Effective Roughness and Displaced Mean Flow over Complex Terrain

Via analysis of velocity and stress fields from Reynolds-Averaged Navier–Stokes simulations over diverse complex terrains spanning several continents, in neutral conditions we find displaced areal-mean logarithmic wind speed profiles. The corresponding effective roughness length (z0,eff), friction velocity (u∗,eff), and displacement height (deff) characterise the drag exerted by the terrain.

Simulations and spectral analyses reveal that the terrain statistics—and consequently deff, u∗ ,eff  and z0,eff—can change significantly with flow direction, including flow in opposite directions. Previous studies over scaled or simulated fractal surfaces reported z0,eff to depend on the standard deviation of terrain elevation (σh), but over real terrains we find z0,eff varies with standard deviation of terrain slopes (σΔh/Δx).

Terrain spectra show the dominant scales contributing to σΔh/Δx vary from ∼ 1–10 km, with power-law behaviour over smaller scales corresponding to fractal terrain used in earlier works. The dependence of z0,eff on σΔh/Δx is consistent with fractal terrain having σΔh/Δx α σh, as well as classic theory for individual hills.

We obtain relationships for z0,eff, deff, and u∗ ,eff in terms of σΔh/Δx, finding that deff acts as a characteristic length scale within z0,eff. Considering flow in opposite directions, use of upslope statistics did not improve z0,eff predictions; sheltering effects likely require more sophisticated treatment.

Our findings impact practical applications and research, including micrometeorological flow, computational fluid dynamics, atmospheric model coupling, and mesoscale and climate modelling. We discuss limitations of the z0,eff formulations developed herein, and provide recommendations for practical use.