Toward a Reduced Complexity Channel Resolving Model for Sedimentary Delta Formation

Predicting styles of delta growth in restoration areas is a challenge as we try to restore impacted coastlines. Cellular and rule-based reduced complexity models offer a worthwhile means of uncovering key dynamics in delta morphodynamics without the need to fully solve the governing transport equations. In terms of modeling sedimentary delta building processes a critical ingredients is accounting for the formation and bifurcation of channels; phenomena that can be related to the formation of levees and mouth-bars. To that end, we have developed a reduced complexity model that uses a simplified shallow-water solver to study channel formation, mouth bar deposition, and delta development under different forcings. Under the assumption that the flow has a very low Froude Number (Fr2<<1), the inertia term is dropped out and only the gravitational term and friction term remain in the momentum equation. The coupled mass conservation equation becomes a non-linear diffusive equation, which is linearized by a Kirchhoff transformation. Directional diffusivity is added to this system to compensate the loss of inertia and promote spreading of the turbulent jet. We test the reduced model against flow over Gaussian-shaped bumps of various heights. Comparison of results from this model with results from a full scale commercial code (Delft3D) show a satisfactory agreement on the critical mouth bar height needed to divert flow around the bar. Based on the same diffusive equation, we develop a low-Froude water-routing method for reduced complexity morphodynamics models. The preliminary results show that the method is capable of producing reasonable channel forms and mouth bar formation, and provides a good starting point for development of a channel resolving delta building model.