Breaking Rossby waves in the barotropic atmosphere with parameterized baroclinic instability

Abstract

In this study, we conducted a series of numerical experiments of breaking Rossby waves in the barotropic atmosphere using a simple barotropic model which implements parametrization of baroclinic instability. Exponential growth of unstable modes must terminate eventually when the waves become finite amplitude. The non-linear evolution of amplified Rossby waves is examined by analyzing the potential vorticity (PV) field in order to assess the criterion of the Rossby wave breaking in a barotropic model atmosphere. For a control run of the wave-6 experiment, growing unstable wavenumber n = 6 is saturated when the wave energy attains approximately 20% of zonal energy of the basic flow. The energy supply at n = 6 is balanced with energy transfer to zonal flow and to its harmonics of n = 12 and 18 by weak non-linear interactions, maintaining a steady configuration of a surf zone structure. The existence of the negative meridional gradient of PV is the necessary condition for the wave saturation. We then attempted to break the waves intentionally by increasing the growth rate of the unstable mode. It is found that the regularity of Rossby wave progression is lost and the overturning of high and low PV centers occurs when the growth rate is increased by 30%. Associated with the Rossby wave breaking, not only the harmonic waves but all zonal waves are amplified by the fully non-linear interactions among all waves. It is demonstrated that the transition from the weakly non-linear regime to fully non-linear regime in the energy transfer is the key factor for the Rossby wave breaking so that the supplied energy is effectively dissipated by all waves.