In this paper, a new transient forced quasi-resonant triad interaction theory in a beta channel is proposed to investigate the interaction between planetary-scale diffluent flow composed of zonal wavenumbers 1-3 and synoptic-scale waves produced continuously by a synoptic-scale vorticity source fixed upstream of an incipient blocking region during the life cycle of blocking. It is shown that the superposition of initial three Rossby waves for zonal wavenumbers 1 (monopole), 2 (dipole), and 3 (monopole), which permit triad quasi-resonance, can represent an incipient blocking event. The synoptic-scale eddies may act to amplify the incipient blocking and to excite a blocking circulation with a strong meander, whose flow pattern depends on the initial amplitudes of the planetary waves and both the intensity and location of preexisting synoptic-scale waves. The onset (decay) of the planetary-scale split-flow blocking is mainly represented by a strong increase (decrease) in the amplitude of the zonal wavenumber 2 component, having a dipole meridional structure related to the preexisting synoptic-scale eddies. The typical persistence time of the model blocking was of about 20 days, consistent with observations of blocking patterns. In our model, isolated asymmetric dipole blocking is formed by synoptic-scale waves. The instantaneous fields of total streamfunctions exhibit a remarkable resemblance to the synoptic maps observed during the life cycle of blocking. During the onset stage, the synoptic-scale waves are enhanced and split into two branches around the blocking region due to the feedback of the amplified blocking, in agreement with the observed changes of synoptic-scale waves in real blocking events. In addition, a diagnostic case study of blocking is presented to confirm the forced quasi-resonant triad interaction theory proposed here.
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