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Viscous flow near a corner in three dimensions

Published online by Cambridge University Press:  29 March 2006

N. Tokuda
N. Tokuda
Affiliation:
Department of Mathematics, University of Southampton Present address: 3-6-22, Sekiguchi, Bunkyo-kn, Tokyo.
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Abstract

The nature of a three-dimensional viscous flow along a corner near its junction has been clarified in this paper by constructing a Stokes slow-flow solution. We have further demonstrated that this Stokes solution can be matched onto an inertial-flow solution in principle by establishing an overlap domain along one sector of an inertial-flow region, namely along the flow symmetry line. This Stokes solution reveals a remarkably complex structure of the flow as characterized by a separating streamwise velocity profile in addition to a sequence of Moffatt's viscous eddies in a cross-flow plane.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 53 , Issue 1 , 9 May 1972 , pp. 129 - 148
Copyright
© 1972 Cambridge University Press

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References

Burggraf, O. R. 1966 Analytical and numerical studies of the structure of steady separated flows. J. Fluid Mech. 24, 113.Google Scholar
Carrier, G. F. 1947 The boundary layer in a corner. Quart. Appl. Math. 4, 4.Google Scholar
Carrier, G. F. & LIN, C. C. 1948 On the nature of the boundary layer near the leading edge of a flat plate. Quart. Appl. Math. 6, 63.Google Scholar
Kaplum, S. 1967 Fluid Mechanics and Singular Perturbations (ed. P. A. Lagerstrom et al.). Academic.
Lagerstrom, P. A. 1964 Theory of Laminar Flows (ed. F. K. Moor), chap. B. Princeton University Press.
Lewis, J. A. & Carrier, G. F. 1949 Some remarks on the flat-plate boundary layer. Quart. Appl. Math. 7, 228.Google Scholar
Lugt, H. J. & Schwiderski, E. W. 1964 Flows around dihedral angles. Part I. Proc. Roy. SOC. A 285, 382.Google Scholar
Maskell, E. C. 1955 Flow separation in three dimensions. Aero. Res. Counc. Rep. no. 18063. (See also 1955 R.A.E. Aero. Rep. no. 2565.)Google Scholar
Motz, H. 1946 The treatment of singularities of partial differential equations by relaxation methods. Quart. App1. Math. 4, 371.Google Scholar
Moffatt, H. K. 1964 Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18, 1.Google Scholar
Pal, A. & Rubin, S. G. 1969 Viscous flow along a corner. Part 1. Asymptotic features of the corner-layer equations. P.I.B.A.L. Rep. no. 69-18.Google Scholar
Pearsox, J. R. A. 1957 Homogeneous turbulence and laminar viscous flow. Ph.D. thesis, Carnbridge University.
Proudman, I. & Pearson, J. R. A. 1957 Expansions at small Reynolds number for the flow past a sphere and a cylinder. J. Fluid Mech. 2, 237.Google Scholar
Rubin, S. G. 1966 Incompressible flow along a corner. J. Fluid Mech. 26, 97.Google Scholar
Rubin, S. G. & Grossman, B. 1969 Viscous flow along a corner. Part 2. Numerical solution of corner-layer equations. P.T.B.A.L. Rep. no. 69-33.Google Scholar
Stewartson, K. 1961 Viscous flow past a quarter-infinite plate. J. Aero. Sci. 28, 1.Google Scholar
Tokuda, N. 1972 Viscous flow past a semi-infinite flat plate. To be published.
Van Dyke, M. D. 1966 The circle at low Reynolds number as a test of the method of series truncation. Proc. 11th Int. Congress of Appl. Mech. Berlin.Google Scholar
Zamir, M. 1970 Boundary-layer theory and the flow in a streamwise corner. Aeron. J. 74, 330.Google Scholar
Zamir, M. & Young, A. D. 1970 Experimental investigation of the boundary layer in a streamwise corner. Aeron. Quart. 21, 313.Google Scholar