## 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 language | English |
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Pages (from-to) | 560-570 |

Number of pages | 11 |

Journal | Lobachevskii Journal of Mathematics |

Volume | 38 |

Issue number | 3 |

DOIs | |

Publication status | Published - 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