Wave Packets in Simple Equilibrated Baroclinic Systems

Abstract

The zonal modulation of baroclinic disturbances is studied in a quasigeostrophic two-layer periodic channel. The system is relaxed toward an unstable state with a uniform flow in each layer. For small criticality, two weakly nonlinear systems are then developed, which differ in the choice of boundary condition used for the correction to the basic flow. Each system is described by an amplitude equation that determines the evolution of the wave envelope over ?long? time- and space scales. For the first system the amplitude equation allows wave packet formation. Depending upon the ratio of the length scale of the packets to the channel length, either a steady wave train, stable solitonlike wave packets, or chaotically evolving wave packets are observed. The mechanism that leads to wave packet formation is then discussed with reference to the instability criterion of the amplitude equation. For the second system the amplitude equation is found to allow convergence to a steady, uniform wave train only. A numerical model is then used to investigate the finite criticality extension of the second weakly nonlinear system. At low criticality, the assumptions that underpin the weakly nonlinear theory are tested by analyzing the convergence to a uniform wave train. As the criticality is increased, the effects of full nonlinearity cause the weakly nonlinear theory to become invalid. Initially, resonant triads of waves that have fixed amplitudes become excited owing to the dissipative nature of the system. As the criticality is increased further, other waves are excited and the system approaches full baroclinic chaos. Wave packet?like structures are then observed that evolve rapidly, growing, decaying, merging, and dividing.