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Concerning marginal singularities in the boundary-layer flow on a downstream-moving surface

  • S. N. Timoshin (a1)
Abstract

The formation of separation singularities in solutions of the classical boundary-layer equations is studied numerically and analytically for the case of a two-dimensional incompressible steady flow near a solid surface moving in the direction of the main stream. Unlike the previously studied regime of the incipient separation located at the maximum point in the external pressure distribution, the breakdown in this work occurs under an adverse pressure forcing and involves a regular flow field upstream of the Moore-Rott-Sears point with an algebraic non-analyticity downstream. Small deviations from the precisely regular approach to the singular point are shown to result in an exponential amplification of linear disturbances; in the subsequent nonlinear stage the solution terminates in a finite-distance blow-up singularity or, alternatively, continues in a regular fashion across the singular station. The case of asymptotically small slip velocities is considered and a connection with marginal separation on a fixed wall is discussed.

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Brown, S. N. & Stewartson, K.1983On an integral equation of marginal separation. SIAM J. Appl. Maths43, 11191126.

Cowley, S. J., Hocking, L. M. & Tutty, O. R.1985The stability of solutions of the classical unsteady boundary-layer equation. Phys. Fluids28, 441443.

Cowley, S. J., Dommelen, L. L. Van & Lam, S. T.1990On the use of lagrangian variables in descriptions of unsteady boundary-layer separation. Phil. Trans. R. Soc. Lond. A 333, 343378.

Elliott, J. W., Smith, F. T. & Cowley, S. J.1983Breakdown of boundary layers: (i) on moving surfaces; (ii) in semi-similar unsteady flow; (iii) in fully unsteady flow. Geophys. Astrophys. Fluid Dyn.25, 77138.

Goldstein, S.1948On laminar boundary-layer flow near a position of separation. Q. J. Mech. Appl. Maths1, 4369.

Riley, N.1975Unsteady laminar boundary layers. SIAM rev.17, 274297.

Smith, F. T.1982aOn the high Reynolds number theory of laminar flows. IMA J. Appl. Maths28, 207281.

Smith, F. T. 1982b Concerning dynamic stall. Aeronaut. Q. 33, 331352.

Smith, F. T.1984Concerning upstream influence in separating boundary layers and downstream influence in channel flow. Q. J. Mech. Appl. Maths37, 389399.

Smith, F. T.1986 Steady and unsteady boundary-layer separation. Ann. Rev. Fluid Mech.18, 197220.

Smith, F. T., Brighton, P. W. M., Jackson, P. S. & Hunt, J. C. R. 1981 On boundary layer flow past two-dimensional obstacles. J. Fluid Mech. 113, 123152.

Smith, F. T. & Elliott, J. W.1985On the abrupt turbulent reattachment downstream of leadingedge laminar separation. Proc. R. Soc. Lond. A 401, 127.

Smith, F. T. & Walton, A. G. 1989 Nonlinear interaction of near-planar TS waves and longitudinal vortices in boundary-layer transition. Mathematika 36, 262289.

Stewartson, K.1958On Goldstein's theory of laminar separation. Q. J. Mech. Appl. Maths11, 399410.

Stewartson, K.1974Multistructured boundary layers on flat plates and related bodies. Adv. Appl Mech.14, 145239.

Stewartson, K., Smith, F. T. & Kaups, K.1982Marginal separation. Stud. Appl. Maths67, 4561.

Telionis, D. P.1981Unsteady Viscous Flows.Springer.

Telionis, D. P. & Werle, M. J.1973Boundary-layer separation from downstream moving boundaries. Trans. ASME J. Appl. Mech.40, 369374.

Timoshin, S. N. & Smith, F. T.1995Singularities encountered in three-dimensional boundary layers under an adverse or favourable pressure gradient. Phil. Trans. R. Soc. Lond. A 352, 4587.

Williams, J. C.1977Incompressible boundary-layer separation. In Ann. Rev. Fluid Mech.9, 113144.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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