The Miles Theorem and the First Boundary Value Problem for the Taylor-Goldstein Equation
| Autor: | A. A. Gavril’eva, M. P. Lebedev, Yu. G. Gubarev |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Plane (geometry)
Applied Mathematics Mathematical analysis 02 engineering and technology 01 natural sciences Industrial and Manufacturing Engineering Physics::Fluid Dynamics 010101 applied mathematics Taylor–Goldstein equation 020303 mechanical engineering & transports 0203 mechanical engineering Gravitational field Inviscid flow Compressibility Boundary value problem 0101 mathematics Boussinesq approximation (water waves) Mathematics Linear stability |
| Zdroj: | Journal of Applied and Industrial Mathematics. 13:460-471 |
| ISSN: | 1990-4797 1990-4789 |
| DOI: | 10.1134/s1990478919030074 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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