Analytical models for the mean flow inside dense canopies on gentle hilly terrain

Abstract

AbstractSimplifications and scaling arguments employed in analytical models that link topographic variations to mean velocity perturbations within dense canopies are explored using laboratory experiments. Laser Doppler anemometry (LDA) measurements are conducted in a neutrally‐stratified boundary‐layer flow within a large recirculating flume over a train of gentle hills covered by a dense canopy. The hill and canopy configuration are such that the mean hill slope is small and the hill is narrow in relation to the canopy (H/L ≪ 1 and Lc/L ≈ 1, where H is the hill height, L the half‐length, and Lc the canopy adjustment length‐scale). The LDA data suggest that the often‐criticized linearizations of the advective terms, turbulent‐shear‐stress gradients and drag force appear reasonable except in the deep layers of the canopy. As predicted by a previous analytical model, the LDA data reveal a recirculation region within the lower canopy on the lee slope. Adjusting the outer‐layer pressure perturbations by a virtual ground that accounts for the mean streamline distortions induced by this recirculation zone improves this model's performance. For the velocity perturbations in the deeper layers of the canopy, a new analytical model, which retains a balance between mean horizontal advection, mean pressure gradient and mean drag force but neglects the turbulent‐shear‐stress gradient, is developed. The proposed model reproduces the LDA measurements better than the earlier analytical model, which neglected advection but retained the turbulent‐shear‐stress gradient in the lower layers of the canopy and near the hill top. This finding is consistent with the fact that the earlier model was derived for tall hills in which advection inside the canopy remains small. In essence, the newly‐proposed model for the narrow hill studied here assumes that in the deeper layers of the canopy the spatial features of the mean flow perturbations around their background state can be approximated by the inviscid mean‐momentum equation. We briefly discuss how to integrate all these findings with recent advances in canopy lidar remote‐sensing measurements of general topography and canopy height. Copyright © 2008 Royal Meteorological Society