Resonant instability of large-amplitude topographic gravity waves

When density-stratified air is forced by winds over elevated terrain, the vertical displacement of the flow results in gravity wave oscillations. Under conditions of constant stratification and uniform upstream wind, the steady streamlines for flow over a two-dimensional ridge are given by Long's theory (1953). Numerical simulations have found that for multiply-peaked terrain, this steady flow can become unstable to a growing oscillatory wave that seems to emanate from the lee of the ridge farthest downstream. The summit heights of the terrain are into the nonlinear flow regime, but well below that required for flow overturning. The unstable dynamics, however, is such that a stable, steady flow will eventually develop overturning isentropes.

The stability of the steady, finite-amplitude Long's solution has also been investigated by direct computation of the linear eigenmodes. While a physical mechanism for the instability has yet to be identified, it can be clearly demonstrated that the instabilities are due to a triad resonance between two linear waves and the topographic flow. The resonance signature will be used to determine if and how the dynamics identified here are related to the known instabilities of freely-propagating, finite-amplitude gravity waves.