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Potential/complex-lamellar velocity decomposition and its relevance to turbulence

Published online by Cambridge University Press:  19 April 2006

Ronald L. Panton
Ronald L. Panton
Affiliation:
Mechanical Engineering Department, University of Texas, Austin
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Abstract

In discussing turbulent shear layers, experimentalists have divided the flow into a turbulent region, which is vortical, and a non-turbulent region, which is irrotational but unsteady. This paper introduces a theoretical method of decomposing the velocity field into potential and vortical components that is compatible with the experimentalists’ viewpoint. Specifically, only potential motions will exist in the non-turbulent region, while the decomposition shows that the turbulent region consists of both potential and vortical motions. The kinematic decomposition used is called a potential/complex-lamellar decomposition. Compared with the standard Helmholtz decomposition, the complex-lamellar decomposition is not widely known, and this article includes a discussion of its properties and characteristics. The vector components in this decomposition may be represented by three scalar potentials: ϕ, ψ and χ. One of the important physical interpretations of the potentials concerns vortex lines. Vortex lines are defined by the intersection of a surface ψ = constant with a surface χ = constant. Since these surfaces are a function of time, this establishes a sound kinematic theory for following the history of vortex lines in a turbulent or viscous flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 88 , Issue 1 , 13 September 1978 , pp. 97 - 114
Copyright
© 1978 Cambridge University Press

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References

AscRIS, R. 1962 Vectors, Tensors and the Basic Equations of Fluid Mechanics. Prentice-Hall.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Brand, L. 1947 Vector and Tensor Analysis. Wiley.
Clebsch, A. 1858 J. Math. 56, 1.
Corrsin, S. 1943 N.A.C.A. Wartime Rep. W-94.
Helmholtz, H. 1857 J. reine angew. Math. 55, 25.
Hussain, A. K. M. F. & Reynolds, W. C. 1970 J. Fluid Mech. 41, 241.
Ince, E. L. 1956 Ordinary Differential Equations. Dover.
Kellogg, O. D. 1953 Foundations of Potential Theory. Dover.
Kelvin, Lord 1851 Phil. Trans. Roy. Soc. 141, 243.
Kovasznay, L. S. G., Kibens, V. & Blackwelder, R. F. 1970 J. Fluid Mech. 41, 283.
Lamb, H. 1945 Hydrodynamics. Dover.
Landahl, M. T. 1967 J. Fluid Mech. 29, 441.
Libby, P. 1975 J. Fluid Mech. 68, 273.
Phillips, H. B. 1933 Vector Analysis. Wiley.
Richardson, S. M. & Cornish, A. R. H. 1977 J. Fluid Mech. 82, 309.
Stokes, G. G. 1851 Trans. Camb. Phil. Soc. 9, 1. (See also Papers, vol. 2, p. 243. Cambridge University Press.)
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.
Truesdell, C. A. 1954 The Kinematics of Vorticity. Indiana University Press.