Pullin, D. I. and Saffman, P. G. (1993) On the Lundgren–Townsend model of turbulent fine scales. Physics of Fluids A, 5 (1). pp. 126-145. ISSN 0899-8213 http://resolver.caltech.edu/CaltechAUTHORS:PULpofa93
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The strained-spiral vortex model of turbulent fines scales given by Lundgren [Phys. Fluids 25, 2193 (1982)] is used to calculate vorticity and velocity-derivative moments for homogeneous isotropic turbulence. A specific form of the relaxing spiral vortex is proposed modeled by a rolling-up 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] ([partial-derivative]u/[partial-derivative]x)2p + 1/[([partial-derivative]u/[partial-derivative]x)2](2p + 1)/2 to the hyperflatness F2p[equivalent]([partial-derivative]u/[partial-derivative]x)2p/[([partial-derivative]u/[partial-derivative]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 vortex-sheet-induced 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=Omega-hat 2pR<sub> lambda </sub><sup>p/2 - 3/4</sup>, F2p=F-hat 2pR<sub> lambda </sub><sup>p/2 - 3/4</sup> and S2p + 1=S-hat 2p + 1R<sub> lambda </sub><sup>p/2 - 3/4</sup>, p=2,3,..., with explicit calculation of the numbers Omega-hat 2p, F-hat 2p, and S-hat 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)].
|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 velocity-derivative 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. DE-FG03-89ER 25073.|
|Subject Keywords:||TURBULENT FLOW; VELOCITY FIELDS; VORTICITY; VORTICES; HOMOGENEITY; ISOTROPY; CORRELATION FUNCTIONS; REYNOLDS NUMBER; NAVIER–STOKES EQUATIONS; STRUCTURE FUNCTIONS; ENERGY SPECTRA|
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|Deposited On:||25 May 2006|
|Last Modified:||26 Dec 2012 08:53|
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