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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[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. I. Derivation of the equations for flow along a general curved surface*, Philos. Mag. (7)**42**(1951), 239–243. MR**0041610****[3]**Franklin K. Moore,*Three-dimensional compressible laminar boundary-layer flow*, Tech. Notes Nat. Adv. Comm. Aeronaut.,**1951**(1951), no. 2279, 38. MR**0041615****[4]**Wallace D. Hayes,*The three-dimensional boundary layer*, Tech. Memo. RRB-105, U. S. Naval Ordnance Test Station, Inyokern, Calif., 1950. MR**0041614****[5]**Aristotle D. Michal,*Matrix and Tensor Calculus with Applications to Mechanics, Elasticity, and Aeronautics*, John Wiley and Sons, Inc., New York; Chapman and Hall, Limited, London, 1947. MR**0020334****[6]**J. L. Synge and A. Schild,*Tensor Calculus*, Mathematical Expositions, no. 5, University of Toronto Press, Toronto, Ont., 1949. 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]**Saul Kaplun,*The role of coordinate systems in boundary-layer theory*, Z. Angew. Math. Physik**5**(1954), 111–135. 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. II. The flow near a stagnation point*, Philos. Mag. (7)**42**(1951), 1433–1440. MR**0044974****[11]**W. Mangler,*Zusammenhang zwischen ebenen und rotationssymmetrischen Grenzschichten in kompressiblen Flüssigkeiten*, Z. Angew. Math. Mech.**28**(1948), 97–103 (German, with Russian summary). MR**0025351**, https://doi.org/10.1002/zamm.19480280401**[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. Physics**32**(1953), 83–101. MR**0062571**

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
76.0X

Retrieve articles in all journals with MSC: 76.0X

Additional Information

DOI:
https://doi.org/10.1090/qam/93234

Article copyright:
© Copyright 1957
American Mathematical Society