Two-dimensional hydrodynamic and transport models were applied to a 34-mile reach of the Ohio River from Cincinnati, Ohio, upstream to Meldahl Dam near Neville, Ohio. The hydrodynamic model was based on the generalized finite-element hydrodynamic code RMA2 to simulate depth-averaged velocities and flow depths. The generalized water-quality transport code RMA4 was applied to simulate the transport of vertically mixed, water-soluble constituents that have a density similar to that of water. Boundary conditions for hydrodynamic simulations included water levels at the U.S. Geological Survey water-level gaging station near Cincinnati, Ohio, and flow estimates based on a gate rating at Meldahl Dam. Flows estimated on the basis of the gate rating were adjusted with limited flow-measurement data to more nearly reflect current conditions. An initial calibration of the hydrodynamic model was based on data from acoustic Doppler current profiler surveys and water-level information. These data provided flows, horizontal water velocities, water levels, and flow depths needed to estimate hydrodynamic parameters related to channel resistance to flow and eddy viscosity. Similarly, dye concentration measurements from two dye-injection sites on each side of the river were used to develop initial estimates of transport parameters describing mixing and dye-decay characteristics needed for the transport model.

A nonlinear regression-based approach was used to estimate parameters in the hydrodynamic and transport models. Parameters describing channel resistance to flow (Manning’s “n”) were estimated in areas of deep and shallow flows as 0.0234, and 0.0275, respectively. The estimated RMA2 Peclet number, which is used to dynamically compute eddy-viscosity coefficients, was 38.3, which is in the range of 15 to 40 that is typically considered appropriate. Resulting hydrodynamic simulations explained 98.8 percent of the variability in depth-averaged flows, 90.0 percent of the variability in water levels, 93.5 percent of the variability in flow depths, and 92.5 percent of the variability in velocities.

Estimates of the water-quality-transport-model parameters describing turbulent mixing characteristics converged to different values for the two dye-injection reaches. For the Big Indian Creek dye-injection study, an RMA4 Peclet number of 37.2 was estimated, which was within the recommended range of 15 to 40, and similar to the RMA2 Peclet number. The estimated dye-decay coefficient was 0.323. Simulated dye concentrations explained 90.2 percent of the variations in measured dye concentrations for the Big Indian Creek injection study. For the dye-injection reach starting downstream from Twelvemile Creek, however, an RMA4 Peclet number of 173 was estimated, which is far outside the recommended range. Simulated dye concentrations were similar to measured concentration distributions at the first four transects downstream from the dye-injection site that were considered vertically mixed. Farther downstream, however, simulated concentrations did not match the attenuation of maximum concentrations or cross-channel transport of dye that were measured. The difficulty of determining a consistent RMA4 Peclet was related to the two-dimension model assumption that velocity distributions are closely approximated by their depth-averaged values. Analysis of velocity data showed significant variations in velocity direction with depth in channel reaches with curvature. Channel irregularities (including curvatures, depth irregularities, and shoreline variations) apparently produce transverse currents that affect the distribution of constituents, but are not fully accounted for in a two-dimensional model. The two-dimensional flow model, using channel resistance to flow parameters of 0.0234 and 0.0275 for deep and shallow areas, respectively, and an RMA2 Peclet number of 38.3, and the RMA4 transport model with a Peclet number of 37.2, may have utility for emergency-planning purposes. Emergency-response efforts would be enhanced by continuous streamgaging records downstream from Meldahl Dam, real-time water-quality monitoring, and three-dimensional modeling. Decay coefficients are constituent specific.