Comparative Analysis of Numerical and Analytical Studies of Hydrodynamic Processes in Shallow Water Bodies

The study aims to develop a foundation for determining when a depth-averaged two-dimensional model is sufficient for simulating hydrodynamic processes in shallow water bodies, such as the Sea of Azov, and when a three-dimensional model is advisable to achieve satisfactory results. It is shown that certain combinations of relatively high velocities ( \(u > 1\) m/s) and water depths ( \(d > 50\) m) can lead to significant differences between results obtained with two-dimensional and three-dimensional models. The findings are validated by numerical modeling of steady and unsteady periodic flows in a schematic rectangular basin. The results obtained with the three-dimensional and two-dimensional models are compared, with both cases showing agreement with analytical solutions.