Stochastic theory of turbulence and sediment transport and its application to 3D numerical modeling

Numerical simulation of turbulent flow and sediment transport processes in engineering problems, such as local scour at bridge piers, is challenging work. The difficulty comes from the fact that both turbulent flow and sediment transport are stochastic processes that no formulas can describe thus far.;In this dissertation, a nonlinear stochastic turbulence closure model coupled with the kappa -- epsilon model is developed based on characteristics of a turbulent vortex and mathematical analysis. Other models of turbulent closure are outlined as special cases of this model for the purpose of comparison. Based on the stochastic behavior of sediment transport, a general equation of suspended sediment transport and a general equation of bed load transport are derived. Eight experimental cases of suspended sediment transport are simulated numerically by using the general suspended sediment transport equation. Very good agreement is obtained and the advantage of the general diffusion equation is proven. These two equations can help explain other research results on these two topics. The stochastic formula is developed, taking into account the influence of vortices, secondary motion and turbulent intensity for predicting sediment transport in the local scour of bridge piers both for bed load and suspended load. The special numerical schemes for general bed load and suspended sediment transport equations are derived. All of those considerations have been included in the 3D numerical model, RIVER3D, developed by this author.;To verify the nonlinear stochastic Reynolds-Stress model, the 2D uniform open channel flow case and the backward-facing step case are simulated numerically and compared with the measured data. For the application purpose of both the nonlinear stochastic Reynolds-Stress model and the stochastic theory of sediment transport, an experimental case of local scour around a cylindrical bridge pier is simulated. The comparison between the numerical and the experimental results shows that the stochastic theory of turbulence, the stochastic theory of sediment transport, the general suspended sediment diffusion equation, the numerical discretization schemes for high-order derivatives of the Reynolds-Stresses, and the up-winding scheme for bed load transport, are all successful.;Furthermore, the methodology of numerical modeling of particle saltation dynamics is derived. Five authors' experimental cases are simulated and compared with measured data. The hypothesis, that it produces reliable results to treat some parameters in dynamic equations of particle saltation as random variables, was proven by the testing. The numerical model was shown to be useful in simulating the particle behavior as saltation.