Abstract
The low-amplitude interaction of a 2D wave with a 3D detuned wave in parallel shear flows is considered. Experiments and numerical simulation have shown that detuned wave interaction provides an alternate route to transition. When the interaction is quasiperiodic (irrationally related streamwise wavenumbers) the nonlinear theory for the wave interaction is difficult because of small divisors. Spatial centre-manifold theory and normal form transformations are used to construct a theory for bifurcating spatially quasiperiodic (q-p) states. The q-p interaction is shown to be a general feature of parallel shear flows with a thumb neutral curve.
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References
Bridges, T. [1991] A dynamical systems approach to boundary layer transition, Preprint 2-1991, University of Warwick.
Bridges, T. [1991] Spatially quasiperiodic states in shear flows, in preparation.
Broer, H., Huitema, G. B., & Takens, F. [1990] Unfoldings of quasiperiodic tori, Memoirs AMS 83: 83–175.
Chossat, P., Golubitsky, M., & Keyfitz, B. [1986] Hopf-Hopf mode interactions with O(2)-symmetry, Dyn. and Stab, of Systems 1: 255–292.
Corke, T. [1989] Three-dimensional mode resonances in boundary layers, jets and wakes, Proceedings of ICASE Workshop on Stability and Transition.
Corke, T. & Mangano, R. [1989] Resonant growth of three-dimensional modes in transitioning Blasius boundary layers, J. Fluid Mech. 209: 93–150.
Kundert, K., Sorkin, G., & Sangiovanni, A. [1988] Applying harmonic balance to almost-periodic circuits, IEEE Transactions MTT-36(2): 366–78.
Moser, J. [ 1967 ] Convergent series expansions for quasiperiodic motions, Math. Ann. 169: 136–76.
Ushida, A. & Chua, L. [1981] Algorithms for computing almost periodic steady-state response of nonlinear systems to multiple input frequencies, IEEE Transactions CAS-28: 953–71.
Vanderbauwhede, A. [1989] Centre-manifolds, normal forms and elementary bifurcations, Dynamics Reported 2: 89–169.
Zang, T. and Hussaini, M. Y. [ 1990 ] Multiple paths to subharmonic laminar breakdown in a boundary layer, Phys. Rev. Letters 64: 641–4.
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© 1992 Springer-Verlag New York, Inc.
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Bridges, T.J. (1992). Spatially-Quasiperiodic States in Shear Flows. In: Hussaini, M.Y., Kumar, A., Streett, C.L. (eds) Instability, Transition, and Turbulence. ICASE NASA LaRC Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2956-8_14
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DOI: https://doi.org/10.1007/978-1-4612-2956-8_14
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