Critical level resonance in three-dimensional flow past isolated mountains

A set of numerical simulations with a three-dimensional nonhydrostatic model is used to investigate the behavior of the atmospheric flow past idealized isolated mountains in the presence of an environmental critical level aloft. The study addresses the problem of three-dimensional effects on the generation of high-drag Bow regimes as a function of the critical level height, concluding that those effects can lead to significant changes in the preferred heights for resonance. The results are compared with theories that have been proposed to explain the high-drag states in two-dimensional flow with critical levels and it is found that, while some of their predictions hold in three dimensions, there is not only an overall change in the amplitude of the effects but also an essential modification of the preferred locations of the critical level height lending to resonance. Whereas two-dimensional studies have shown a vertical spacing between resonant critical level heights very close to one hydrostatic wavelength, the present results show a clear half-wavelength periodicity, as in classic linear resonance. Both the latter result and the much reduced ''resonance shift'' observed in the present study seem to indicate that the two-dimensional hydraulic theory cannot be applied to circular mountains without significant modification. Some other significant differences between two- and three-dimensional results are shown and related to both the linear and nonlinear behavior of the three-dimensional unsheared flow. For comparison, some three-dimensional simulations of Bow past infinite ridges are also presented and they are found to be very similar to previous two-dimensional studies.