Effects of Mountain Width on Downslope Windstorm Occurrence

Abstract This study demonstrates the impact of mountain width on the occurrence of downslope windstorms by deriving a solution for 2D flow past an idealized mountain range, including nonhydrostatic effects. Additionally, idealized numerical simulations were conducted to validate the solution. The novel solution revealed the physical process of the mountain width effect after wave breaking. As the mountain width decreased, more wave crests appeared per unit horizontal distance, indicating an increase in the horizontal wavenumber of mountain waves. A higher horizontal wavenumber leads to a lower vertical wavenumber, resulting in a longer vertical wavelength. As the vertical wavelength increased, the nondimensional mountain height normalized using this wavelength decreased. A reduced nondimensional mountain height inhibits the occurrence of downslope winds after wave breaking. The solution extends the local hydraulic theory to nonhydrostatic conditions and advances local wind studies. The idealized numerical simulations yielded similar results as from the proposed analytical solution. The simulations showed that narrow mountain ranges required higher heights than wide ones to generate downslope winds. Specifically, no downslope winds occurred after the wave broke in the simulation within the narrow mountain range of a particular height. In contrast, downslope winds occurred after the wave broke in the simulation with a wide mountain range of the same height. Moreover, wave breaking did not occur when the mountain height was sufficiently low. Mountain waves propagate upward and downstream within narrow mountain ranges. In contrast, mountain waves propagate upward only over wide mountain ranges. When the mountain height was sufficiently high, downslope winds occurred after the wave broke regardless of the mountain width. Significance Statement This study demonstrates the effect of mountain width on downslope windstorm occurrence by deriving a solution for 2D flow past an idealized mountain range, including nonhydrostatic effects. Additionally, idealized numerical simulations were conducted to validate the solution. The analytical solution and idealized numerical simulations showed that narrow mountain ranges require a greater height to induce downslope windstorms than that for wide mountain ranges because of the increased vertical wavelength of mountain waves. This study extends the local hydraulic theory to nonhydrostatic conditions, such as airflows over narrow mountain ranges, and advances local wind studies.