The Miles Theorem and the First Boundary Value Problem for the Taylor-Goldstein Equation

A. A. Gavril’eva, Yu G. Gubarev, M. P. Lebedev

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We study the problem of the linear stability of stationary plane-parallel shear flows of an inviscid stratified incompressible fluid in the gravity field between two fixed impermeable solid parallel infinite plates with respect to plane perturbations in the Boussinesq approximation and without it. For both cases, we construct some analytical examples of steady plane-parallel shear flows of an ideal density-heterogeneous incompressible fluid and small plane perturbations in the form of normal waves imposed on them, whose asymptotic behavior proves that these perturbations grow in time regardless of whether the well-known result of spectral stability theory (the Miles Theorem) is valid or not.

Original languageEnglish
Pages (from-to)460-471
Number of pages12
JournalJournal of Applied and Industrial Mathematics
Volume13
Issue number3
DOIs
Publication statusPublished - 1 Jul 2019

Keywords

  • analytical solution
  • asymptotic expansion
  • instability
  • Miles Theorem
  • small perturbation
  • stationary flow
  • stratified fluid
  • Taylor-Goldstein equation

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