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A streamline coordinate system for distorted two-dimensional shear flows

Published online by Cambridge University Press:  20 April 2006

J. J. Finnigan
J. J. Finnigan
Affiliation:
CSIRO Division of Environmental Mechanics, P.O. Box 821, Canberra City, ACT 2601, Australia
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Abstract

A function ϕ is derived which is constant along the orthogonal trajectories of streamlines in two-dimensional flow. In irrotational flows, ϕ reduces to the velocity potential. The pair of functions ϕ and ψ, where ψ is the stream function, are used to define a coordinate system in rotational fluid flows. Tensor methods are used to transform the equations of motion of a turbulent fluid and the equations for second moments of turbulent fluctuations to this coordinate system. Explicit extra terms appear in the transformed equations embodying the effects of streamline curvature and mean flow acceleration. These extra terms are characterized by two lengthscales which arise naturally from the transformation: the local radius of curvature of the streamline and the ‘e-folding’ distance of the mean streamwise velocity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 130 , May 1983 , pp. 241 - 258
Copyright
© 1983 Cambridge University Press

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References

Aris, R. 1962 Vectors, Tensors and the Basic Equations of Fluid Mechanics. Prentice-Hall.
Bradshaw, P. 1969 The analogy between streamline curvature and buoyancy in turbulent shear flow J. Fluid Mech. 36, 177–191.Google Scholar
Bradshaw, P. 1973 Effects of streamline curvature on turbulent flow. AGAR Dograph no. 169 (ed. A. D. Young) Natl Tech. Info. Service, US Dept Commerce.
Castro, I. P. & Bradshaw, P. 1976 The turbulence structure of a highly curved mixing layer J. Fluid Mech. 73, 265–304.Google Scholar
Crow, S. C. 1968 Viscoelastic properties of fine-grained incompressible turbulence J. Fluid Mech. 33, 1–20.Google Scholar
Durbin, P. A. & Hunt, J. C. R. 1980 On surface pressure fluctuations beneath turbulent flow round bluff bodies J. Fluid Mech. 100, 161–184.Google Scholar
Finnigan, J. J. & Bradley, E. F. 1983 The turbulent kinetic energy budget behind a porous barrier: an analysis in streamline co-ordinates. In Proc. 6th. Intl Conf. on Wind Engineering, Brisbane, Australia. J. Wind Engng & Ind. Aerodyn. (to be published).
Finnigan, J. J. & Einaudi, F. 1981 The interaction between an internal gravity wave and the planetary boundary layer. Part II: Effect of the wave on the turbulent structure. Q. J. R. Met. Soc. 107, 807–832.
Gillis, J. C. & Johnston, J. P. 1980 Experiments on the turbulent boundary layer over convex walls and its recovery to flat wall conditions. Turbulent Shear Flows 2 (ed. L. J. S. Bradbury, F. Durst, B. E. Launder, F. F. W. Schmidt & J. H. Whitelaw), pp. 117–128. Springer.
Howarth, L. 1951 The boundary layer in three dimensional flow – Part I. Derivation of the equations for flow along a general curved surface. Phil. Mag. 42 (7), 239–243.
Ince, E. L. 1956 Ordinary Differential Equations. Dover.
Lighthill, M. J. 1956 Drift J. Fluid Mech. 1, 31–53.Google Scholar
Mamayev, O. I. 1973 Comments on Veronis’ paper: ‘On properties of seawater defined by temperature, salinity and pressure’. J. Mar. Res. 31, 90–92.
Margolis, D. P. & Lumley, J. L. 1965 Curved turbulent mixing layer Phys. Fluids 8, 1775–1783.Google Scholar
Piaggio, H. T. H. 1958 An Elementary Treatise on Differential Equations and Their Applications. Bell.
Raupach, M. R., Thom, A. S. & Edwards, I. 1980 A wind-tunnel study of turbulent flow close to regularly arrayed rough surfaces Boundary-Layer Met. 18, 373–397.Google Scholar
Truesdell, C. 1953 The physical components of vectors and tensors Z. angew. Math. Mech. 33, 345–356.Google Scholar
Veronis, G. 1972 On properties of seawater defined by temperature, salinity and pressure J. Mar. Res. 30, 227–255.Google Scholar