NONLINEAR AMPLIFICATION OF STATIONARY ROSSBY WAVES NEAR RESONANCE .2.

In a preceding paper the authors showed thar planetary waves of very d ifferent amplitudes can be sustained on the same configuration of the zonal wind by asymptotically balancing the energy contributions relate d to Ekman dissipation and orographic drag. The basic physical mechani sm considered, namely, nonlinear self-interaction of the eddy field, w as modeled in a vertically continuous quasigeostrophic model by means of a perturbative approach that relies on an ad hoc choice of the meri dional profile of the wave held itself. Given the mathematical limitat ions of this approach, some important aspects of the mechanism of reso nance bending were not explored; in particular the sensitivity of stat ionary solutions to changes in the zonal wind profile, channel geometr y, and physical parameters such as dissipation coefficients and mounta in height. In the present paper, the robustness of the mechanism of re sonance folding by numerical means is analyzed, in the framework of bo th the barotropic and the two-level quasigeostrophic model. It is demo nstrated that resonance bending is a genetic property of the equations governing atmospheric motions on the planetary scale. In particular, it is shown that multiple stationary solutions can be achieved with re alistic values of Ekman dissipation and mountain height in the context of the two-level quasigeostrophic model. The authors formulate a weak ly nonlinear theory that does not rely on any a priori assumptions abo ut the meridional structure of the solution. Numerical and analytical results are compared, obtaining a satisfactory agreement in the parame ter range in which the asymptotic theory is valid. The authors conclud e that the present model is still a good candidate for the explanation of one of the most relevant statistical property of low-frequency var iability at midlatitudes, namely, that large amplitude fluctuations of ultralong waves correspond to small variations of the zonal wind.