Coherent structures and oscillatory wave packets are among the most striking and most studied features of the large-scale atmospheric circulation. Although their role in atmospheric low-frequency variability, storm track morphology, and extended range forecasting is well established, there are many fundamental questions regarding their connection. For example, under what conditions can coherent structures break down into oscillatory wave packets? Can oscillatory wave packets be organized into coherent structures and, if so, how? More practically speaking, what are the background flow characteristics that allow for the synoptic-scale transient eddies to be organized into large-scale blocking structures?

Here we present a self-consistent, weakly nonlinear theory that examines the connection between coherent structures and oscillatory wave packets in a barotropic atmosphere. In particular, we examine the weakly nonlinear dynamics of isolated anomalies embedded in a meridionally sheared, zonally varying background flow. An amplitude evolution equation is derived analytically, which has the form of a variable coefficient Korteweg DeVries (VC-KDV) equation, wherein the zonally varying background flow modulates the growth and propagation of the disturbance field. This VC-KDV equation possesses both coherent structure and oscillatory wave packet solutions. We show that the zonally varying background flow serves as a catalyst for the transformation between coherent structures and oscillatory wave packets. We derive conservation laws for mass, momentum and energy in order to provide insights into this transformation process. The application of these results to the genesis, maintenance, and breakdown of atmospheric blocking events also will be addressed.