Scales of Linear Baroclinic Instability and Macroturbulence in Dry Atmospheres

Linear stability analyses are performed on a wide range of mean flows simulated with a dry idealized general circulation model. The zonal length scale of the linearly most unstable waves is similar to the Rossby radius. It is also similar to the energy-containing zonal length scale in statistically steady states of corresponding nonlinear simulations. The meridional length scale of the linearly most unstable waves is generally smaller than the energy-containing meridional length scale in the corresponding nonlinear simulations. The growth rate of the most unstable waves increases with increasing Eady growth rate, but the scaling relationship is not linear in general. The available potential energy and barotropic and baroclinic kinetic energies of the linearly most unstable waves scale linearly with each other, with similar partitionings among the energy forms as in the corresponding nonlinear simulations. These results show that the mean flows in the nonlinear simulations are baroclinically unstable, yet there is no substantial inverse cascade of barotropic eddy kinetic energy from the baroclinic generation scale to larger scales, even in strongly unstable flows. Some aspects of the nonlinear simulations, such as partitionings among eddy energies, can be understood on the basis of linear stability analyses; for other aspects, such as the structure of heat and momentum fluxes, nonlinear modifications of the waves are important.