Breaking Rossby waves in the barotropic atmosphere with parameterized baroclinic instability

In this study, we conducted a series of numerical experiments of breaking R ossby waves in the barotropic atmosphere using a simple barotropic model wh ich implements parametrization of baroclinic instability. Exponential growt h of unstable modes must terminate eventually when the waves become finite amplitude. The non-linear evolution of amplified Rossby waves is examined b y analyzing the potential vorticity (PV) field in order to assess the crite rion of the Rossby wave breaking in a barotropic model atmosphere. For a co ntrol run of the wave-6 experiment, growing unstable wavenumber n = 6 is sa turated when the wave energy attains approximately 20% of zonal energy of t he 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 inte ractions, maintaining a steady configuration of a surf zone structure. The existence of the negative meridional gradient of PV is the necessary condit ion for the wave saturation. We then attempted to break the waves intention ally by increasing the growth rate of the unstable mode. It is found that t he regularity of Rossby wave progression is lost and the overturning of hig h and low PV centers occurs when the growth rate is increased by 30%. Assoc iated with the Rossby wave breaking, not only the harmonic waves but all zo nal waves are amplified by the fully non-linear interactions among all wave s. 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 th e Rossby wave breaking so that the supplied energy is effectively dissipate d by all waves.