R/S method for unevenly sampled time series: Application to detecting long-term temporal dependence of droplets transiting through a fixed spatial point in gas–liquid two-phase turbulent jets

We perform rescaled range analysis upon the signals measured by a Dual Particle Dynamical Analyzer in gas–liquid two-phase turbulent jets. A novel rescaled range analysis is proposed to investigate these unevenly sampled signals. The Hurst exponents of velocity and other passive scalars in the bulk of spray are obtained to be 0.59 ± 0.02 and the fractal dimension is hence 1.41 ± 0.02, which is in remarkable agreement with and much more precise than previous results. These scaling exponents are found to be independent of the configuration and dimensions of the nozzle and the fluid flows. Therefore, such type of systems form a universality class with invariant scaling properties.