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The main aim of this talk is to describe the dynamic transitions in geophysical fluid flows. The focus will be on the the two-dimensional, barotropic vorticity equation in a periodic zonal channel, one of the cornerstone dynamical model of the ocean and atmospheric circulation. The equation admits a steady state solution which represents a zonal jet. In this talk, the recent advances in this problem which addresses the stability problem of the bifurcated periodic solutions will be considered. In particular, it will be shown that the modelled flow exhibits either a continuous or catastrophic transition as the basic zonal jet loses its stability. This is a joint work with Henk Dijkstra(Utrecht University), Jie Shen(Purdue University) and Shouhong Wang(Indiana University).