1/f Noise and Turbulence from a Self-Similar Decay of Fluctuation

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Abstract
On the basis of a self-similarity assumption for the decay of fluctuations we examine the 1/f noise spectrum and the turbulent spectra in a fluid. A cascade process with frictionless motion and frictional motion is renormalized. This renormalization provides us with an average kinetic coefficient, which is given by the geometric mean of associated kinetic coefficients. This is because the fluctuation obeys a log-normal distribution on the cadcade process. For a turbulent state we arrive at Kolmogorov’s dimensional assumption for the energy spectrum in a general case. The 1/f noise is found where the system is not far from equilibrium state.