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On velocity structure functions and the spherical vortex model for isotropic turbulence

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. 2019-2029. ISSN 1070-6631. doi:10.1063/1.1367870.

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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 even-order 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 log-normal distribution of vortex radii. We calculate the statistical properties of the model, in particular order-n velocity structure functions defined by rank-n 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.

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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.
Subject Keywords:turbulence; vortices; stochastic processes
Issue or Number:7
Record Number:CaltechAUTHORS:AIVpof01
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1988
Deposited By: Archive Administrator
Deposited On:28 Feb 2006
Last Modified:08 Nov 2021 19:44

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