Orographic Gravity Waves Close to the Nonhydrostatic Limit of Vertical Propagation

Abstract

Orographic gravity waves excited by a narrow mountain ridge are investigated with the aid of numerical simulations. When the nondimensional mountain half-width Na/U is around 1—N, a, and U being the Brunt–Väisälä frequency, the dimensional half-width, and the ambient wind speed, respectively—only part of the gravity wave spectrum excited by the mountain is able to propagate vertically. In this case, linear theory, as well as numerical simulations with low mountains, show two wind maxima: one at the mountain crest and one in the lee of the mountain. As Na/U is reduced below 1, the wind maximum in the lee weakens and moves farther downstream, and the maximum at the crest intensifies rapidly with decreasing Na/U. Simulations in which a gap with a level axis is embedded in the mountain ridge demonstrate that the wind perturbations along the gap axis are qualitatively similar to those over the adjacent mountain ridge. However, their magnitude is substantially lower, and the tendency to form a wind maximum at the gap center (corresponding to a maximum at the mountaintop) is rather weak. When the mountain is high enough for nonlinear effects to become important, the flow structure changes substantially. Provided that Na/U is not below 1, there is a range of nondimensional mountain heights where gravity wave breaking establishes a flow structure very similar to that typical for wider mountains, including strong downslope winds in the lee of the mountain and a pressure drag well above the linear value. The results indicate that nonlinearity can shift the primary wind maximum from the mountain crest into the lee. For Na/U ≈ 0.75, gravity wave breaking no longer occurs, and the wind maximum is reached at the top of the mountain regardless of its height. Along a gap axis, however, there is a tendency for a pronounced wind maximum on the lee side even for narrow mountain ridges. In agreement with the results known for wider mountains, surface friction is found to reduce the wind speed close to the ground, to promote flow separation from the ground over the lee slope of the mountain and to reduce the tendency toward gravity wave breaking. For Na/U ≈ 1 and moderate surface friction, the formation of rotors becomes possible even for uniform large-scale flow.