Explosive Baroclinic Instability

A low-order general circulation model contains all the elements of baroclinic instability, including differential heating to drive the mean zonal shear flow against dissipation. Simulations exhibit vacillation ending in fixed-point solutions and chaotic solutions with significant amplifications of the baroclinic cycles compared to those of vacillation. The chaos sensitivity to initial conditions, covering a broad landscape of initial values, demands analysis of why the chaos occurs and its impact on subsequent storm intensity. Three attractors found in the dynamic system are important. One attractor is the stable fixed-point solution-the ultimate destination of a vacillation trajectory. A second attractor represents an unstable zonal solution. Though this dynamic system is bound, some trajectories get extremely close to the unstable, but strongly attracting, zonal solution. It is while traversing such a trajectory that the buildup of available potential energy is such to allow subsequent explosive baroclinic instability to develop. The roots of the characteristic matrix of the dynamic system are examined at every time step. A single critical value of one of the roots is found to be the cause of the chaos for a given value of the differential heating H. The system becomes more stable with increased values of H; vacillation is stronger and more prominent, and the critical value for chaos increases with H. When chaos does occur, it is stronger and more explosive.