Modified stochastic diffusion particle tracking model driven by skew Brownian motion: Analysis of sediment particle motion in turbulent flow under the effects of ejection and sweep.

Turbulent bursting events have been classified into outward interactions (Q1), ejections (Q2), inward interactions (Q3), and sweeps (Q4) in various studies. Ejections (Q2) and sweeps (Q4) have been identified as significant contributors to time consumption, momentum flux, and sediment flux. Additionally, research has shown that the distribution of these events varies nonuniformly at different bed elevations. Despite extensive investigations into the nonuniform distribution of turbulent bursting events, their impact on sediment transport has been rarely explored. In this work, we developed a modified stochastic diffusion particle tracking model (SD-PTM) driven by skew Brownian motion (SBM) using the stochastic Lagrangian approach to scrutinize sediment particle movement in turbulent flows. The model incorporates turbulent characteristics derived from a direct numerical simulation dataset, allowing for a comprehensive analysis of sediment particle dynamics. Moreover, the proposed model accounts for the nonuniform spatial distribution of ejection and sweep events, as well as the particle movement direction during these events. Numerical simulations of the model were conducted to trace sediment particle trajectories in the streamwise and vertical directions. The analysis of sediment transport involved calculating the variance of particle trajectories to examine anomalous diffusion. The model's performance was evaluated by comparing it with flow velocity and sediment concentration profiles obtained from measurements in previous studies. In conclusion, our study suggests that the motion of sediment particles in turbulent flow can be thoroughly investigated under extreme flow conditions using the modified SD-PTM driven by SBM.

Semi-analytical modeling of sediment-laden open-channel flows with the effects of stratification, hindered settling, and eddy viscosities.

This study proposes semi-analytical models for simultaneous distribution of fluid velocity and suspended sediment concentration in an open-channel turbulent flow using three kinds of eddy viscosities. Apart from the classical parabolic eddy viscosity which is based on a log-law velocity profile, we consider two recently proposed eddy viscosities based on the concept of velocity and length scales. To deal with the flows with high sediment concentration, several turbulent features such as the hindered settling mechanism and the stratification effect are incorporated in the model. The governing system of highly nonlinear differential equations is solved using the homotopy analysis method (HAM), which produces solutions in the form of convergent series. Numerical and theoretical convergence analyses are provided for all three types of eddy viscosities. The effects of parameters on the derived models are discussed physically. Experimental data on both dilute and non-dilute flows are considered to verify the HAM-based solutions. The effects of the stratification correction factor (ß) and the turbulent Schmidt number (α) reveal that they should be determined optimally for applicability of the proposed models in terms of accurate prediction with data. This optimal procedure required further investigation of these parameters, and, thus, an analysis of ß and α is carried out, which linked them with the particle diameter through particle settling velocity, reference fluid velocity, and reference sediment concentration by proposing regression equations. Furthermore, using the optimal values of the parameters, the proposed models corresponding to the eddy viscosities based on the exponentially decreasing turbulent kinetic energy function and von Karman's similarity hypothesis are seen to be superior to the model corresponding to a parabolic eddy viscosity. Finally, a comment on the HAM is made where it is observed that the method can remove the numerical singularity of the governing equations at the water surface, which arises because of the consideration of vanishing eddy viscosity thereat.

Streamwise velocity profile in open-channel flow based on Tsallis relative entropy.

The present study derives the two-dimensional distribution of streamwise flow velocity in open channels using the Tsallis relative entropy, where the probability density function (PDF) based on the principle of maximum entropy (POME) is selected as the prior PDF. Here, we incorporate the moment constraints based on the normalization constraint, hydrodynamic transport of mass, and momentum through a cross section of an open channel for the formulation of the velocity profile. The minimization of the Tsallis relative entropy produces a nonlinear differential equation for velocity, which is solved using a non-perturbation approach along with the Padé approximation technique. We define two new parameters in terms of the Lagrange multipliers and the entropy index for assessing the velocity profile, which are calculated by solving a system of nonlinear equations using an optimization method. For different test cases of the flow in open channels, we consider a selected set of laboratory and river data for validating the proposed model. Besides, a comparison is made between the present model and the existing equation based on the Tsallis entropy. The study concludes that the inclusion of the POME-based prior significantly improves the velocity profile. Overall, the proposed work shows the potential of the Tsallis relative entropy in the context of application to open the channel flow velocity.