Modeling of the two-dimensional flow caused by sea conditions and wind stresses on the example of Dead Vistula

The article presents the results of two-dimensional modeling of flows caused by the sea conditions and wind stresses on the example of Dead Vistula. Based on the available bathymetric data, a numerical model of the river section was created, which was supplemented with data on the position of the water table depending on hydrometeorological conditions. To describe the flow field in steady conditions, a simplified model of two-dimensional flow in the form of the bi-harmonic Helmholtz equation for the current function has been adopted, taking into account additional impacts caused by wind stresses on the water surface. Then the current function was converted into the velocity vector components. This equation, supplemented with appropriate boundary conditions, has been solved numerically using the finite difference method. On the basis of the available literature, 4 variants of hydrometeorological conditions were adopted, depending on the direction and strength of wind and sea conditions. The obtained results were compared with the results of published measurements taken on the studied section of the river. These calculations were the basis for the implementation of a two-dimensional model of the spread of pollutants in the studied section of the Dead Vistula.