Modeling is a key tool for understanding physical processes, analyzing the global spatial and temporal structure of the ocean, its interaction with the atmosphere, and regional variability in marine and ocean systems. Models also play an important role in processing and assimilating data from field observations. The development of mathematical modeling of ocean dynamics, which has more than a century of experience, has led to a significant increase in understanding of the physical processes occurring in the marine environment, as well as improved methods and models for their analysis. In addition, in recent years there has been increasing interest in studying the patterns of baroclinic fields, disturbances, and anomalies in the ocean, including the analysis of observational data, theoretical studies of the propagation of disturbances in a simplified oceanic environment, and numerical modeling. The basic principles of the theory of the baroclinic layer in the ocean can be derived from a complete set of primitive equations, including horizontal projections of the momentum balance equations, the hydrostatic equation, the mass conservation equation, the heat and salt diffusion equations, and the equation of state.

This article discusses the fictitious domain method for the nonlinear stationary problem of the baroclinic ocean. A generalized solution to the problem is given and its uniqueness is proved. The theorem of existence and convergence of solutions to approximate models obtained using the fictitious domain method are studied.