The mathematical model of large scale ocean and atmosphere dynamics is studied in the paper. The initial boundary value problem describes this model in a cylindrical domain , where is a smooth bounded domain in
Here is the horizontal velocity, is the three-dimensional velocity, is the pressure, is the temperature, is the Coriolis parameter, is a given heat source, and are elliptic operators
where are positive constants, is the horizontal Laplacian.
The system (1) is complemented with boundary and initial conditions
where is the wind stress on the ocean surface, is the normal vector to , is the typical temperature distribution on the top surface of the ocean.
It is shown that the problem (1), (2), (3) has unique strong solution which continuously depends on initial data for a general cylinder and for any initial data.