Abstract: We concerns with two-dimentional zonally symmetric one layer quasi-gestrophic flow in a bounded periodic zonal channel. A best nonlinear stability criterion is established for the flow. For Benzi’s model, the nonlinear stability criterion is shown identical to the linear one. Moreover, explicit rigorous upper bounds are obtained on both the disturbance energy and disturbance potential enstrophy.

Key words: disturbance development, nonlinear stability, two-dimentional quasi-gestrophic flow, disturbance development, nonlinear stability