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On the starting process of strongly nonlinear vortex/Rayleigh-wave interactions

Part of:Incompressible viscous fluids

Published online by Cambridge University Press:  26 February 2010

P. G. Brown,
S. N. Brown,
F. T. Smith and
S. N. Timoshin
P. G. Brown
Affiliation:
9 Esparto Street, London. SW18 4DQ.
S. N. Brown
Affiliation:
Department of Mathematics, University College London, Gower Street, London. WC1E6BT.
F. T. Smith
Affiliation:
Department of Mathematics, University College London, Gower Street, London. WC1E6BT.
S. N. Timoshin
Affiliation:
Department of Mathematics, University College London, Gower Street, London. WC1E6BT.
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Abstract

An oncoming two-dimensional laminar boundary layer that develops an unstable inflection point and becomes three-dimensional is described by the Hall-Smith (1991) vortex/wave interaction equations. These equations are now examined in the neighbourhood of the position where the critical surface starts to form. A consistent structure is established in which an inviscid core flow is matched to a viscous buffer-layer solution where the appropriate jump condition on the transverse shear stress is satisfied. The final result is a bifurcation equation for the (constant) amplitude of the wave pressure. A representative classical velocity profile is considered to illustrate solutions of this equation for a range of values of the wave-numbers.

MSC classification

Secondary:76D10: Boundary-layer theory, separation and reattachment, higher-order effects

Information

Type
Research Article
Information
Mathematika , Volume 40 , Issue 1 , June 1993, pp. 7 - 29
Copyright
Copyright © University College London 1993

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References

Blackaby, N. D. (1991). On viscous, inviscid and centrifugal instability mechanisms in compressible boundary layers, including non-linear vortex/ wave interactions and the effects of large Mach number on transition. Ph.D. Thesis, University of London.Google Scholar
Davis, D. A. R. (1992). On linear and nonlinear instabilities in boundary layers with cross-flow. Ph.D. Thesis, University of London.Google Scholar
Gajjar, J. and Smith, F. T. (1983). On hypersonic self-induced separation, hydraulic jumps and boundary layers with algebraic growth. Mathematika, 59, 77.CrossRefGoogle Scholar
Hall, P. and Smith, F. T. (1988). The nonlinear interaction of Tollmien-Schlichting waves and Taylor-Gortler vortices in curved channel flows. Proc. Roy. Soc. Lond. A, 417, 255.Google Scholar
Hall, P. and Smith, F. T. (1989). Nonlinear Tollmien-Schlichting wave/vortex interaction in boundary layers. Eur. J. Mech., 8, 151.Google Scholar
Hall, P. and Smith, F. T. (1990). Theory on instability and transition. Proc. ICASE Workshop on Instability and Transition, Vol. II (ed. Hussaini, M. Y. and Voigt, R. G.) pp. 5–39. Springer.Google Scholar
Hall, P. and Smith, F. T. (1991). On strongly nonlinear vortex/wave interactions in boundary-layer transition. j Fluid Mech., 227, 641.CrossRefGoogle Scholar
Klebanoff, P. S. and Tidstrom, K.. D. (1959). Evolution of amplified waves leading to transition in a boundary layer with zero pressure gradient. N.A.S.A. Tech. note, no. D-195.Google Scholar
Smith, F. T. and Blennerhassett, P. (1992). Nonlinear interaction of oblique three-dimensional Tollmien-Schlichting waves and longitudinal vortices in channel flows and boundary layers. Proc. Roy. Soc. Lond. A, 436, 585.Google Scholar
Smith, F. T. and Bodonyi, R. J. (1985). On short-scale inviscid instabilities in flow past surfacemounted obstacles and other non-parallel motions. Aero. Jnl, June/July.Google Scholar
Smith, F. T., Brown, S. N. and Brown, P. G. (1992). Initiation of three-dimensional transition paths from an inflectional profile. Eur. J. Mech. To appear.Google Scholar
Smith, F. T. and Walton, A. G. (1989). Nonlinear interaction of near-planar TS waves and longitudinal vortices in boundary-layer transition. Mathematika, 36, 262.CrossRefGoogle Scholar
Stewart, P. A. and Smith, F. T. (1992). Development of three-dimensional nonlinear blow-up from a nearly planar initial disturbance in boundary-layer transition: theory and experimental comparisons. J. Fluid Mech., 244, 79.CrossRefGoogle Scholar
Walton, A. G. (1991). Theory and computation of three-dimensional nonlinear effects in pipe-flow transition. Ph.D. Thesis, University of London.Google Scholar
Walton, A. G. and Smith, F. T. (1992). Properties of strongly nonlinear vortex/Tollmien-Schlichtingwave interactions. J. Fluid Mech., 244, 649.CrossRefGoogle Scholar