A study of the sensitivity of the model of the Black Sea current dynamics to the surface boundary conditions

A numerical scheme for solving the equation for a free surface within the framework of the model of ocean dynamics is proposed and used. The use of the equation for a free surface instead or the rigid lid approximation in the models of ocean current dynamics allows description of the ocean current dynamics under essentially unsteady conditions such as tides, geostrophic adjustment of barotropic motions, and offset-onset phenomena in the shallow-water parts of the ocean. In addition, this makes it possible to Simulate the global variations in the World Ocean level as well as seasonal and interannual variations of the level in semiclosed and closed seas since, in this case, there is no need to require a zero total water flow through the boundaries of the domain. This paper presents a study of the effect of the boundary conditions at the sea surface (the rigid lid condition and the equation for a free surface) on the description of the fast response of currents to an initial perturbation in the framework of the model of the Black Sea current dynamics. It is shown that, in the model with a free surface, the behavior of unsteady motions on synoptic time scales in the shelf sea regions changes significantly in the initial period (about a day) of transition to a steady current regime after the initial perturbation.