2‐D Bed Evolution in Natural Watercourses—New Simulation Approach

Abstract

A new mathematical formulation is established for two‐dimensional (plan view) unsteady water flow, sediment transport, and bed evolution in natural watercourses such as reservoirs, estuaries, and coastal waters, where depth averaging is appropriate. Sediment mixtures in natural watercourses are represented through a suitable, and unlimited, number of discrete size classes, any of which may be subject to either suspended‐load or bedload transport (or both) depending on prevailing local hydraulic conditions. Governing equations for water and sediment are transformed (completely) into curvilinear coordinates and then depth‐averaged, when appropriate. The system of governing sediment equations at a computational point is solved in a new implicit, finite‐difference, fully coupled manner. Furthermore, the sediment equations are coupled with the water flow in an iterative manner in order to account for the feedback between the flow field and changes in both bed elevation and bed‐surface size distribution. The mathematical formulation and associated numerical solution, incorporated into the new MOBED2 computational code, are tested through simulation of mobile‐bed dynamics in the Cor‐alville Reservoir on the Iowa River, Iowa. Initial proof‐of‐concept tests confirm the feasibility of the new approach by reproducing the proper qualitative behavior of the overall modeling concept.