Probability distribution of turbulence in curvilinear cross section mobile bed channel

Abstract

The present study investigates the probability density functions (PDFs) of two-dimensional turbulent velocity fluctuations, Reynolds shear stress (RSS) and conditional RSSs in threshold channel obtained by using Gram–Charlier (GC) series. The GC series expansion has been used up to the moments of order four to include the skewness and kurtosis. Experiments were carried out in the curvilinear cross section sand bed channel at threshold condition with uniform sand size of d50 = 0.418 mm. The result concludes that the PDF distributions of turbulent velocity fluctuations and RSS calculated theoretically based on GC series expansion satisfied the PDFs obtained from the experimental data. The PDF distribution of conditional RSSs related to the ejections and sweeps are well represented by the GC series exponential distribution, except that a slight departure of inward and outward interactions is observed, which may be due to weaker events. This paper offers some new insights into the probabilistic mechanism of sediment transport, which can be helpful in sediment management and design of curvilinear cross section mobile bed channel.