The decay form of the time correlation function $U_n\left(t\right)$ of a state variable $u_n\left(t\right)$ with a small wave number $k_n$ has been shown to take the algebraic decay $1/\left\{1+{\left({\gamma }_{na}t\right)}^2\right\}$ in the initial regime $t<{\tau }_n^{\left(\gamma \right)}$ and the exponential decay ${\alpha }_{ne}\text{exp}\left(-{\gamma }_{ne}t\right)$ in the final regime $t>{\tau }_n^{\left(\gamma \right)}$, where ${\tau }_n^{\left(\gamma \right)}$ denotes the decay time of the memory function ${\Gamma }_n\left(t\right)$. This dual structure of $U_n\left(t\right)$ 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 $U_n\left(t\right)$ obeys a hydrodynamic scaling law in the final regime $t>{\tau }_n^{\left(\gamma \right)}$ with scaling exponent $z=2$ and a dynamic scaling law in the initial regime $t<{\tau }_n^{\left(\gamma \right)}$ with scaling exponent $z=1$. If $k_n$ is increased so that the decay time ${\tau }_n^{\left(u\right)}$ of $U_n\left(t\right)$ becomes equal to the decay time ${\tau }_n^{\left(\gamma \right)}$, then the decay form of $U_n\left(t\right)$ becomes the power-law decay $t^{-3/2}$ in the final regime.

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