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

Aditya Heru Prathama, Carlos Pantano

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Article numberR4
JournalJournal of Fluid Mechanics
Volume826
DOIs
StatePublished - Sep 10 2017

Keywords

  • baroclinic flows
  • instability

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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