Entrainment of coarse grains in turbulent flows: An extreme value theory approach

The occurrence of sufficiently energetic flow events characterized by impulses of varying magnitude is treated as a point process. It is hypothesized that the rare but extreme magnitude impulses are responsible for the removal of coarse grains from the bed matrix. This conjecture is investigated utilizing distributions from extreme value theory and a series of incipient motion experiments. The application of extreme value distributions is demonstrated for both the entire sets of impulses and the maxima above a sufficiently high impulse quantile. In particular, the Frechet distribution is associated with a power law relationship between the frequency of occurrence and magnitude of impulses. It provides a good fit to the flow impulses, having comparable performance to other distributions. Next, a more accurate modeling of the tail of the distribution of impulses is pursued, consistent with the observation that the majority of impulses above a critical value are directly linked to grain entrainments. The peaks over threshold method is implemented to extract conditional impulses in excess of a sufficiently high impulse level. The generalized Pareto distribution is fitted to the excess impulses, and parameters are estimated for various impulse thresholds and methods of estimation for all the experimental runs. Finally, the episodic character of individual grain mobilization is viewed as a survival process, interlinked to the extremal character of occurrence of impulses. The interarrival time of particle entrainment events is successfully modeled by the Weibull and exponential distributions, which belong to the family of extreme value distributions.