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Calculation of velocity structure functions for vortex models of isotropic turbulence

Saffman, P. G. and Pullin, D. I. (1996) Calculation of velocity structure functions for vortex models of isotropic turbulence. Physics of Fluids, 8 (11). pp. 3072-3084. ISSN 1070-6631. doi:10.1063/1.869081.

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Velocity structure functions (u'p–up)m are calculated for vortex models of isotropic turbulence. An integral operator is introduced which defines an isotropic two-point field from a volume-orientation average for a specific solution of the Navier–Stokes equations. Applying this to positive integer powers of the longitudinal velocity difference then gives explicit formulas for (u'p–up)m as a function of order m and of the scalar separation r. Special forms of the operator are then obtained for rectilinear stretched vortex models of the Townsend–Lundgren type. Numerical results are given for the Burgers vortex and also for a realization of the Lundgren-strained spiral vortex, and comparison with experimental measurement is made. In an Appendix, we calculate values of the velocity-derivative moments for the Townsend–Burgers model.

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Additional Information:©1996 American Institute of Physics. Received 1 March 1996; accepted 16 July 1996. The authors wish to thank Patrick Tabeling for supplying unpublished measurements of longitudinal velocity structure functions. D.I.P. was partially supported by NSF Grant No. CTS-9311811 and P.G.S. was partially supported by the Department of Energy under Grant No. DE-FG03-89ER25073. We thank Dan Meiron and Donal Gallagher for helping with the asymptotic expansion of (34) for large r.
Subject Keywords:SPIRAL VORTEX
Issue or Number:11
Record Number:CaltechAUTHORS:SAFpof96
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9609
Deposited By: Tony Diaz
Deposited On:18 Feb 2008
Last Modified:08 Nov 2021 21:00

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