Abstract:
Our purpose is twofold, to derive a 2-dimensional model of streambed erosion and to develop a solution procedure to solve the equations of our model. The flow domain, which varies in time, is bounded above by a free surface and is bounded below by an erodable streambed. An initial flow and streambed configuration are given and we would like to determine the streambed evolution. Our basic approach to modeling this process is to combine the interaction of a viscous flow with boundary constraints which represent an erodable streambed. Flow over a bed of sand causes the bed to undergo a distinct evolution. At slow flows, the bed remains flat. With increasing flow velocity, the bed passes through a set of stages: smooth, ripples, dunes, flat with chaotic flow, waves and finally antidunes. One of our main purposes is to obtain a model which has the potential of addressing this evolutionary process. We obtain a model which exhibits the general nature of streambed erosion. Specifically, we obtain classic dune migration. One indirect but significant result is that the vorticity of the flow near the streambed is shown to be a fundamental factor in the erosion process. Another indirect result is the wealth of open questions which have arisen as a result of this work.
