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Author(s):
S. Goto and S. Kida
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Title:
Sparseness of Nonlinear Coupling
Date of publication:
Dec. 1999
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Key words:
Nonlinear dynamical system, direct-interaction approximation,turbulence, Gaussianity
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Abstract:
It is not weakness of nonlinearity but sparseness of nonlinear couplings that plays a key role in the direct-interaction approximation (DIA), which is an excellent moment closure theory for nonlinear dynamical systems.Homogeneous Navier-Stokes turbulence is an example of dynamical systems in which nonlinearity is strong in magnitude but sparse in coupling. In order to clarify the importance of sparseness of coupling,we formulate DIA for a model equation which has three parameters:coupling density, strength of nonlinearity and the number of degrees of freedom. By the help of numerical simulations, it is shown that DIA is applicable when the coupling density is much smaller than the square root of the number of degrees of freedom, even if the strength of nonlinearity is infinitely large. This implies that the applicability of DIA has nothing to do with the Gaussianity of a dynamical variable, although DIA is often explained as a theory based on it.
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