Stochastic Modeling of Bedload Transport and Bar Development in Shallow Flow: Linear Stability Analysis and Numerical Simulation

Field surveys and laboratory experiments show that bedload transport rates may vary to within one order of magnitude for a given water discharge. One of today's major challenges is to account for these large transport rate fluctuations in computational hydraulics models. To that end, we developed a two-dimensional stochastic bedload model computing the random time variations in particle activity (i.e., the number of moving particles per streambed area). This model differs from most current bedload transport model, in which mean bedload transport rates are related to flow rate deterministically. The stochastic model was coupled to the two-dimensional Saint-Venant--Exner equations. The one-dimensional version of this model was successfully tested by Bohorquez and Ancey [1]. In this study, we focused on the development of two-dimensional bedforms under varied flow conditions. We conducted linear stability analysis to determine the flow conditions for which these bedforms develop, and then compare the resulting criteria with experimental evidence. We implemented a numerical algorithm based on the finite-volume method [2]. We used it to study gravel bar development in a long flume under steady state conditions, and compared the numerical simulations with experimental data [3]. The bed surface was initially flat at t=0, and one small perturbation was imposed. Figure 1 shows an example of alternate bars simulated by our code. The numerical simulations captured the stages of bar formation, from inception and migration, consistently with experimental data. [1] Bohorquez, P. and Ancey, C., 2015. Stochastic-deterministic modeling of bed load transport in shallow water flow over erodible slope: Linear stability analysis and numerical simulation. Advances in water resources, 83, pp.36-54. [2] LeVeque, R.J., 2011. A well-balanced path-integral f-wave method for hyperbolic problems with source terms. Journal of scientific computing, 48, pp.209-226. [3] Dhont, B.E.M., 2017. Sediment pulses in a gravel-bed flume with alternate bars (No. THESIS). EPFL.