Investigation and the numerical solution of the problem of modeling of the circulation in water areas with «liquid» boundaries

In geophysical fluid dynamics a problem of modeling physical processes in water areas with «liquid» boundaries is known. One way to solve this problem is to apply the optimal control theory and data assimilation methods. In this paper the problem of unknown function calculation in the boundary condition of the system of «shallow-water equations» is considered. By using the known methods for inverse problems investigation and optimal control theory an iteration algorithm is proposed. Conditions for the unique and dense solvability of the considered problem and conditions for the iteration algorithm convergence are obtained as well. The results of numerical implementation of this algorithm related to Baltic Sea area are also demonstrated in this work.