Abstract
The effects of topography are examined in a class of low-order quasi-geostrophic models on a midlatitude β-plane. In the absence of topography the models are capable of producing qualitatively realistic zonal-mean circulations. The maintenance of the zonally symmetric and asymmetric circulations are examined with different spectral truncations and topographic configurations. The response to an isolated mountain peak is the most thoroughly investigated.
When the model is run without wave–wave interactions, the time-mean wave pattern forced by the isolated mountain is a superposition of waves which are either in phase or 180° out of phase with the mountain. When they are included, transient wave-wave interactions alter the mean zonal flow, which leads to a substantial modification of the time-mean wave. Specifically, the amplitude of the longest planetary wave in the model is enhanced as that wave is pushed closer to resonance by the change in the midlevel zonal flow. A phase shift relative to the topography is also induced. A reduction in surface zonal wind caused by the nonlinear wave interactions leads to weaker topographic forcing and smaller time-mean amplitudes for shorter waves. Although the heat and vorticity budgets of the time-mean wave are dominated by “linear” wave–mean flow interactions for the planetary wave, the nonlinear advective terms are of significant magnitude and generally act to oppose the corresponding linear terms for short waves. At least five meridional modes are required to produce qualitatively realistic stationary waves, which remain relatively unchanged as the resolution is further increased.
A (5,5) model (which has 5 zonal waves, a zonal flow, and 5 meridional modes) and higher order models exhibit a significant amount of low-frequency variability and produce persistent anomalies whose time scales are not unlike those of observed anomalies. The planetary wave is not confined to a small region of phase, but undergoes considerable fluctuations in position and amplitude as evidenced by large variability in mountain-induced kinetic energy conversions. The most frequently occurring anomaly pattern can be described as an amplification and slight upstream shifting of the time-mean wave pattern. Low-frequency variability is much less pronounced in more severe truncations.
