ROMA (Rank-Ordered Multifractal Analysis) of Intermittency in Space Plasmas

Abstract:

The hallmark of nonlinear complexity phenomena in plasmas as well as in all natural sciences is the appearance of intermittent fluctuating events. Such intermittent fluctuations are the results of the dynamic interactions of multiple coherent structures of varied sizes in stochastic media. We discuss here a unique procedure, the Rank-Ordered Multifractal Analysis (ROMA), that is both physically explicable and quantitatively accurate in deciphering the multifractal characteristics of intermittency. The generic character of the procedure provides a natural connection between the implicit spectrum based on parametric rank ordering and the one-parameter scaling idea of monofractals. Such an implicit multifractal spectrum has several advantages over the results obtainable using the conventional structure functions. Firstly, the utility of the spectrum is to fully collapse the unscaled PDFs. Secondly, the physical interpretation is clear. It indicates how intermittent the scaled fluctuations are once the spectrum is given. Thirdly, the determination of the values of the fractal nature of the grouped fluctuations is not affected by the statistics of other fluctuations that do not exhibit the same fractal characteristics.

The method has been used to study results obtained from large-scale incompressible fluid simulations and large-scale MHD simulations as well as observations of the magnetic field fluctuations of the solar wind, the extreme ultraviolet emissions of the solar corona, and the broadband electric field fluctuations in the auroral zone. The method and some of these applications will be presented.