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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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