Comparison of Hydrodynamic Processes Modelling Results in Shallow Water Bodies Based on 3D Model and 2D Model Averaged by Depth

Introduction. Two-dimensional hydrodynamic models have proven their ability to adequately describe the processes of runoff and transportation in rivers, lakes, estuaries, deltas and seas. Practice shows that even where significant three-dimensional effects are expected, for example, with wind flows, a two-dimensional approach can work effectively. However, in some cases, the two-dimensional model does not accurately reflect the actual flow structures. For example, in shallow waters with complex bathymetry, heterogeneous terrain and dynamics can lead to a non-uniform velocity profile. The aim of the study is to develop a basis for determining in which cases a two-dimensional model averaged in depth is sufficient for modelling hydrodynamic processes in shallow waters like the Azov Sea, and in which cases it is advisable to use a three-dimensional model to obtain accurate results.

Materials and Methods. Local analytical solutions have been obtained for the propagation of the predominant singular progressive wave in a shallow, well-mixed reservoir. Advective terms and Coriolis terms are neglected, the vortex viscosity is assumed to be constant, and the lower friction term is linearized. Special attention is paid to the latter, since the characteristics of the models significantly depend on the method of determining the coefficients of lower friction. The analytical method developed in the study shows that certain combinations of higher flow velocities (u ≈˃ 1 m/s) and water depths (d ˃ 50 m) can cause significant differences between the results of the depth-averaged model and the model containing vertical information.

Results. The results obtained are verified by numerical simulation of stationary and non-stationary periodic flows in a schematized rectangular basin. The results obtained as a result of three-dimensional modelling are compared with the results of two-dimensional modelling averaged in depth. Both simulations show good compliance with analytical solutions.

Discussion and Conclusions. Analytical solutions were found by linearization of the equations, which obviously has its limitations. A distinction is made between two types of nonlinear effects — nonlinearities caused by higher-order terms in the equations of motion, i.e. terms of advective acceleration and friction, and nonlinear effects caused by geometric nonlinearities, this is due, for example, to different water depths and reservoir widths, which will be important when modelling a real sea.

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