Stability boundaries and sufficient stability conditions for stably stratified, monotonic shear flows

Makoto Hirota, Philip J. Morrison

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Linear stability of inviscid, parallel, and stably stratified shear flow is studied under the assumption of smooth strictly monotonic profiles of shear flow and density, so that the local Richardson number is positive everywhere. The marginally unstable modes are systematically found by solving a one-parameter family of regular Sturm-Liouville problems, which can determine the stability boundaries more efficiently than solving the Taylor-Goldstein equation directly. By arguing for the non-existence of a marginally unstable mode, we derive new sufficient conditions for stability, which generalize the Rayleigh-Fjørtoft criterion for unstratified shear flows.

Original languageEnglish
Pages (from-to)1856-1860
Number of pages5
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume380
Issue number21
DOIs
Publication statusPublished - 2016 Jan 1

Keywords

  • Hydrodynamic stability
  • Stratified shear flow
  • Sturm-Liouville problem

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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