Layer Integrated Modeling of Three-Dimensional Recirculating Flows in Model Tidal Basins

Details are given of a numerical model study to refine a layer integrated model, applied to scaled hydraulic model rectangular tidal basins with large aspect ratios (i.e., $L∕B=1∕4–4∕1$ ), and using two- and zero-equation turbulence models. For the zero-equation turbulence model the mixing length model was deployed to calculate the horizontal eddy viscosity coefficient, whereas for the two-equation model, the depth integrated $k\text{-}\epsilon$ turbulence model was used. Likewise, the layer integrated mixing length and $k\text{-}\epsilon$ turbulence models were used to determine the vertical eddy viscosity coefficient. The model was first applied to idealized channel flows, with the agreement between the predicted values and experimental data being satisfactory. The model was then tested by applying it to an idealized set of data for wind driven currents in a closed rectangular basin, with good agreement again being obtained between the numerical model results and published experimental data. The model was finally applied to a set of hydraulic model studies, undertaken by the writers for a number of different model rectangular tidal basin configurations (or aspect ratios), each with an asymmetric entrance, a flat bed, and vertical sidewalls. The numerical model results obtained using the $k\text{-}\epsilon$ and mixing length turbulence models in the horizontal plane were compared graphically with the experimental results to indicate the best model setup for these model basin configurations. Model simulations were also undertaken to investigate the sensitivity of the eddy circulation structure to the closed boundary representation, within the finite difference scheme, and three different boundary conditions were considered including: the no-slip, semislip, and partial-slip representations. The numerical model results showed that the horizontal current structure obtained using the $k\text{-}\epsilon$ model was similar to the results obtained using the mixing length turbulence model. The velocity distributions for the different layers were similar, except near the bed, and the horizontal velocity distribution only showed small variations through much of the water column. The three different representations of the closed boundary condition gave very different tidal circulation patterns within the basins, showing that the representation of the closed boundary was crucial for modeling vorticity in such basins. The model results for the $k\text{-}\epsilon$ and mixing length turbulence models were found to be in closest agreement with the experimental results when the no-slip and partial-slip conditions were used, respectively.