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The Wiener-Hermite expansion applied to decaying isotropic turbulence using a renormalized time-dependent base

Published online by Cambridge University Press:  12 April 2006

H. D. Hogge  and
W. C. Meecham
H. D. Hogge
Affiliation:
School of Engineering and Applied Science, University of California, Los Angeles Present address: Poseidon Research, 11777 San Vicente Boulevard, Los Angeles, California 90049.
W. C. Meecham
Affiliation:
School of Engineering and Applied Science, University of California, Los Angeles
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Abstract

The problem of decaying isotropic turbulence has been studied using a Wiener-Hermite expansion with a renormalized time-dependent base. The theory is largely deductive and uses no modelling approximations. It has been found that many properties of large Reynolds number turbulence can be calculated (at least for moderate time) using the moving-base expansion alone. Such properties found are the spectrum shape in the dissipation range, the Kolmogorov constant, and the energy cascade in the inertial subrange. Furthermore, by using a renormalization scheme, it is possible to extend the calculation to larger times and to initial conditions significantly different from the equilibrium form. If the initial spectrum is the Kolmogorov spectrum perturbed with a spike or dip in the inertial subrange, the process proceeds to eliminate the perturbation and relax to the preferred spectrum shape. The turbulence decays with the proper dissipation rate and several other properties are found to agree with measured data. The theory is also used to calculate the energy transfer and the flatness factor of turbulence.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 85 , Issue 2 , 21 March 1978 , pp. 325 - 347
Copyright
© 1978 Cambridge University Press

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