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Author(s):
S. Goto and S. Kida
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Title:
Direct-interaction Approximation and Reynolds-number Reversed Expansion for a Dynamical System
Date of publication:
July 1997
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Key words:
Direct-interaction approximation, Dynamical system, Turbulence
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Abstract:
The condition of validity of the direct-interaction approximation and the Reynolds-number reversed expansion truncated at the lowest nontrivial order is assessed numerically for a dynamical system composed of coupled equations of many variables with quadratic-nonlinear terms of weak or strong coupling as well as linear-viscous and randomly forcing terms. Although these two theories lead to an identical set of integro differential equations for the correlation function of the dependent variables and the response function, their parameter regions of validity are different from each other. The direct-interaction approximation works well for larger number of degrees of freedom if the nonlinear couplings are as weak as the Navier-Stokes equation, but not when the nonlinear coupling is strong. The Reynolds-number reversed expansion, on the other hand, works well whenever the nonlinear term is smaller in magnitude than the other terms irrespective of the strength of the nonlinear coupling
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