A STUDY ON THE EXCITATION, ESTABLISHMENT AND TRANSITION OF MULTIPLE EQUILIBRIUM STATES PRODUCED BY NEARLY RESONANT THERMAL FORCING---- PART I: ASYMPTOTIC SOLUTIONS　OF MULTIPLE EQUILIBRIUM STATES

A two-layer quasi-geostrophic baroclinic model in a narrow, longitudinally periodic channel on a β-plane is used, which involves near-resonant thermal forcing, frictional dissipation and a uniformly sheared basic current. By means of the multi-scale technique, a system of simplified differential equations or disturbances due to the steady thermal-forcing waves projected on the X-T plane is derived, which contains the nonlinear interactions between forced waves and free waves. The asymptotic solutions of the equilibrium states of these equations are analytically obtained by a singular perturbation method. The results show that these mul-tiple equilibrium state (MES) solutions can exist in a wide range of the parameters used.