Multi-level segment analysis: definition and application in turbulent systems

Abstract

For many complex systems the interaction of different scales is among the most interesting and challenging features. It seems not very successful to extract the physical properties in different scale regimes by the existing approaches, such as the structure-function and Fourier spectrum method. Fundamentally, these methods have their respective limitations, for instance scale mixing, i.e. the so-called infrared and ultraviolet effects. To make improvements in this regard, a new method, multi-level segment analysis (MSA) based on the local extrema statistics, has been developed. Benchmark (fractional Brownian motion) verifications and the important case tests (Lagrangian and two-dimensional turbulence) show that MSA can successfully reveal different scaling regimes which have remained quite controversial in turbulence research. In general the MSA method proposed here can be applied to different dynamic systems in which the concepts of multiscale and multifractality are relevant.