Turbulent pressure and velocity perturbations induced by gentle hills covered with sparse and dense canopies

Within the inner layer, these intense shear zones improve predictions of the spatial perturbation by K-theory, especially for the phase relationships between the shear stress (∼ ∂∆u/∂z) and the velocity variances, where z is the height. For the upper canopy layers, wake production increases with increasing leaf area density resulting in a vertical velocity variance more in phase with ∆u than with∂∆u/∂z.

However, background turbulence and inactive eddies may have dampened this effect for the longitudinal velocity variance. The increase in leaf area density does not significantly affect the phase relationship between mean surface pressure and topography for the two simulations, though the LES results here confirm earlier findings that the minimum mean pressure shifts downstream from the hill crest. The increase in leaf area density and associated flow separation simply stretches this difference further downstream.

This shift increases the pressure drag, the dominant term in the overall drag on the hill surface, by some 15%. With regards to the normalized pressure variance, increasing leaf area density increases σp/u2 ∗ near the canopy top, where u∗ is the longitudinally averaged friction velocity at the canopy top and σp is the standard deviation of the pressure fluctuations. This increase is shown to be consistent with a primitive scaling argument on the leading term describing the mean-flow turbulent interaction.

This scaling argument also predicts the spatial variations in σp above the canopy reasonably well for both simulations, but not inside the canopy.