Stagnation points and bifurcation in 3-D mountain airflow

The effect of non-linearity on the formation of mountain-wave induced stagnation points is examined using the scaling laws for ideal hydrostatic flow and a series of runs with decelerating winds in a numerical model. In the limit of small deceleration rate (i.e., near steady state) runs with a variety of mountain heights and widths give similar results; i.e., the speed extrema values in the 3-D wave fields collapse onto “universal curves”. For a Gaussian hill with circular contours, stagnation first occurs at a point above the lee slope. This result contradicts the result of linear theory that stagnation begins on the windward slope. The critical value of ĥ for stagnation above a Gaussian hill is ĥ_crit = 1.1 ± 0.1. For a 3/2-power hill, the critical height is slightly higher, ĥ_crit = 1.2 ± 0.2. These values are significantly larger than the value for a ridge (ĥ_crit = 0.85), due to dispersion of wave energy aloft. The application of Sheppard's rule and the vorticity near the stagnation point are discussed. As expected from linear theory, the presence of positive windshear suppresses stagnation aloft. With Richardson number = 20 for example, stagnation first begins at the ground at a value ofĥ = 1.6 ± 0.2. When a stagnation point first forms aloft in the unsheared case, the flow field begins to evolve in the time domain and the scaling laws are violated. We interpret these events as a wave-breaking induced bifurcation which leads to stagnation on the windward slope and the formation of a wake.