Coherent structures in fully-developed pipe turbulence

TL;DR

This paper investigates the structure of fully-developed pipe turbulence, predicting and validating the existence of near-wall and large-scale coherent structures through optimal growth calculations and numerical simulations.

Contribution

It introduces a linear approach with simple eddy viscosity assumptions that accurately predicts the growth and characteristics of large-scale and near-wall turbulent structures in pipe flow.

Findings

Good quantitative match with experimental spanwise wavelengths.

Linear growth predicts large-scale mode amplification.

Harmonic forcing response aligns with direct numerical simulations.

Abstract

A turbulent mean profile for pipe flow is prescribed which closely matches experimental observations. The nature of perturbations superimposed upon this profile is then considered. Optimal growth calculations predict two distinct classes of structures, clearly associated with near-wall and large-scale structures. Quantitative correspondence of the spanwise wavelength of wall-structures with experimental observations is very good. The response to harmonic forcing is also considered, and the linear growth tested with direct numerical simulation of forced turbulence. Despite the very simple eddy viscosity assumption, this linear approach predicts well the surprisingly large growth of outer-scale modes in the bulk flow. Un profil moyen turbulent est prescrit dans une conduite cylindrique, en adequation avec les observations experimentales. Nous considerons ensuite la nature des perturbations a cet ecoulement synthetique. Le calcul des croissances optimales predit deux types de structures, associees respectivement aux structures de proche-paroi et de grande echelle. Un excellent accord quantitatif est trouve avec les resultats experimentaux quant a la longueur d'onde transversale. La reponse harmonique est egalement etudiee, et la croissance lineaire observee comparee a des simulations numeriques directes de turbulence forcee. Malgre de l'hypothese simple de type `Eddy viscosity', cette approche lineaire predit efficacement la croissance spectaculaire des modes de grande echelle au coeur de l'ecoulement.