RNG Analysis of Turbulence Models (III)
Date Issued
2002-10-31
Date
2002-10-31
Author(s)
DOI
902212E002237
Abstract
In this study, we continue with a recursive renormalization
group (RG) analysis of incompressible turbulence, aiming
at investigating various turbulent properties of threedimensional
magneto-hydrodynamics (MHD). In particular,
we are able to locate the fixed point (i.e. the invariant effective
eddy viscosity) of the RG transformation under the
following conditions. (i) The mean magnetic induction is
relatively weak compared to the mean flow velocity. (ii)
The Alfv´en effect holds, that is, the fluctuating velocity and
magnetic induction are nearly parallel and are approximately
equal in magnitude. It is found under these conditions that
re-normalization does not incur an increment of the magnetic
resistivity, while the coupling effect tends to reduce the invariant
effective eddy viscosity. Both the velocity and magnetic
energy spectra are shown to follow the Kolmogorov k−5/3
in the inertial subrange; this is consistent with some laboratory
measurements and observations in astronomical physics.
By assuming further that the velocity and magnetic induction
share the same specified form of energy spectrum, we
are able to determine the dependence of the (magnetic) Kolmogorov
constant CK (CM) and the model constant CS of the
Smagorinsky model for large-eddy simulation on some characteristic
wavenumbers.
Subjects
Renormalization group analysis
magnetohydrodynamic
turbulence
turbulence
Alfv´en effect
effective eddy
viscosity
viscosity
magnetic resistivity
Publisher
臺北市：國立臺灣大學應用力學研究所
Type
report
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