On the growth of Taylor-Görtler vortices along highly concave walls
Author:
A. M. O. Smith
Journal:
Quart. Appl. Math. 13 (1955), 233-262
MSC:
Primary 76.0X
DOI:
https://doi.org/10.1090/qam/87409
MathSciNet review:
87409
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Abstract: The primary objective of this study has been to prepare a chart for computing the growth of Taylor-Görtler vortices in laminar flow along walls of both high and low concave curvature. Taylor-Görtler vortices are streamwise vortices having alternate right- and left-hand rotation that may develop in the laminar boundary layer along a concave surface.
S. Goldstein, Modern developments in fluid dynamics, vol. 1, Clarendon Press, Oxford, 1938
Lord Rayleigh, On the dynamics of revolving fluids, Proc. Roy. Soc. (London) A(93), 148-154 (1917)
G. I. Taylor, Stability of a viscous liquid contained between two rotating cylinders, Phil. Trans. Roy. Soc. (London) A(223) 289-343 (1923)
H. Görtler, Über eine dreidimensionale Instabilität laminarer Grenzschichten an konkaven Wänden, Ges. d. Wiss. Göttingen, Nachr. a. d., Math., 2, No. 1 (1940)
H. W. Liepmann, Investigation of boundary layer transition on concave walls, NACA Wartime Report ACR No. 4J28, Feb. 1945
W. W. Hagerty, Use of an optical property of glycerine-water solutions to study viscous fluid-flow problems, J. Appl. Mech. 17, 54-58 (1950)
- D. Meksyn, Stability of viscous flow over concave cylindrical surfaces, Proc. Roy. Soc. London Ser. A 203 (1950), 253–265. MR 38774, DOI https://doi.org/10.1098/rspa.1950.0138
W. J. Duncan, Galerkin’s method in mechanics and differential equations, British Reports and Memoranda No. 1798, (1937)
A. M. O. Smith, Improved solutions of the Falkner and Skan boundary layer equation, Sherman Fair-child Fund Paper No. FF-10, Inst. Aeronaut. Sci. (1954)
R. A. Frazer, W. J. Duncan, A. R. Collar, Elementary matrices, Cambridge University Press, Cambridge, 1950
- E. L. Ince, Ordinary Differential Equations, Dover Publications, New York, 1944. MR 0010757
E. J. Richards, W. S. Walker, J. R. Greening, Tests of a Griffith Aerofoil in the $13ft. \times 9ft.$. wind tunnel, British Reports and Memoranda No. 2148, March 1944 A personal communication from the N.P.L. supplied much additional and more detailed data than available in the R & M. Furthermore, the factor 1.36, page 9 of R & M 2148 was changed to the correct value 0.54
- Günther Hämmerlin, Über das Eigenwertproblem der dreidimensionalen Instabilität laminarer Grenzschichten an konkaven Wänden, J. Rational Mech. Anal. 4 (1955), 279–321 (German). MR 68387, DOI https://doi.org/10.1512/iumj.1955.4.54010
S. Goldstein, Modern developments in fluid dynamics, vol. 1, Clarendon Press, Oxford, 1938
Lord Rayleigh, On the dynamics of revolving fluids, Proc. Roy. Soc. (London) A(93), 148-154 (1917)
G. I. Taylor, Stability of a viscous liquid contained between two rotating cylinders, Phil. Trans. Roy. Soc. (London) A(223) 289-343 (1923)
H. Görtler, Über eine dreidimensionale Instabilität laminarer Grenzschichten an konkaven Wänden, Ges. d. Wiss. Göttingen, Nachr. a. d., Math., 2, No. 1 (1940)
H. W. Liepmann, Investigation of boundary layer transition on concave walls, NACA Wartime Report ACR No. 4J28, Feb. 1945
W. W. Hagerty, Use of an optical property of glycerine-water solutions to study viscous fluid-flow problems, J. Appl. Mech. 17, 54-58 (1950)
D. Meksyn, Stability of viscous flow over concave cylindrical surfaces, Proc. Roy. Soc. (London) A(203), 253-265 (1950)
W. J. Duncan, Galerkin’s method in mechanics and differential equations, British Reports and Memoranda No. 1798, (1937)
A. M. O. Smith, Improved solutions of the Falkner and Skan boundary layer equation, Sherman Fair-child Fund Paper No. FF-10, Inst. Aeronaut. Sci. (1954)
R. A. Frazer, W. J. Duncan, A. R. Collar, Elementary matrices, Cambridge University Press, Cambridge, 1950
E. L. Ince, Ordinary differential equations, Dover Publications
E. J. Richards, W. S. Walker, J. R. Greening, Tests of a Griffith Aerofoil in the $13ft. \times 9ft.$. wind tunnel, British Reports and Memoranda No. 2148, March 1944 A personal communication from the N.P.L. supplied much additional and more detailed data than available in the R & M. Furthermore, the factor 1.36, page 9 of R & M 2148 was changed to the correct value 0.54
Günther Hämmerlin, Über das Eigenwertproblem dreidimensionalen Instabilität laminarer Grenzschichten längs konkaven Wänden, J. Ratl. Mech. Anal. 4, 279-321 (1955).
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Article copyright:
© Copyright 1955
American Mathematical Society
