Resonance of stationary waves in a model atmosphere

The resonance of stationary waves in a mid-latitude (beta)-plane model is examined. In a series of linear experiments it is found that a large, quasi-resonant response occurs even in the presence of realistic damping. With forcing of reasonable amplitude the resonant growth rates are found to be such that a period of several weeks is required for the resonant mode to achieve large amplitude in the troposphere. When nonlinear effects are included the growing resonant wave is found to cause a stratospheric warming and zonal wind reversal and thus drives the system off resonance. We therefore examine flow configurations for which the nonlinear terms vanish. It is found that these flow configurations can resemble realistic blocking patterns. When diabatically forced, the resonant growth of these patterns does not give rise to any nonlinear interactions, although such interactions do occur if other models, which do not satisfy the non-interaction conditions, are present. We conclude that resonant growth can lead to the establishment of large-amplitude, stationary, long waves even when realistic damping and non-linear effects are operating.