Study of the influence of Bottom Boundary Layer (BBL) and Suspended Sediment Transport (SST) for the computation of the evolution of natural sand bars

The present thesis, studies, based on numerical simulations, the nearshore hydro-morphodynamics as forced by waves and currents. To do this, some modifications are implemented to the robust finite-volume model of Brocchini et al. [1]. The model contains two distinct parts: (1) a hydrodynamic solver, which employs a space-splitting approach for the integration of Nonlinear Shallow Water Equations (NSWEs) over a horizontally two-dimensional domain; and (2) a morphodynamic solver that updates the bed profile via the resolution of the Exner equation. In this study, special care is put in the modeling of the well-balancing of the available NSWE solver; the influence of the Bottom Boundary Layer (BBL) on both hydrodynamic and morphodynamics parts of the solver; and on Suspended Sediment Transport (SST) for the evaluation of the morphological evolution of the seabed. The final aim being that of applying the resulting, improved model to assess the evolution of natural sand bars. To well-balance the solver, a two-step predictor-corrector procedure is exploited in which the predictor step provides the initial solution of the Riemann Problem while the corrector step solves the nonlinear system of equations employing an iterative procedure starting from the predictor step solution. The BBL concept is implemented into the solver by coupling the NSWE with the momentum integral equation for the BBL. By introducing a dimensionless parameter, the momentum equation, which is integrated across the boundary layer thickness for the boundary layer flow, becomes an ordinary differential equation. The equation is solved based on the Runge-Kutta fourth-order scheme and the result is the bed shear stress (or consequently friction velocity and Chézy coefficient). We exploited the time and spatial varying Chézy coefficient to update the hydrodynamic components (total water depths and velocities) of the solver. The morphodynamic module of the solver updates the bed profile based on the solution of the depth-averaged Exner equation. In the solver, the Exner equation is discretized and integrated based on the finite-volume approach with the application of the Weighted Averaged Flux (WAF) method. Accordingly, the bed profile is updated using the averaged total sediment intercell fluxes, bedload, and suspended load sediment fluxes. Since the accuracy of the available SST closure formulae exploited in the NSWE solver is under debate, the calculation of the SST flux is done by solving the advection-diffusion equation for the suspended sediment concentration. Accordingly, efficient formulations of the BBL and SST are presented. The performance of the proposed solver is validated against two sets of benchmark data including (1) exact solutions and experimental studies, and (2) field observations. In the first phase, we considered several bathymetries with a bed step and compared the exact solutions with the numerical results obtained using the modified solver. To do this, the theoretical and numerical campaign performed by Rosatti and Begnudelli (2010) is exploited. Then, the experimental studies by Kikkert et al. (2012), Briganti et al. (2011), and O'Donoghue et al. (2010) are exploited to evaluate the performance of the modified solver. The focus of these validations is on the role of the BBL, which significantly influences the hydrodynamic components across the entire nearshore. In the second phase, the morphological evolution of an Italian sandy beach in Senigallia (Senigallia Estuary) is reproduced. The beach evolution before and after February 28, 2016, Scirocco storm (ESE) lasted for 18 hours, is investigated using the numerical results of the enhanced solvers. The sand bar migration and shoreline position resulting from the numerical simulations are compared with those of video imagery data sets presented by Melito et al. [2]. Such a validation revealed that the enhanced models significantly outperform the original model in terms of seabed evolution, sandbar migration, and shoreline position. This improvement is both qualitative and quantitative. The original model fails to well capture the movement of the bars at the left lateral boundary of the numerical domain while the enhanced models especially the model enhanced with both BBL and SST solvers make a fairly good prediction of the bar migration pattern. All in all, the numerical results revealed that the enhanced models accurately predict the flow parameters and the bed evolution, and sand bar migration. Further, the inclusion of the BBL physics enables the model to calculate the friction factor close to reality and consequently, the sediment fluxes and flow hydrodynamics can be simulated with high accuracy. Calculating the suspended sediment flux based on the numerical solution of the depth-averaged advection-diffusion equation makes the seabed profile predictions more reliable. For future investigations, it is recommended that the bedload sediment flux, which is of great importance in updating the bed profile, is determined by some robust approaches. Further, the Exner equation may contain the pickup and deposition terms as suggested by some researchers. The enhanced models can be implemented to reproduce the bed profile at the toe of some coastal structures such as breakwaters and seawalls under the action of standing or breaking waves. The model performance can be improved to predict the hydro-morphodynamics of porous and permeable beaches.