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Continuing invariant solutions towards the turbulent flow

Article dans une revue avec comité de lecture
Author
PARENTE, Enza
FARANO, Mirko
DE PALMA, Pietro
CHERUBINI, Stefania
ccROBINET, Jean-Christophe
134975 Laboratoire de Dynamique des Fluides [DynFluid]

URI
http://hdl.handle.net/10985/21936
DOI
10.1098/rsta.2021.0031
Date
2022-05
Journal
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Abstract

A new mathematical framework is proposed for characterizing the coherent motion of fluctuations around a mean turbulent channel flow. We search for statistically invariant coherent solutions of the unsteady Reynolds-averaged Navier–Stokes equations written in a perturbative form with respect to the turbulent mean flow, using a suitable approximation of the Reynolds stress tensor. This is achieved by setting up a continuation procedure of known solutions of the perturbative Navier–Stokes equations, based on the continuous increase of the turbulent eddy viscosity towards its turbulent value. The recovered solutions, being sustained only in the presence of the Reynolds stress tensor, are representative of the statistically coherent motion of turbulent flows. For small friction Reynolds number and/or domain size, the statistically invariant motion is almost identical to the corresponding invariant solution of the Navier–Stokes equations. Whereas, for sufficiently large friction number and/or domain size, it considerably departs from the starting invariant solution of the Navier–Stokes equations, presenting spatial structures, main wavelengths and scaling very close to those characterizing both large- and small-scale motion of turbulent channel flows. This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 2)’.

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