Abstract
In many practical situations where Görtier vortices occur the boundary layers are 3-D. Linear studies have found that this three-dimensionality has a stabilising effect and that, for a weak crossflow, inviscid Görtier modes possess some of the largest growth rates whilst also being neutral at certain other wavenumbers. Furthermore, these inviscid modes are governed by an equation very similar to the Taylor-Goldstein equation which governs the linear stability of stratified shear flows. In [1] this close connection was considered and a generalised Richardson number for such vortex instabilities given. We initially considered, using non-equilibrium critical-layer theory, the nonlinear evolution of modes on an unstable stratified shear layer in [2]. In this study it was found that there were three different base integro-differential equations (IDEs) that could govern the amplitude of a disturbance. The three different equations were an IDE with a cubic non-linearity due to viscous effects, an IDE with a cubic nonlinearity due to a novel mechanism and an IDE with a quintic nonlinearity. The choice as to which of these base IDEs is relevant for a given mode depends on the wa.venumber and the relative sizes of parameters representing viscosity, disturbance amplitude and the growth rate of the disturbance.
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References
Blackaby, N.D. & Choudhari, M. (1993). Inviscid vortex motions in weakly three-dimensional boundary layers and their relation with instabilities in stratified shear flows. Proc. R. Soc. Lond. A., 440, 701–710.
Blackaby, N.D., Dando, A.H. & Hall, P. (1993). The nonlinear evolution of modes on unstable stratified shear layers. ICASE Report No. 93–36 and submitted to J. Fluid Mech.
Blackaby, N.D., Dando, A.H. & Hall, P. (1995). The nonlinear evolution of inviscid Gů̄rtier vortices in three-dimensional boundary layers. Submitted as an ICASE Report.
Churilov, S.M. & Shukhman, I.G. (1988). Nonlinear stability of a stratified shear flow in the regime with an unsteady critical layer. J. Fluid Mech., 194. 187–216.
Drazin, P.G. (1958). The stability of a shear layer in an unbounded heterogeneous inviscid fluid. J. Fluid Mech., 4, 214–224.
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© 1996 Kluwer Academic Publishers
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Dando, A. (1996). The Nonlinear Evolution of Inviscid Görtler Vortices in 3-D Boundary Layers: The Effects of Non-Dominant Viscosity in the Critical Layer. In: Duck, P.W., Hall, P. (eds) IUTAM Symposium on Nonlinear Instability and Transition in Three-Dimensional Boundary Layers. Fluid Mechanics and Its Applications, vol 35. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1700-2_8
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DOI: https://doi.org/10.1007/978-94-009-1700-2_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7261-8
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