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Boundary-layer development at a two-dimensional rear stagnation point

  • A. J. Robins (a1) and J. A. Howarth (a1)

This paper examines the nature of the development of two-dimensional laminar flow of an incompressible fluid at the rear stagnation point on a cylinder which is started impulsively from rest. Proudman & Johnson (1962) first examined this type of flow, andobtainedasimilarity solution of the inviscid form of the equations of motion. This solution describes the nature of the flow at large distances from the surface, for large times after the start of the motion. Here, the flow at the rear stagnation point is examined in greater detail. The solution found by Proudman & Johnson constitutes the leading term in an asymptotic expansion, valid for large times. Further terms in this expansion are now calculated, and the method of matched asymptotic expansions is used to obtain an inner solution describing the flow near the surface. A numerical integration of the full initial-value problem gives good agreement with the analytical solution.

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Blasius, H.1908 Z. angew. Math. Phys. 56, 1.
Goldstein, S. & Rosenread, L.1936 Proc. Camb. Phil. Soc. 32, 392.
Hiemenz, K.1911 Dingl. Poly tech. J. 326, 321.
Kelly, R. E.1962 J. Fluid Mech. 13, 449.
Proudman, I. & Johnson, K.1962 J. Fluid Mech. 12, 161.
Wundt, H.1955 Ingen-Arch. 23, 212.
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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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