Fluids}) is examined. The resolvent analysis of a pipe flow is extended in order to consider the influence of finite domain length on the flow dynamics, which restricts the possible wavespeeds in the flow. This analysis shows that large sparse amplifications take place when one of the allowable wavespeeds is equal to the local wavespeed via the critical layer mechanism. A connection between amplification and energy is presented through the similar features displayed by the most energetically relevant flow structures, emerging from a dynamic mode decomposition of direct numerical simulation data, and the resolvent modes associated with the most amplified sparse frequencies. These findings support the viability of reduced-order models based on the selection of the most amplified modes arising from the resolvent model, with the potential to drastically decrease the computational costs required to represent turbulent flows.