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 thebarotropic atmosphere using a simple barotropic model which implements parametrization ofbaroclinic instability. Exponential growth of unstable modes must terminate eventually whenthe waves become finite amplitude. The non-linear evolution of amplified Rossby waves isexamined by analyzing the potential vorticity (PV) field in order to assess the criterion of theRossby wave breaking in a barotropic model atmosphere. For a control run of the wave-6experiment, growing unstable wavenumber n=6 is saturated when the wave energy attainsapproximately 20% of zonal energy of the basic flow. The energy supply at n=6 is balancedwith energy transfer to zonal flow and to its harmonics of n=12 and 18 by weak non-linearinteractions, maintaining a steady configuration of a surf zone structure. The existence of thenegative meridional gradient of PV is the necessary condition for the wave saturation. We thenattempted 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 highand low PV centers occurs when the growth rate is increased by 30%. Associated with theRossby wave breaking, not only the harmonic waves but all zonal waves are amplified by thefully non-linear interactions among all waves. It is demonstrated that the transition from theweakly non-linear regime to fully non-linear regime in the energy transfer is the key factor forthe Rossby wave breaking so that the supplied energy is effectively dissipated by all waves.