Resonant instability in mountain waves: Breaking at subcritical mountain heights

Wave breaking over terrain can lead to phenomena such as clear-air turbulence and downslope windstorms, which can be hazardous to human life and property. It is well known that wave breaking occurs when the nondimensional height of the terrain (Nh/U) exceeds a critical value, so that isentropes in the wave steepen and overturn. However, breaking is also possible at smaller (subcritical) mountain heights, if the mountain wave is subject to wave-wave instabilities. This instability causes the subcritical waves to oscillate and grow, ultimately leading to wave overturning and turbulence.

The present study reviews wave-wave instabilities at subcritical mountain heights for the classical case of flow past a ridge in 2D. The results make use of new methods for finding nonlinear steady-state wave solutions numerically, as well as methods for analyzing the stability of the solutions. Instability thresholds and growth rates are mapped across the full nonlinear 2D parameter space, including both rotating and nonhydrostatic flow. Instability is found for the full range of parameters and flow conditions, but is shown to be most prominent in the nonhydrostatic regime. The mechanics of the instability are illustrated in terms of energy exchanges between resonant triads.

In a companion study, the analysis is extended to more realistic problems, including flows with background wind shear and static stability variations.