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Inviscid linear stability analysis of two vertical columns of different densities in a gravitational acceleration field

Published online by Cambridge University Press:  09 August 2017

Aditya Heru Prathama Open the ORCID record for Aditya Heru Prathama [Opens in a new window]  and
Carlos Pantano
Aditya Heru Prathama*
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Carlos Pantano
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
*
†Email address for correspondence: [email protected]
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Abstract

We study the inviscid linear stability of a vertical interface separating two fluids of different densities and subject to a gravitational acceleration field parallel to the interface. In this arrangement, the two free streams are constantly accelerated, which means that the linear stability analysis is not amenable to Fourier or Laplace solution in time. Instead, we derive the equations analytically by the initial-value problem method and express the solution in terms of the well-known parabolic cylinder function. The results, which can be classified as an accelerating Kelvin–Helmholtz configuration, show that even in the presence of surface tension, the interface is unconditionally unstable at all wavemodes. This is a consequence of the ever increasing momentum of the free streams, as gravity accelerates them indefinitely. The instability can be shown to grow as the exponential of a quadratic function of time.

JFM classification

Geophysical and Geological Flows: Baroclinic flows Instability: Instability
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 826 , 10 September 2017 , R4
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Copyright
© 2017 Cambridge University Press 

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