Probability distribution functions of turbulence using multiple criteria over non-uniform sand bed channel

Abstract

Experimental investigation on fluvial hydraulics needs a correct and accurate estimation of probability distribution function (PDFs) which governs probability distribution of mobile bed sediments in seepage affected alluvial channels typically characterized by the various turbulent parameters. Laboratory experiments were conducted over non-uniform sand bed channel with and without downward seepage. The experimental calculation of PDFs of turbulent parameters such as Reynolds shear stress (RSS) and velocity fluctuations is compared with theoretical expression obtained by Gram–Charlier (GC)-based exponential distribution and GC-based Hermite polynomial. Experimental observations follow the computed PDFs distributions for both no seepage and seepage cases except the point of discontinuity is observed in the joint PDFs of velocity fluctuation obtained by GC series exponential distribution. The PDFs of RSS based on GC series exponential distribution is achieved the higher degree of divergence. Overall, the PDFs calculated by GC series-based Hermite polynomial is well fitted with the experimental data. The purpose of PDFs estimation from experimental data is that it provides a complete numerical description for turbulent flow simulation.