Ageostrophic instabilities in a horizontally uniform baroclinic flow along a slope
The normal modes of a horizontally uniform, vertically sheared flow over a sloping bottom are considered in two active layers underneath a deep motionless third layer. The variations of the layer thickness are assumed to be small to analyse the sixth-order eigenvalue problem for finite-Froude-number...
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Published in | Journal of fluid mechanics Vol. 588; pp. 463 - 473 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Cambridge, UK
Cambridge University Press
10.10.2007
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Subjects | |
Online Access | Get full text |
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Summary: | The normal modes of a horizontally uniform, vertically sheared flow over a sloping bottom are considered in two active layers underneath a deep motionless third layer. The variations of the layer thickness are assumed to be small to analyse the sixth-order eigenvalue problem for finite-Froude-number typical for oceanic currents. The dispersion curves for the Rossby waves and the Poincaré modes of inertia–gravity waves (IGW) are investigated to identify the different types of instabilities that occur if there is a pair of wave components which have almost the same Doppler-shifted frequency related to crossover of the branches when the Froude number increases. Simple criteria for ageostrophic instabilities due to a resonance between the IGW and the Rossby wave because of the thickness gradient in either the lower or middle layer, are derived. They exactly correspond to violation of sufficient Ripa's conditions for the flow stability. In both cases the growth rate and the interval of unstable wavenumbers are shown to be proportional to the square root of the corresponding gradient of the layer thickness. These types of ageostrophic instability can coexist (and with Kelvin–Helmholtz instability). However, their role in generating unbalanced motions and mixing processes in geophysical fluids appears limited due to small growth rates and narrow intervals of the unstable wavenumbers in comparison to Kelvin–Helmholtz instability. |
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Bibliography: | istex:587203183BA49D08F7FBC6AC44C2B4E64285EAF2 ArticleID:00682 ark:/67375/6GQ-T057K25G-G PII:S0022112007006829 ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 ObjectType-Article-2 ObjectType-Feature-1 |
ISSN: | 0022-1120 1469-7645 |
DOI: | 10.1017/S0022112007006829 |