The primitive equations (PEs) of large-scale oceanic flow formulated in
mean vorticity is proposed. In the reformulation of the PEs, the prognostic equation
for the horizontal velocity is replaced by evolutionary equations for the mean vorticity
field and the vertical derivative of the horizontal velocity. The total velocity field
(both horizontal and vertical) is statically determined by differential equations at each
fixed horizontal point. Its equivalence to the original formulation is also presented.