Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Some aspects of three-dimensional boundary layer flows

Author: R. Sedney
Journal: Quart. Appl. Math. 15 (1957), 113-122
MSC: Primary 76.0X
DOI: https://doi.org/10.1090/qam/93234
MathSciNet review: 93234
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Abstract: The equations for laminar boundary layer flow over a general smooth surface in three dimensions are analyzed in a normal coordinate system. The invariance properties of these equations are found using the concept of subtensors. The boundary layer equations are not tensor equations but subtensor equations. Conditions for the Cartesian form of the equations are given and a criterion for no secondary flow is found in terms of the geodesies of the body surface. The displacement effect of the boundary layer is also discussed.

References [Enhancements On Off] (What's this?)

  • [1] W. R. Sears, Boundary layer in three-dimensional flow, Appl. Mech. Revs. 7, (1954)
  • [2] L. Howarth, The boundary layer in three-dimensional flow--part I, Phil. Mag. 42, 239 (1951) MR 0041610
  • [3] F. K. Moore, Three-dimensional compressible laminar boundary layer flow, N.A.C.A., T.N. 2279 (1951) MR 0041615
  • [4] W. D. Hayes, The three-dimensional boundary layer, Nav. Ord. Rep. 1313 (1951) MR 0041614
  • [5] A. D. Michal, Matrix and tensor calculus, John Wiley and Sons, New York, 1947, pp. 103 and 121 MR 0020334
  • [6] J. L. Synge and A. Schild, Tensor calculus, University of Toronto Press, Toronto, 1949, pp. 62-71 MR 0033165
  • [7] P. A. Lagerstrom and S. Kaplun, The role of the coordinate system in boundary layer theory, VIII Intern. Congr. for Theoret. and Appl. Mech., Istanbul, 1952
  • [8] S. Kaplun, The role of coordinate systems in boundary layer theory, Z.A.M.P. 5, 111 (1954) MR 0061961
  • [9] F. K. Moore, Displacement effect of a three-dimensional boundary layer, N.A.C.A. T.N. 2722 (1952)
  • [10] L. Howarth, The boundary layer in three-dimensional flow--part II, Phil. Mag. 42, 1433 (1951) MR 0044974
  • [11] W. Mangler, Zusammenhang zwischen ebenen und rotationssymmetrischen Grenzschichten in kompressiblen Flüssigkeiten, Z.A.M.M. 28, 97 (1948) MR 0025351
  • [12] H. B. Phillips, Vector analysis, John Wiley and Sons, New York, 1933, p. 96
  • [13] Y. H. Kuo, On the flow of an incompressible viscous fluid past a flat plate at moderate Reynolds numbers, J. Math. and Phys. 22, 83 (1953) MR 0062571

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DOI: https://doi.org/10.1090/qam/93234
Article copyright: © Copyright 1957 American Mathematical Society

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