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A small-scale turbulence modelA previously derived analytical model for the small-scale structure of turbulence is reformulated in such a way that the energy spectrum may be computed. The model is an ensemble of two-dimensional (2D) vortices with internal spiral structure, each stretched by an axially symmetric strain flow. Stretching and differential rotation produce an energy cascade to smaller scales in which the stretching represents the effect of instabilities and the spiral structure is the source of dissipation at the end of the cascade. The energy spectrum of the resulting flow may be expressed as a time integration involving only the enstrophy spectrum of the time evolving 2D cross section flow, which may be obtained numerically. Examples are given in which a k exp -5/3 spectrum is obtained by this method. The k exp -5/3 inertial range spectrum is shown to be related to the existence of a self-similar enstrophy preserving range in the 2D enstrophy spectrum. The results are found to be insensitive to time dependence of the strain rate, including even intermittent on-or-off strains.
Document ID
19930059635
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Lundgren, T. S.
(Minnesota Univ. Minneapolis, United States)
Date Acquired
August 16, 2013
Publication Date
June 1, 1993
Publication Information
Publication: Physics of Fluids A
Volume: 5
Issue: 6
ISSN: 0899-8213
Subject Category
Fluid Mechanics And Heat Transfer
Accession Number
93A43632
Distribution Limits
Public
Copyright
Other

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