Nonlinear Resonance and Instability of Planetary Waves and Low-Frequency Variability in the Atmosphere

Abstract

It is demonstrated in this work that linearly unstable planetary waves can be resonantly excited to finite amplitude in a nonlinear barotropic atmosphere with vorticity forcing and dissipation. In a weakly forced/dissipated atmosphere, it is shown that barotropic instability may provide a dynamic mechanism of transition between different ?flow regimes.? It is suggested that nonlinear resonance and instability of planetary waves, which seen to be common with finite amplitude steady free solutions, may play a role in producing low- frequency variability observed in the real atmosphere. A type of nonlinear free solution with realistically sheared zonal flow is described in spherical geometry, and normal-mode instability analysis is performed to examine its stability. A time-dependent spectral model is employed to demonstrate the resonant excitation and breakdown of unstable planetary waves that results in low-frequency variability. The steady free solution is barotropically unstable to large-scale, low-frequency perturbations. Even though unstable, it can be resonantly excited from many initial conditions by a stationary vorticity forcing that projects onto it. The leading low-frequency oscillation has a period of about 20 days and the model flow hemispherically alternates between an almost zonal flow and a blocking regime, reminiscent of the multiple equilibria found by Charney and DeVore.