## 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 language | English |
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Pages (from-to) | 460-471 |

Number of pages | 12 |

Journal | Journal of Applied and Industrial Mathematics |

Volume | 13 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jul 2019 |

## Keywords

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