Abstract
In this paper, we have identified a new type of resonant triad which operates in a parallel or nearly parallel shear flow with a symmetric profile. The triad consists of a planar sinuous mode, an oblique sinuous mode and an oblique varicose mode, but is not of the usual subharmonic-resonance form. We show that the quadratic resonance can cause both the oblique sinuous and varicose modes to grow super-exponentially. We suggest that this resonant-triad is a viable mechanism for the development of three-dimensional structures and varicose components observed in the later stage of a plane wake transition.
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Chen, J.H., Cantwell, B.J. & Mansour, N.N. 1990 The effect of Mach number on the stability of a plane supersonic wake. Phys. Fluids A2, 984–1004.
Cimbala, J.M., Nagib, H.M. & Roshko, A. 1988 Large structure in the far wake of two-dimensional bluff bodies. J. Fluid Mech. 190, 265–298.
Corke, T.C., Krull, J.D. & Ghassemi, M. 1992 Three-dimensional-mode resonance in far wakes. J. Fluid Mech. 239, 99–132.
Cowley, S.J. & Wu, X. 1994 Asymptotic approaches to transition modelling. In Progress in Transition Modelling, AG ARD report 793.
Craik, A.D.D. 1971 Non-linear resonant instability in boundary layers. J. Fluid Mech. 50, 393–413.
Goldstein, M.E. 1994 Nonlinear interaction between oblique waves on nearly planar shear flows. Phys. Fluids A6, 42–65.
Kelly, R.E. 1968 On the resonant interaction of neutral disturbances in two inviscid shear flows. J. Fluid Mech. 31, 789.
Leib, S.J. & Goldstein, M.E. 1989 Nonlinear interaction between the sinuous and varicose instability modes in a plane wake. Phys. Fluids A1, 513–521.
Raetz, G.S. 1959 A new theory of the cause of transition in fluid flows. Northrop Corp. NOR-59–383 BLC-121.
Sato, H. & Kuriki, K. 1961 The mechanism of transition in the wake of a thin flat plate placed parallel to a uniform flow. J. Fluid Mech. 11, 321–353.
Sato, H. & Saito, H. 1978 Artificial control of the laminar-turbulent transition of a two-dimensional wake by external sound. J. Fluid Mech. 84, 657–572.
Williamson, C.H.K. & Prasad, A. 1993a A new mechanism for oblique wave resonance in the ‘natural’ far wake. J. Fluid Mech. 256, 269–313.
Williamson, C.H.K. & Prasad, A. 1993b Acoustic forcing of oblique wave resonance in the far wake. J. Fluid Mech. 256, 315–341.
Wu, X. 1992 The nonlinear evolution of high-frequency resonant-triad waves in an oscillatory Stokes-layer at high Reynolds number. J. Fluid Mech. 245, 553–597.
Wu, X. 1995a Viscous effects on fully-coupled resonant triad interactions: an analytical approach. J. Fluid Mech. 292, 377–407.
Wu, X., Lee, S.S. & Cowley, S.J. 1993 On the weakly nonlinear three-dimensional instability of shear flows to pairs of oblique waves: the Stokes layer as a paradigm. J. Fluid Mech. 253, 681.
Wu, X. & Stewart, P.A. 1995 Interaction of phase-locked modes: a new mechanism for the rapid growth of three-dimensional disturbances. J. Fluid Mech., (to appear).
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© 1996 Kluwer Academic Publishers
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Wu, X. (1996). An Active Resonant Triad of Mixed Modes in a Symmetric Shear flow. 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_3
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DOI: https://doi.org/10.1007/978-94-009-1700-2_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7261-8
Online ISBN: 978-94-009-1700-2
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