Mourad Bellal's PhD Thesis

Usually, a fluvial regime prevails in alluvial rivers. The most drastic alterations in river morphology happen during floods and are thus associated with fast changes in discharge and water level, as well as intense erosion and deposition that may disrupt the river topography. Regime discontinuities may appear, such as hydraulic jumps and control sections, leading to transcritical flow.
The present dissertation aims at modeling the morphodynamics of super- and transcritical flows using two complementary approaches: laboratory experiments and novel analytical solutions. Three series of experiments were conducted: (i) aggradation and degradation in supercritical flow under sediment overloading and underloading conditions, (ii) formation of a hydraulic jump over mobile bed and (iii) evolution of a critical section into a migrating knickpoint.
Mathematical modeling of these phenomena was achieved using a linear diffusion equation that can be obtained considering that the flow is everywhere close to the steady uniform regime defined by the local bed gradient. Based on the linear diffusion model, the analytical solution for channels of finite length and fixed boundary conditions matching aggradation and degradation problems is well-known to admit general solutions, typically constructed using Fourier series. For moving boundary problems corresponding to transcritical flows, the problem is non-linear and the mathematical solution becomes more complex. This is the case for the prograding sediment front where the moving boundary travels in the downstream direction, and for the case of the erosive knickpoint front where the boundary travels in the upstream direction, To address these problems, exact self-similar solutions have been derived by exploiting the symmetries of the diffusion equation. The results of the developed analytical approaches have been satisfactory compared to the experiments.

Jury:
Professeur Yves ZECH (UCL), Promoteur
Professeur Jean-François REMACLE (UCL), Président
Professeur Sandra SOARES-FRAZAO (UCL), Secrétaire
Professeur Jean BERLAMONT (KUL)
Professeur Jean-Michel HIVER (ULB)