The motion of ocean and atmosphere is affected by the earth's rotation and thus, the Coriolis force should be involved when studying the dynamics of such large-scale flows. In this talk, we discuss the dynamics near a shear flow under the beta-plane approximation. The dynamical behavior around the shear flow turns out to be different or richer, compared with the non-Coriolis case. The spectral properties of the linearized operator around the shear flow play an important role in understanding the richer dynamics.