Aivazis, Keri A. and Pullin, D. I. (2001) On velocity structure functions and the spherical vortex model for isotropic turbulence. Physics of Fluids, 13 (7). pp. 20192029. ISSN 10706631. http://resolver.caltech.edu/CaltechAUTHORS:AIVpof01

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Abstract
We investigate a stochastic model for homogeneous, isotropic turbulence based on Hill's spherical vortex. This is an extension of the method of Synge and Lin [Trans. R. Soc. Can. 37, 45 (1943)], to the calculation of higher evenorder velocity structure functions. Isotropic turbulence is represented by a homogeneous distribution of eddies, each modeled by a spherical vortex. The cascade process of eddy breakdown is incorporated into the statistical model through an average over an assumed lognormal distribution of vortex radii. We calculate the statistical properties of the model, in particular ordern velocity structure functions defined by rankn tensors for the ensemble average of a set of incremental differences in velocity components. We define Di[centered ellipsis]s = <(ui(x + xi )–ui(x))[centered ellipsis](us(x + xi )–us(x))>, where <[centered ellipsis]> denotes the ensemble average. Specifically Dij, Dijkl, and the longitudinal component of Dijklmn are calculated directly from the spherical vortex ensemble. Matching the longitudinal components of Dij and Dijkl with experimental results fixes two independent model parameters. The lateral and mixed components of Dijkl and the longitudinal component of Dijklmn are then model predictions.
Item Type:  Article 

Additional Information:  ©2001 American Institute of Physics. (Received 30 November 2000; accepted 6 March 2001) The authors acknowledge many useful discussions with Philip Saffman. We also thank Patrick Tabeling for supplying detailed measurements of longitudinal velocity structure functions. 
Group:  GALCIT 
Subject Keywords:  turbulence; vortices; stochastic processes 
Record Number:  CaltechAUTHORS:AIVpof01 
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:AIVpof01 
Alternative URL:  http://dx.doi.org/10.1063/1.1367870 
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  1988 
Collection:  CaltechAUTHORS 
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Deposited On:  28 Feb 2006 
Last Modified:  21 Sep 2016 22:36 
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