Pullin, D. I. and Saffman, P. G. (1993) On the Lundgren–Townsend model of turbulent fine scales. Physics of Fluids A, 5 (1). pp. 126145. ISSN 08998213. http://resolver.caltech.edu/CaltechAUTHORS:PULpofa93

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Abstract
The strainedspiral vortex model of turbulent fines scales given by Lundgren [Phys. Fluids 25, 2193 (1982)] is used to calculate vorticity and velocityderivative moments for homogeneous isotropic turbulence. A specific form of the relaxing spiral vortex is proposed modeled by a rollingup vortex layer embedded in a background containing opposite signed vorticity and with zero total circulation at infinity. The numerical values of two dimensionless groups are fixed in order to give a Kolmogorov constant and skewness which are within the range of experiment. This gives the result that the ratio of the ensemble average hyperskewness S2p + 1[equivalent] ([partialderivative]u/[partialderivative]x)2p + 1/[([partialderivative]u/[partialderivative]x)2](2p + 1)/2 to the hyperflatness F2p[equivalent]([partialderivative]u/[partialderivative]x)2p/[([partialderivative]u/[partialderivative]x)2] p, p=2,3,..., is constant independent of Taylor–Reynolds number Rlambda, as is the ratio of the 2pth moment of one component of the vorticity Omega2p[equivalent]omega<sup>2p</sup><sub>x</sub>/(omega<sup>2</sup><sub>x</sub>)p to F2p. A cutoff in a relevant time integration is then used to eliminate vortexsheetinduced divergences in the integrals corresponding to omega<sup>2p</sup><sub>x</sub>, p=2,3,..., and an assumption is made that the lateral scale of the spiral vortex in the model is the geometric mean of the Taylor and the Kolmogorov microscales. This gives Omega2p=Omegahat 2pR<sub> lambda </sub><sup>p/2  3/4</sup>, F2p=Fhat 2pR<sub> lambda </sub><sup>p/2  3/4</sup> and S2p + 1=Shat 2p + 1R<sub> lambda </sub><sup>p/2  3/4</sup>, p=2,3,..., with explicit calculation of the numbers Omegahat 2p, Fhat 2p, and Shat 2p + 1. The results of the model are compared with experimental compilation of Van Atta and Antonia [Phys. Fluids 23, 252 (1980)] for F4 and with the isotropic turbulence calculations of Kerr [J. Fluid Mech. 153, 31 (1985)] and of Vincent and Meneguzzi [J. Fluid Mech. 225, 1 (1991)].
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Additional Information:  Copyright © 1993 American Institute of Physics (Received 14 May 1992; accepted 24 August 1992) The authors wish to thank Dr. T. S. Lundgren, Dr. D. I. Meiron, and Professor D. W. Moore for valuable comments. Thanks are also due to Dr. Maurice Meneguzzi for providing unpublished data on velocityderivative moments and to Dr. Robert Kerr for providing spectral data obtained from 1283 numerical simulations. One of us (PGS) thanks the Department of Energy for support under Grant No. DEFG0389ER 25073. 
Subject Keywords:  TURBULENT FLOW; VELOCITY FIELDS; VORTICITY; VORTICES; HOMOGENEITY; ISOTROPY; CORRELATION FUNCTIONS; REYNOLDS NUMBER; NAVIER–STOKES EQUATIONS; STRUCTURE FUNCTIONS; ENERGY SPECTRA 
Record Number:  CaltechAUTHORS:PULpofa93 
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:PULpofa93 
Alternative URL:  http://dx.doi.org/10.1063/1.858798 
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ID Code:  3262 
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Deposited On:  25 May 2006 
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