The dimension of an attractor generated by equations of 2D viscous noncompressible liquid dynamics on a revolving sphere

Let us write the equation describing the dynamics of a two dimensional viscous noncompressible liquid on a revolving sphere as follows: , (1) where is the current function (here is the vorticity); l is the Coriolis parameter (here, is the angular velocity of the Earths revolution, is the latitude); J is the Jacobian (here, a is the Earths radius, f is the external effect, which we consider time independent for simplicity, and is the Laplasian operator on a sphere).