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Generalized expressions for secondary vorticity using intrinsic co-ordinates

Published online by Cambridge University Press:  29 March 2006

B. Lakshminarayana
Affiliation:
Department of Aerospace Engineering, The Pennsylvania State University, University Park, Pa 16802
J. H. Horlock
Affiliation:
Engineering Department, University of Cambridge

Abstract

Equations for the development of streamwise (or secondary) vorticity, for stationary and rotating systems, are derived directly from the vector equation for vorticity, using intrinsic co-ordinates. This approach places emphasis on the coupled equations for the vorticity components parallel and normal to the streamline. The equations derived are more general than those hitherto available, being valid for compressible, stratified and viscous flow. Some interpretation is given of the physical mechanism causing secondary flow.

Type
Research Article
Copyright
© 1973 Cambridge University Press

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References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics, p. 267. Cambridge University Press.
Bjøsrgum, O. 1951 Universitet J. Bergen, Naturvitenskapalig rekke, no. 1, pp. 185.
Drazin, P. G. 1961 Tellus, 13, 239.
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Hawthorne, W. R. 1951 Proc. Roy. Soc. A, 206, 374.
Hawthorne, W. R. 1954 J. Aero Sci. 21, 588.
Hawthorne, W. R. 1955a Proc. Camb. Phil. Soc. 51, 737.
Hawthorne, W. R. 1955b Quart. J. Mech. Appl. Math. 8, 266.
Hawthorne, W. R. 1966 Gas Turbine Lab. (M.I.T.) Rep. no. 88.
Hawthorne, W. R. 1967 Fluid Mechanics of Internal Flow (ed. G. Sovran). Elsevier.
Hawthorne, W. R. & Martin, M. E. 1955 Proc. Roy. Soc. A, 232, 184.
Hildebrand, F. B. 1962 Advanced Calculus for Applications, p. 274. Prentice Hall.
Horlock, J. H. & Lakshminarayana, B. 1973 Ann. Rev. Fluid Mech. 5, 247.
Lakshminarayana, B. & Horlock, J. H. 1963 Int. J. Mech. Sci. 5, 287.
Loos, H. G. 1956 J. Aero Sci. 23, 76.
Louis, J. F. 1956 Proc. 9th Int. Cong. Appl. Mech. 3, 306.
Marris, A. W. 1963 Trans. A.S.M.E. E30, 525.
Marris, A. W. 1964 J. Fluid Mech. 20, 177.
Marris, A. W. 1966 Trans. A.S.M.E. D88, 533.
Pedlosky, J. 1972 Mathematical Problems in Geophysical Sciences (ed. W. H. Reid). Am. Math. Soc.
Scorer, R. S. & Wilson, S. D. R. 1963 Quart. J. Roy. Met. Soc. 89, 532.
Smith, A. G. 1957 Aero. Quart. 8, 369.
Squire, H. B. & Winter, K. G. 1951 J. Aero Sci. 18, 271.