The miles theorem and new particular solutions to the Taylor–Goldstein equation

A. A. Gavrilieva, Yu G. Gubarev, M. P. Lebedev

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

The direct Lyapunov method is used to prove the absolute linear instability of steadystate plane-parallel shear flows of an inviscid stratified incompressible fluid in the gravity field with respect to plane perturbations both in the Boussinesq and non-Boussinesq approximations. A strict description is given for the applicability of the known necessary condition for linear instability of steady-state plane-parallel shear flows of an ideal nonuniform (by density) incompressible fluid in the gravity field both in the Boussinesq and non-Boussinesq approximations (the Miles theorem). Analytical examples of illustrative character are constructed.

Original languageEnglish
Pages (from-to)560-570
Number of pages11
JournalLobachevskii Journal of Mathematics
Volume38
Issue number3
DOIs
Publication statusPublished - 1 May 2017

Keywords

  • a priori estimate
  • analytical solutions
  • Bessel functions
  • Boussinesq approximation
  • direct Lyapunov method
  • ideal stratified fluid
  • instability
  • Miles theorem
  • plane perturbations
  • stability
  • steady-state flows
  • Whittaker functions

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