Modeling flow and pressure distribution by multilayer averaged equations

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A multilayer model is in fact the solution of layer averaged momentum equations (which are similar to depth averaged equations) in a number of layers. One of the advantages of a multi-layer system is that due to this similarity, a three-dimensional multilayer model can be developed from any two-dimensional depth-averaged program. To upgrade any depth-averaged model, additional terms should be added to the momentum equations to account for friction and mass transfer between the layers. The momentum equations can be solved in a similar manner for each layer. Following this step, the flow depth is updated and the iteration process continues until convergence is achieved. A few researchers have also applied the multilayer method in open channels with the same assumption of horizontal layers of constant thickness. This assumption causes some restriction in channel flows since the top layer must accommodate all of the water surface variation, it may become too thick and model accuracy is reduced in different locations. An additional complication occurs when the lower layers of flow intersect the bed topography and the imposing boundary conditions become very complicated.  The proposed model proposed herein incorporates the multilayer modeling and depth-averaged equations to become the multilayer depth averaged model with modifications in layer selection and turbulence model. The model differs from classical multilayer models and classical depth averaged models so that the proposed model will simulate not only the averaged velocities and flow depth but also predict the velocity and shear profiles over the depth. The model will be modified and expanded for simulations of hydraulic jump and flow in curved open channels. Modeling results will be compared with experimental data and numerical results by other three-dimensional hydrodynamatic models. These will verify whether the model has the capability to predict flows in complex three-dimensional flow conditions.