Statistical-Physical Approach to Chaos and Turbulence (50 Years of the Linear Response Theory――Toward Nonlinear and Nonequilibrium Physics)

Abstract

The decay form of the time correlation function U_n(t)≡<u_n(t)u^*_n(0)> of the mode u_n(t) with a small wavenumber k_n is explored for the chaotic Kuramoto-Sivashinsky equation, and is shown to be the algebraic decay 1/[1+(γ_<na>t)^2] in the initial regime and the exponential decay exp(-γ_<ne>t) in the final regime. In this article, such dual structures of chaos and turbulence, and their dynamic scaling laws are formulated in terms of the projection operator method.