Resonant Instability in Mountain Waves: Variable Background States

A Newton solver has been developed for both finding steady nonlinear mountain-wave solutions in a general 2D background flow and examining the stability of those solutions. A companion study used the solver to explore the stability of mountain waves with constant background wind and static stability for a single Gaussian ridge. The results showed a resonant wave-wave instability at subcritical mountain heights, and showed that the instability strengthens with increasing nonhydrostatic effects. The focus here is on wave-wave instability for more realistic terrain and background conditions. Instability strength and spatial characteristics are examined given various profiles of shear and static stability over varied terrain. The hypothesis is tested that backsheared environments, complex terrain, and sharp static stability gradients near the mountain crest all serve to widen the spectrum of possible nonlinear interactions. This widened spectrum results in increased growth rates for the instability, relative to cases with simple terrain and constant background states.