We consider the equivalent barotropic vorticity equation on the sphere, with simplified forcing, dissipation and topography. Twenty‐five modes are retained in a spherical harmonics expansion of the stream function. Solutions are studied as a function of the nondimensional intensity of the forcing and dissipation.Stationary solutions show the nonlinear orographic resonance of Charney and DeVore. A second resonance at lower, more realistic values of the forcing appears as a result of the larger number of modes. Among the multiple equilibria associated with the second, more complex resonance are a zonal and a blocked flow pattern which present marked similarities with the synoptically defined normal and blocked Northern Hemisphere midlatitude flows.Wave‐wave interactions influence strongly the stability properties of the equilibria and time evolutions of nonequilibrium solutions. The latter show persistent sequences which occur in the phase‐space vicinity of the zonal and blocked equilibria. Composite flow patterns of the persistent sequences are similar to the equilibria nearby. The mean life times of the sequences are longer than in reality due to the lack of baroclinic processes in the model. A recurrent hyper‐predictable sequence with both persistent and agitated episodes, lasting a total of 500 simulated days, is also exhibited and discussed.