Behavior of flow over step orography

A two-dimensional nonhydrostatic version of the NCEP regional Eta Model tog ether with analytic theory are used to examine flow over isolated mountains in numerical simulations using a step-terrain vertical coordinate. Linear theory indicates that a singularity arises in the steady flow over the step corners for hydrostatic waves and that this discontinuity is independent o f height. Analytic solutions for both hydrostatic and nonhydrostatic waves reveal a complex behavior that varies with both horizontal and vertical res olution. Witch of Agnessi experiments are performed with a 2D version of the Eta Mod el over a range of mountain half-widths. The simulations reveal that for in viscid flow over a mountain using the step-terrain coordinate, flow will no t properly descend along the lee slope. Rather, the flow separates downstre am of the mountain and creates a zone of artificially weak flow along the l ee slope. This behavior arises due to artificial vorticity production at th e corner of each step and can be remedied by altering the finite differenci ng;adjacent to the step to minimize spurious vorticity production. In numerical simulations with the step-terrain coordinate for narrow mounta ins where nonhydrostatic effects are important, the disturbances that arise at step corners may be of the same horizontal scale as those produced by t he overall mountain, and the superposition of these disturbances may reason ably approximate the structure of the continuous mountain wave. For wider m ountains, where perturbations are nearly hydrostatic, the disturbances abov e the step corners have horizontal scales that are much smaller than the ov erall scale of the mountain and appear as sharp spikes in the flow field. T he deviations from the "classic" Witch of Agnesi solution are significant u nless the vertical resolution is very small compared to the height of the m ountain. In contrast, simulations with the terrain-following vertical coord inate produce accurate solutions provided the vertical grid interval is sma ll compared to the vertical wavelength of the mountain waves (typically at least an order of magnitude larger than the mountain height).