The frequency spectrum of mountain waves

Mountain waves are often assumed to remain steady with respect to time, but measurements of their vertical wind velocity by radar are known to show a clear time dependence. Specifically, the vertical wind W obeys a power law, where the spectral density varies as ω −5/3 over at least three orders of magnitude, and ω is the frequency. Power laws in the frequency and wave‐number spectra of parameters such as horizontal wind have been widely studied, but the frequency spectrum of mountain waves remains, by comparison, poorly understood. It is found that errors arising from the VHF radar measurement technique are not sufficient to explain the power law, and a previous model invoking vortical modes or two‐dimensional turbulence does not, on its own, explain entirely the W data. However, even a surprisingly simple model, in which the mountain‐wave pattern drifts upwind or downwind in a random walk, gives a similar time dependence to the observed W data. The radar data are contrasted with other observations and models, where W time variations have been interpreted in terms of lee‐wave trains with non‐zero phase speed; the relationship to other systems showing time‐scale invariant ω β behaviour, such as 1/ f noise, is also discussed.