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Absolute instability of plane incompressible jets

Published online by Cambridge University Press:  28 April 2023

Vasily Vedeneev Open the ORCID record for Vasily Vedeneev [Opens in a new window]  and
Nikolay Nikitin Open the ORCID record for Nikolay Nikitin [Opens in a new window]
Vasily Vedeneev*
Affiliation:
Institute of Mechanics, Lomonosov Moscow State University, Moscow 119192, Russia
Nikolay Nikitin
Affiliation:
Institute of Mechanics, Lomonosov Moscow State University, Moscow 119192, Russia
*
†Email address for correspondence: vasily@vedeneev.ru
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Abstract

In this paper, the possibility of absolute instability in a plane unidirectional jet is analysed. We consider a parametrized family of velocity profiles with variable inflection point location and shear layer thickness. Using the inviscid saddle-point analysis, we show that absolute instability can occur in the case of a sufficiently low velocity at the inflection point or a sufficiently thin shear layer. Then we proceed to the viscous analysis and find the critical Reynolds numbers separating the zones of convective and absolute instability. We obtained a minimum value $Re = 315$. As an independent verification of the theoretical results, we conduct a direct numerical simulation of the evolution of a localized pulse perturbation in the framework of the linearized Navier–Stokes equations. The calculated absolute/convective instability boundary is in a good agreement with theoretical results of the saddle-point analysis.

JFM classification

Instability: Absolute/convective instability Instability: Shear-flow instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 962 , 10 May 2023 , A4
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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