Dual structures of chaos and turbulence, and their dynamic scaling laws.

The decay form of the time correlation function U-n(t) of a state variable u(n)(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 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 更多