Summary
The unsteady boundary layer equations are studied close to a separation point. A perturbation procedure, based on an idea of Kaplun, leads to a nonlinear integro-differential equation for the skin-friction. A uniformly valid small-time analysis of this equation shows how an initial square-root singularity at a separation point is smoothed out by unsteady processes.
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J. Buckmaster, The behavior of a laminar compressible boundary layer on a cold wall near a point of zero skinfriction,J. Fluid Mech, 44 (1970) 237.
J. Buckmaster, Separation and the Compressible Boundary Layer,J. Eng. Math., 5 (1971) 71.
J. Buckmaster, Effect of Transverse Curvature on the Singularity at Separation for a Laminar Boundary Layer,Physics of Fluids 14 (1971) 1593.
J. Buckmaster, Perturbation Technique for the Study of Three-Dimensional Separation,Physics of Fluids, 15 (1972) 2106.
D. Catherall, K. Stewartson, and P. G. Williams, Viscous flow past a plate with uniform injection,Proc. Roy. Soc. A 284 (1965) 370.
S. Goldstein, On Laminar Boundary-Layer Flow,Quart. J. Mech. Appl. Math. 1 (1948) 43.
S. Kaplun inFluid Mechanics and Singular Perturbations edited by P. A. Lagestrom, L. N. Howard, and C. S. Liu (Academic, New York, 1967) p. 145.
I. Proudman, and K. Johnson, Boundary layer growth near a rear stagnation point,J. Fluid Mech., 12 (1962) 161.
W. R. Sears and D. Telionis, Unsteady Boundary-Layer Separation, To appear in theProceedings of the 1971 I.U.T.A.M. Symposium on Unsteady Boundary Layers.
K. Stewartson, On Goldstein's Theory of Laminar Separation,Quart. J. Mech. Appl. Math., 11 (1958) 399.
K. Stewartson, The behaviour of a laminar compressible boundary layer near a point of zero skin-friction,J. Fluid Mech., 12 (1962) 117.
D. Telionis,Unsteady Boundary-Layer Separation, Ph. D. Thesis, Cornell University, School of Engineering (1970).
R. M. Terrill, Laminar Boundary-Layer Flow Near Separation with and without Suction,Phil. Trans., A 253 (1960) 55.
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Buckmaster, J. The unsteady evolution of the singularity at separation. J Eng Math 7, 223–230 (1973). https://doi.org/10.1007/BF01535283
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DOI: https://doi.org/10.1007/BF01535283