Resonant wave-wave instability and wave breaking in flows past simple and complex terrain profiles

Recent work on flow past a two-peak terrain profile shows that mountain waves can be subject to resonant instability even at relatively small values of the non-dimensional terrain height. Here some of the properties and consequences of the instability are considered. It is shown that the instability applies even for flow past an isolated peak, although the growth rates in this case tend to be small and the range of unstable mountain heights is relatively narrow. With additional terrain peaks the growth rate increases and the threshold mountain height for the instability is significantly lowered. For 4 terrain peaks the threshold terrain height can be as low as 0.2. In all cases the instability leads to intermittent wave breaking, with the intermittency being particularly pronounced in cases with multiple peaks. The growth of the instability leads to a marked increase in mean pressure drag and produces a relatively complex pattern of vertical momentum flux. In the case of transient background flows, the instability is shown to be favored during the accelerating phase of the flow and suppressed while the flow is decelerating.