Two-Dimensional mathematical model for flow computation (flow simulation) in sine-generated river bends

Rivers are a dynamic and increasingly important part of our physical environment. Their behavior is of interest in a wide variety of contexts, ranging from disaster prevention, such as by flood control, to water resources development for navigation and recreation. For these reasons, studies of river flow and morphology are urgently needed. One of the parts of rivers is bends that calls Meander. The flow pattern in river bends is known to be fairly complex due to presence of strong secondary flow or spiral (helical) flow, in a direction perpendicular to the longitudinal direction of flow. Secondary flow is due mainly to 1-difference between velocities near the center of the channel and near the walls due to friction on the channel walls, 2- centrifugal force, which deflects the particles of water from a rectilinear, or straight-line motion, and 3- a vertical velocity distribution which exists in the approach channel and thus initiates a spiral motion in the flow. In this research a two dimensional mathematical model for a meandering river is developed in a curvilinear co-ordinate system. Grid mapping for the computational domain of the entire area is developed based on sine-generated curve plan-form. The model is based on the integration of depth-averaged main flow equations including the convective influence of secondary flow. In this model we suppose that the depth is small compared with the width, the width is constant and its small compared with the radius of curvature, Froude number is small, the flow is mainly friction controlled and the longitudinal component of the velocity dominates the other velocity components. The model is developed, tested and verified with flume experiments. The results show that there are good agreements between flow distributions that simulated by the numerical model and the experimental results.