Instabilities and transient growth of the stratified Taylor-Couette flow in a Rayleigh-unstable regime

Junho Park, Paul Billant, Jong Jin Baik

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The stability of the Taylor-Couette flow is analysed when there is a stable density stratification along the axial direction and when the flow is centrifugally unstable, i.e. in the Rayleigh-unstable regime. It is shown that not only the centrifugal instability but also the strato-rotational instability can occur. These two instabilities can be explained and well described by means of a Wentzel-Kramers-Brillouin-Jeffreys asymptotic analysis for large axial wavenumbers in inviscid and non-diffusive limits. In the presence of viscosity and diffusion, numerical results reveal that the strato-rotational instability becomes dominant over the centrifugal instability at the onset of instability when the axial density stratification is sufficiently strong. Linear transient energy growth is next investigated for counter-rotating cylinders in the stable regime of the Froude number-Reynolds number parameter space. We show that there exist two types of transient growth mechanism analogous to the lift up and the Orr mechanisms in homogeneous fluids but with the additional effect of density perturbations. The dominant mechanism depends on the stratification: when the stratification is strong, non-axisymmetric three-dimensional perturbations achieve the optimal energy growth through the Orr mechanism while for moderate stratification, axisymmetric perturbations lead to the optimal transient growth by a lift-up mechanism involving internal waves.

Original languageEnglish
Pages (from-to)80-108
Number of pages29
JournalJournal of Fluid Mechanics
Volume822
Early online date31 May 2017
DOIs
Publication statusPublished - 10 Jul 2017
Externally publishedYes

Keywords

  • instability
  • stratified flows
  • Taylor-Couette flow

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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