Abstract
The aim of this paper is to propose an identification technique of dynamical systems in order to describe the local evolution of modes which dominate the dynamics of transitional shear flows. By using the linear eigenmodes of viscous flows, a numerical investigation was performed to model the dynamical evolution of disturbances which arise in a transitional symmetric shear flow when a planar mode interacts in a phase-locked mechanism with one or more oblique three-dimensional modes. Numerical results highlighted a good qualitative agreement with the experimental ones and showed furthermore some interesting correspondences with the phenomenological conclusion of recent theoretical investigations obtained by spatial stability of inviscid flows. Our investigation confirmed that only some nonlinear triadic interactions can be active, depending on the sinuous or varicose nature of the selected modes. In particular, mechanisms of coupling among more triadic systems turned out to be of remarkable interest, in that they can induce a preferential amplification of oblique modes in spite of their dumped-varicose nature.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Boniforti, M.A., Morganti, M. and Sciortino, G., (1996), “Triadic resonant modes: dynamical model and truncation criterion”, Fluid Dynamics Research (to appear).
Corke, T., Krull, J.D. and Ghassemi, M., (1992), “Three-dimensional mode resonance in the far wake”, J. Fluid Mech., Vol. 239, pp. 99.
Craik, A.D.D.,(1985) Wave interactions and fluid flows. Cambridge University Press.
Craik, A.D.D., (1971), “Nonlinear resonant instability in boundary layers”, J. Fluid Mech., Vol. 50, pp. 393–413.
Herbert, T., (1978) “Secondary instability of boundary layers”, Ann. Rev. Fluid Mech., Vol. 20, pp. 487–526
Mele, P., Morganti M. and Boniforti M.A., (1993), “Triadic resonance in transitional shear flows: a low-dimensional model”, in Some Applied Problems in Fluid Mechanics, Indian Statistical Institute.
Raetz, G. S., (1959) “A new theory of the cause of transition in fluid flows”, Northrop Corp. NOR-59-383 BLC-121.
Williamson, C.H.K. and Prasad, A., (1993), “Acoustic forcing of oblique wave resonance in the far wake”, J. Fluid Mech., Vol. 256, pp. 315–341.
Wu, X. and Stewart, P.A., (1996), “Interaction of phase-locked modes: a new mechanism for the rapid growth of three-dimensional disturbances”, J. Fluid Mech., Vol. 316, pp. 335–372.
Wu, X., (1996), “On an active resonant triad of mixed modes in symmetric shear flows: a plane wake as a paradigm”, J. Fluid Mech., Vol. 317, pp. 337–368.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Sciortino, G., Morganti, M., Boniforti, M.A. (1999). Sinuous and Varicose Modes in Phase-Locked Interaction. In: Sørensen, J.N., Hopfinger, E.J., Aubry, N. (eds) IUTAM Symposium on Simulation and Identification of Organized Structures in Flows. Fluid Mechanics and Its Applications, vol 52. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4601-2_41
Download citation
DOI: https://doi.org/10.1007/978-94-011-4601-2_41
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5944-2
Online ISBN: 978-94-011-4601-2
eBook Packages: Springer Book Archive