Processing of Field Measurement Data from Expedition Research for Mathematical Modeling of Hydrodynamic Processes in the Sea of Azov

The paper presents a three-dimensional hydrodynamic mathematical model that takes into account the processes of salt and heat transport in the Sea of Azov and makes it possible to obtain three-dimensional fields of water flow velocities, pressure, sea water density, salinity, and temperature. The model includes the Navier–Stokes equations of motion, the continuity equation in the case of variable density, and the equations of heat and salt transport. Boundary and initial conditions are specified. The diffusion–convection–reaction equation is approximated in time using weighted schemes. Approximation in spatial variables in the problem of determining the velocity field of the aquatic environment was performed by the balance method, taking into account the filling factors of the control regions. The initial distributions of salinity and temperature, which have a sufficient degree of smoothness at the points of setting their values, was performed using the Laplace equation. Maps of salinity and temperature of the Sea of Azov were obtained by interpolation and superimposing the boundaries of the region. Stationary regimes of heat and salt transfer have been studied. Based on the results of monitoring the water area, three-dimensional mathematical models of the movement of the aquatic environment were built, designed to predict possible scenarios for the development of the Azov Sea ecosystem, making it possible to study how anaerobic contamination areas emerge and take timely measures to localize them. To refine the input data of the mathematical model, an algorithm based on the Kalman filter was developed and implemented, which made it possible to obtain the minimum variance of the unbiased estimate of the state of the dynamic system. The elements of the software package are listed, making it possible to simulate hydrodynamic processes in shallow water bodies with complex spatial structures of currents with the transport of salts and heat.