... that the Stokes operator in the domain M , subject to the boundary conditions (37), is equal to the −Δ operator.As a result of the above and (36) we apply a generalized version of the Stokes theorem ... account for the buoyancy forces and stratification effects under the Boussinesq approximation. Moreover, and due to the shallowness of the oceansand the atmosphere, i.e., the depth of the fluid layer ... to the radius of the earth, the vertical large scale motion in the oceansand the atmosphere is much smaller than the horizontal one, which in turnleads to modeling the vertical motion by the...