Abstract
Nonlinear crossflow vortices in an incompressible three-di-mensional boundary layer are computed by weakly nonlinear theory and direct numerical simulations. The parallel basic flow is defined by Falkner-Skan-Cooke similarity profiles. The temporal evolution of spanwise periodic, quasi-two-dimensional disturbances without variations along the vortex axis is considered. The nonlinear theory is based on the approach of Herbert [3, 4]. The theory predicts the existence of the finite amplitude equilibrium states seen in earlier simulations. When the disturbance amplitudes are small, there is very good quantitative agreement in the fundamental disturbance velocity components between the theory and the simulations.
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
Reed, H.L., Saric, W.S. Stability of three-dimensional boundary layers. Ann. Rev. Fluid Mech., 21:235–284, 1989.
Mack, L.M. Boundary-layer linear stability theory. AGARD Report No. 709, 3–1—3–81, 1984.
Herbert, T. Nonlinear stability of parallel flows by high-order amplitude expansions. AIAA J. 18:243–248, 1980.
Herbert, T. On perturbation methods in nonlinear stability theory. J. Fluid. Mech. 126:167–186, 1983.
Meyer, F., Kleiser, L. Numerical investigation of transition in 3D boundary layers. In: Fluid Dynamics of Three-Dimensional Turbulent Shear Flows and Transition, AGARD-CP-438:16–1—16–17, 1989.
Meyer, F. Numerische Simulation der Transition in dreidimensionalen Grenzschichten. DLR-FB 89–12, 1989.
Rosenhead, L. (ed.) Laminar Boundary Layers. Oxford University Press, 1963.
Zang, T.A., Hussaini, M.Y. Numerical simulation of nonlinear interactions in channel and boundary layer transition. In: Nonlinear Wave Interactions in Fluids (eds. R.W. Miksad et al.). ASME, AMD vol. 87, 131–145, 1987.
Laurien, E., Kleiser, L. Numerical simulation of boundary-layer transition and transition control. J. Fluid Mech. 199:403–440, 1989.
Spalart, P.R., Yang, K.-S. Numerical study of ribbon-induced transition in Blasius flow. J. Fluid Mech. 178:345–365, 1987.
Ehrenstein, U. Rechenprogramm DFVLR LISA * T (Linear - Incompressible Flow - Stability - Analyzer * Temporal Theory). Internal Report DFVLR-IB 221–87A12, 1987.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag New York Inc.
About this paper
Cite this paper
Singer, B.A., Meyer, F., Kleiser, L. (1990). Nonlinear Development of Crossflow Vortices. In: Hussaini, M.Y., Voigt, R.G. (eds) Instability and Transition. ICASE/ NASA LaRC Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3432-6_24
Download citation
DOI: https://doi.org/10.1007/978-1-4612-3432-6_24
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97324-1
Online ISBN: 978-1-4612-3432-6
eBook Packages: Springer Book Archive