In this contribution, a subgrid artificial viscosity method for approximating solutions to the incompressible Navier–Stokes equations in a rotating frame of reference is considered. The method considers the viscous term as a combination of the vorticity and the grad-div stabilization. Global stabilization is obtained by adding a locution via an artificial viscosity and then removing it only on the coarse mesh scale. We show that the approximate solutions of the method are unconditionally stable and optimally convergent. Several numerical tests are presented for validating the support of the derived theoretical results and demostrate the efficiency and accuracy of the method.