Three-Dimensional Numerical Modeling of a River Section under Extreme Discharge Conditions from a Tropical Storm: The Santa Catarina River Case Study, Mexico

In this study, the hydrodynamic behavior of a section of the Santa Catarina River in Nuevo León, Mexico, during Tropical Storm Alberto was investigated. A three-dimensional numerical simulation of river flow was performed using unsteady Reynolds-Averaged Navier-Stokes (RANS) equations coupled with the Volume of Fluid (VOF) method to model the water-air interface. The computational domain was constructed based on the specific area Digital Elevation Model (DEM), accurately capturing the river's morphology, with a structured mesh refined near the riverbed to resolve localized velocity gradients. The simulations focused on high-density water flows induced by extreme precipitation, analyzing key parameters, including velocity distribution, turbulence intensity, and effective viscosity, to evaluate the performance of turbulence models in replicating fluvial dynamics. Validation was achieved using velocity data derived from video footage of the storm, tracked via motion analysis techniques and compared against simulation outputs to ensure accuracy.

The comparative study included the Spalart-Allmaras, standard k-ε, realizable k-ε, and standard k-ω turbulence models. A sensitivity analysis and mesh independence verification ensured robust numerical predictions validated against field data obtained from video-derived velocity measurements.

Findings reveal distinct model performance under varying turbulence conditions. The realizable k-ε model captured peak effective viscosity (μ_eff) values of up to 820 kg/m·s at low turbulence intensities, demonstrating its suitability for flows with strong energy gradients and lower dissipation rates. Conversely, the standard k-ω model excelled under high turbulence intensity, effectively resolving dissipation dynamics and exhibiting μ_eff ​ values between 150–500 kg/m·s. These results highlight the capacity of these models to represent different aspects of riverine hydrodynamics, although neither achieved full optimization across all conditions.

Velocity profiles showed significant gradients near the riverbed, where high shear stress and energy dissipation dominated, reinforcing the importance of mesh refinement in capturing localized effects. Turbulence intensity exhibited a sharp decrease in shallow areas and near structural boundaries, directly influencing μ_eff ​ distributions.

While the evaluated turbulence models provided reliable frameworks for simulating complex fluvial flows, further refinements are needed. Incorporating advanced turbulence models, such as Reynolds Stress Models (RSM) or Large Eddy Simulations (LES), could enhance predictions, particularly for cases involving sediment transport and fluid-structure interactions.

This study contributes to the development of robust methodologies for river modeling under extreme conditions, with practical implications for flood management, hydraulic structure design, and sediment transport assessments. Future research should explore the performance of these models in simulating freshwater flows, assess their application under varying sediment concentrations, and investigate their capability to account for fluid-structure interactions related to bridge columns and other critical infrastructure.