Spectra of Velocity components over Complex Terrain

Spectra have been measured over a variety of types of complex terrain: on tops of hills and escarpments, over land downstream of a water surface, and over rolling terrain. Differences between spectra over many types of complex terrain, and over uniform terrain, can be explained by these hypotheses: When air moves over terrain with changed characteristics, then (1) for wavelengths very short relative to the fetch over the new terrain, the spectral densities are in equilibrium with the new terrain. (1) for wavelengths long compared to this fetch, spectral densities remain unchanged if the ground is horizontal, and decrease when the flow is uphill, for the longitudinal velocity component only.

Since vertical-velocity spectra contain relatively less low wavenumber energy than horizontal-velocity spectra, energetic vertical-velocity fluctuations tend to be in equilibrium with local terrain.