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Instability of a dusty Kolmogorov flow

Published online by Cambridge University Press:  26 November 2021

Alessandro Sozza Open the ORCID record for Alessandro Sozza [Opens in a new window] ,
Massimo Cencini Open the ORCID record for Massimo Cencini [Opens in a new window] ,
Stefano Musacchio  and
Guido Boffetta
Alessandro Sozza*
Affiliation:
Department of Physics and INFN, University of Torino, via P. Giuria, 10125 Torino, Italy Istituto dei Sistemi Complessi, ISC-CNR, via dei Taurini 19, 00185 Roma, Italy INFN sezione Roma 2 “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma, Italy Laboratoire de Physique, UMR 5672, École Normale Supérieure de Lyon 46 Allée d'Italie, 69007 Lyon, France
Massimo Cencini
Affiliation:
Istituto dei Sistemi Complessi, ISC-CNR, via dei Taurini 19, 00185 Roma, Italy INFN sezione Roma 2 “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma, Italy
Stefano Musacchio
Affiliation:
Department of Physics and INFN, University of Torino, via P. Giuria, 10125 Torino, Italy
Guido Boffetta
Affiliation:
Department of Physics and INFN, University of Torino, via P. Giuria, 10125 Torino, Italy
*
†Email address for correspondence: asozza.ph@gmail.com
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Abstract

Suspended particles can significantly alter the fluid properties and, in particular, can modify the transition from laminar to turbulent flow. We investigate the effect of heavy particle suspensions on the linear stability of the Kolmogorov flow by means of a multiple-scale expansion of the Eulerian model originally proposed by Saffman (J. Fluid Mech., vol. 13, issue 1, 1962, pp. 120–128). We find that, while at small Stokes numbers particles always destabilize the flow (as already predicted by Saffman in the limit of very thin particles), at sufficiently large Stokes numbers the effect is non-monotonic in the particle mass fraction and particles can both stabilize and destabilize the flow. Numerical analysis is used to validate the analytical predictions. We find that in a region of the parameter space the multiple-scale expansion overestimates the stability of the flow and that this is a consequence of the breakdown of the scale separation assumptions.

JFM classification

Complex Fluids: Suspensions Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 931 , 25 January 2022 , A26
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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