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The decay form of the time correlation function U_n(t) of a state variable un(t) with a small wave number k_n has been shown to take the algebraic decay 1/{1+(gamma_{na}t)^2} in the initial regime t<t...au^(gamma)_n and the exponential decay alpha_{ne} exp(-gamma_{ne}t) in the final regime t>tau^(gamma)_n, where tau^(gamma)_n denotes the decay time of the memory function Gamma_n(t). This dual structure of U_n(t) is generated by the deterministic short orbits in the initial regime and the stochastic long orbits in the final regime, thus giving the outstanding features of chaos and turbulence. The k_n dependence of gamma_{na}, alpha_{ne}, and gamma_{ne} is obtained for the chaotic Kuramoto-Sivashinsky equation, and it is shown that if k_n is sufficiently small, then the dual structure of U_n(t) obeys a hydrodynamic scaling law in the final regime t>tau^(gamma)_n with scaling exponent z=2 and a dynamic scaling law in the initial regime t<tau^(gamma)_n with scaling exponent z=1. If k_n is increased so that the decay time tau^(u)_n of U_n(t) becomes equal to the decay time tau^(gamma)_n, then the decay form of U_n(t) becomes the power-law decay t^{-3/2} in the final regime.続きを見る
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Mendeley出力
PhysRevE.80.051124