Dispersive Stresses at the Canopy Upstream Edge

Abstract

The derivation of flow and mass transfer models in canopy and porous media environments involves the spatial-averaging of the flow properties and their subscale equations. The averaging of the momentum equation generates the dispersive stress terms that represent the subscale spatial variations of the unresolved velocity field. While previous studies ignored the dispersive stresses in their flow models, recent evidence indicates that the dispersive stresses may be important. Here we focus our attention on the magnitude of the normal dispersive stresses in the entry region of a ‘forest patch’, where the in-canopy velocities are large and the longitudinal derivatives do not cancel out. Highly detailed particle image velocimetry measurements, at a temporal and spatial resolution of 5 Hz and 1.4 mm, are obtained inside and around a 1-m long model canopy which consists of transparent vertical cylinders 6 mm in diameter and 74.3 mm high (h). The cylinders are randomly distributed to form a relatively sparse forest patch with a leaf area density of 7.56 m−1 and a fluid volume fraction (porosity) of 0.965. We present results of the double averaged flow properties at three different regions of the forest patch; the upstream edge (x ≈ 0), the fully-developed interior region (x ≈ 10h) and the downstream edge (x ≈ 13h). We find that the normal dispersive stresses around the entry region of the forest patch are significantly larger than the normal Reynolds stresses. An order of magnitude analysis of the relevant terms in the momentum equation indicates that the longitudinal derivatives of the dispersive stresses are of the same order of magnitude as that of the drag force and similar to that of the horizontal convection term. The longitudinal derivatives of the Reynolds stresses are smaller, though cannot be ignored. Comparing these results with the characteristic profiles measured in the fully-developed region indicates that the dispersive stresses, which are generated at the forest patch entrance, decrease along an adjustment region while maintaining their profile shape. We find that the dispersive stresses influence the rate at which momentum penetrates into the canopy. These observations suggest that under certain flow conditions, dispersive stresses may dominate the momentum balance and therefore must be considered in future canopy and porous media flow models.