The study of the laws of fluid motion has always been an important aspect of the development of both technical and natural sciences. The solution to various problems arising in the analysis of fluid dynamics can be carried out both at the theoretical level and through carefully designed physical experiments. However, in many cases, creating models to study fluid phenomena is challenging, especially in laboratory or field studies. Physical experiments aimed at the detailed study of fluid motion often encounter technical difficulties and require significant resources and financial costs. In addition, the data obtained from such experiments are often limited in their applicability. This is why mathematical modeling plays a significant role in research in fluid dynamics. This makes it possible to more efficiently and cheaply study various aspects of fluid motion, and also provides the opportunity to apply the results obtained more widely. Modeling allows you to consider various factors affecting fluid movement and analyze their impact on the final result. Thus, mathematical modeling becomes an important tool for understanding and improving fluid movement concepts in various science and technology fields. This article discusses the fictitious domain method for a linear ocean flow problem. 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.