Attractor sets and multiple equilibria in the resonance of topographically forced waves

The resonance of topographically forced waves is studied using a quasi-geostrophic spectral model on the rotating sphere. The use of complete spectral expansions without truncation leads to the exact solutions of the nonlinear coupling equations by means of the random phase approximation and the projection operator techniques under the dissipation-vanishing limit. The energy transfer process between topographically forced wave ensemble and zonal mean flow is described.It is shown that the dynamical system loses stability and further bifurcation takes place when the to-pographic force has occurred. There are two sorts of equilibrium point in the resonance system. The unstable equilibrium is an isolated equilibrium point and, therefore, is hardly observed to occur. The stable equilibrium is an attractor set which is related to the phenomenon of blocking.