Generalized Batchelor functions of isotropic turbulence
Date Issued
January 11, 2015
Author(s)
DOI
10.1063/1.4905326
Abstract
We generalize Batchelor's parameterization of the autocorrelation functions
of isotropic turbulence in a form involving a product expansion with multiple
small scales. The richer small scale structure acquired this way, compared to
the usual Batchelor function, is necessary so that the associated energy
spectrum approximate well actual spectra in the universal equilibrium range. We
propose that the generalized function provides an approximation of arbitrary
accuracy for actual spectra of isotropic turbulence over the universal
equilibrium range. The degree of accuracy depends on the number of higher
moments which are determinable and it is reflected in the number of small
scales involved. The energy spectrum of the generalized function is derived,
and for the case of two small scales is compared with data from high-resolution
direct numerical simulations. We show that the compensated spectra (which
illustrate the bottleneck effect) and dissipation spectra are encapsulated
excellently, in accordance with our proposal.
of isotropic turbulence in a form involving a product expansion with multiple
small scales. The richer small scale structure acquired this way, compared to
the usual Batchelor function, is necessary so that the associated energy
spectrum approximate well actual spectra in the universal equilibrium range. We
propose that the generalized function provides an approximation of arbitrary
accuracy for actual spectra of isotropic turbulence over the universal
equilibrium range. The degree of accuracy depends on the number of higher
moments which are determinable and it is reflected in the number of small
scales involved. The energy spectrum of the generalized function is derived,
and for the case of two small scales is compared with data from high-resolution
direct numerical simulations. We show that the compensated spectra (which
illustrate the bottleneck effect) and dissipation spectra are encapsulated
excellently, in accordance with our proposal.
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