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Axial motion and scalar transport in stretched spiral vortices

Pullin, D. I. and Lundgren, T. S. (2001) Axial motion and scalar transport in stretched spiral vortices. Physics of Fluids, 13 (9). pp. 2553-2563. ISSN 1070-6631. doi:10.1063/1.1388207.

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We consider the dynamics of axial velocity and of scalar transport in the stretched-spiral vortex model of turbulent fine scales. A large-time asymptotic solution to the scalar advection-diffusion equation, with an azimuthal swirling velocity field provided by the stretched spiral vortex, is used together with appropriate stretching transformations to determine the evolution of both the axial velocity and a passive scalar. This allows calculation of the shell-integrated three-dimensional spectra of these quantities for the spiral-vortex flow. The dominant term in the velocity (energy) spectrum contributed by the axial velocity is found to be produced by the stirring of the initial distribution of axial velocity by the axisymmetric component of the azimuthal velocity. This gives a k(-7/3) spectrum at large wave numbers, compared to the k(-5/3) component for the azimuthal velocity itself. The spectrum of a passive scalar being mixed by the vortex velocity field is the sum of two power laws. The first is a k(-1) Batchelor spectrum for wave numbers up to the inverse Batchelor scale. This is produced by the axisymmetric component of the axial vorticity but is independent of the detailed radial velocity profile. The second is a k(-5/3) Obukov-Corrsin spectrum for wave numbers less than the inverse Kolmogorov scale. This is generated by the nonaxisymmetric axial vorticity and depends on initial correlations between this vorticity and the initial scalar field. The one-dimensional scalar spectrum for the composite model is in satisfactory agreement with experimental measurement.

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Additional Information:Copyright © 2001 American Institute of Physics. Received 29 November 2000; accepted 10 May 2001. D.I.P. was supported in part by the National Science Foundation under Grant No. CTS-9978551.
Subject Keywords:vortices; turbulence
Issue or Number:9
Record Number:CaltechAUTHORS:PULpof01
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2086
Deposited By: Tony Diaz
Deposited On:07 Mar 2006
Last Modified:08 Nov 2021 19:45

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