Journal of Fluid Mechanics

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

S. N.  Timoshin a1
a1 Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK and Central Aerohydrodynamical Institute, Zhukovsky, Russia, 140160

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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.

(Published Online April 26 2006)
(Received September 19 1994)
(Revised August 23 1995)