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Decomposition of the temporal growth rate in linear instability of compressible gas flows

Published online by Cambridge University Press:  31 July 2015

Mario Weder ,
Michael Gloor  and
Leonhard Kleiser
Mario Weder*
Affiliation:
Institute of Fluid Dynamics, ETH Zurich, 8092 Zurich, Switzerland Institute of Mechanical Systems, ETH Zurich, 8092 Zurich, Switzerland
Michael Gloor
Affiliation:
Institute of Fluid Dynamics, ETH Zurich, 8092 Zurich, Switzerland
Leonhard Kleiser
Affiliation:
Institute of Fluid Dynamics, ETH Zurich, 8092 Zurich, Switzerland
*
†Email address for correspondence: weder@imes.mavt.ethz.ch
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Abstract

We present a decomposition of the temporal growth rate ${\it\omega}_{i}$ which characterises the evolution of wave-like disturbances in linear stability theory for compressible flows. The decomposition is based on the disturbance energy balance by Chu (Acta Mech., vol. 1 (3), 1965, pp. 215–234) and provides terms for production, dissipation and flux of energy as components of ${\it\omega}_{i}$ . The inclusion of flux terms makes our formulation applicable to unconfined flows and flows with permeable or vibrating boundaries. The decomposition sheds light on the fundamental mechanisms determining temporal growth or decay of disturbances. The additional insights gained by the proposed approach are demonstrated by an investigation of two model flows, namely compressible Couette flow and a plane compressible jet.

JFM classification

Compressible Flows: Compressible Flows Instability: Instability

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 778 , 10 September 2015 , pp. 120 - 132
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© 2015 Cambridge University Press 

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