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Influence of interface pollution on the linear stability of a rotating flow

Published online by Cambridge University Press:  17 August 2020

Antoine Faugaret Open the ORCID record for Antoine Faugaret [Opens in a new window] ,
Yohann Duguet Open the ORCID record for Yohann Duguet [Opens in a new window] ,
Yann Fraigneau Open the ORCID record for Yann Fraigneau [Opens in a new window]  and
Laurent Martin Witkowski Open the ORCID record for Laurent Martin Witkowski [Opens in a new window]
Antoine Faugaret
Affiliation:
Collège Doctoral, Sorbonne Université, F-75005Paris, France Université Paris-Saclay, CNRS, LIMSI, 91400Orsay, France
Yohann Duguet
Affiliation:
Université Paris-Saclay, CNRS, LIMSI, 91400Orsay, France
Yann Fraigneau
Affiliation:
Université Paris-Saclay, CNRS, LIMSI, 91400Orsay, France
Laurent Martin Witkowski*
Affiliation:
Université Paris-Saclay, CNRS, LIMSI, 91400Orsay, France Faculté des Sciences et Ingénierie, UFR d'Ingénierie, Sorbonne Université, F-75005Paris, France
*
†Email address for correspondence: laurent.martin_witkowski@sorbonne-universite.fr
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Abstract

The boundary conditions at a liquid–gas interface can be modified by the presence of pollutants. This can in turn affect the stability of the associated flow. We consider this issue in the case of a simple open cylindrical cavity flow where a liquid is set in motion by the rotation of the bottom. The problem is addressed using an experimental set-up, a linear stability code and direct numerical simulation. A robust mismatch between numerical and experimental predictions of the onset of instability is found. We model the possible effect of unidentified pollutants at the interface using an advection–diffusion equation and a closure equation linking the surface tension to the superficial pollutant concentration. The chosen closure is inspired by studies of free-surface flows with surfactants. Numerical stability analysis reveals that the base flow and its linear stability threshold are strongly affected by the addition of pollutants. Pollutants tend to decrease the critical Reynolds number; however, the nonlinear dynamics is less rich than without pollutants. For sufficiently high pollution levels, the most unstable mode belongs to a different family, in agreement with experimental findings.

JFM classification

Geophysical and Geological Flows: Rotating flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 900 , 10 October 2020 , A42
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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