The effect of canopy roughness density on the constitutive components of the dispersive stresses

Abstract

How to represent the effects of variable canopy morphology on turbulence remains a fundamental challenge yet to be confronted. Planar averaging over some minimal area can be applied to average-out this sort of spatial variability in the time-averaged mean momentum balance. Because of the multiply connected air-spaces, spatial averaging gives rise to covariance or dispersive stress terms that are produced by the spatial correlations of the time-averaged quantities. These terms are “unclosed” and require parameterization, which to date remains lacking due to the absence of data. Here, flume experiments were conducted to quantify the magnitude and sign of the dispersive stresses for a cylindric canopy where the rod density was varied but the individual rod dimensions (rod height h _c and rod diameter d _r) remained the same. Quadrant analysis was used to explore the genesis of their spatial coherency inside the canopy for a wide range of rod densities. When compared to the conventional turbulent stresses, these dispersive stresses can be significant in the lowest layers of sparse canopies. For dense canopies, the dispersive terms remain negligible when compared to the conventional momentum fluxes at all the canopy levels consistent with previous experiments in vegetated and urban canopies. It was also shown that the spatial locations contributing most to the dispersive terms were in the immediate vicinity downstream of the rods. In the deeper layers of sparse canopies, these positions contributed large and negative stresses, but in the upper levels of the canopy, they contributed large but positive stresses. Because the longitudinal velocity spatial perturbation $({\bar{u}}^{\prime\prime})$ behind the rods is negative, the switch in sign in these stresses was connected with the sign of the vertical velocity spatial perturbation $({\bar{w}}^{\prime\prime}).$ Simplified scaling arguments, using a reduced mean continuity equation and the vertical mean momentum balance for the flow field near the rods, offer clues as to why ${\bar{w}}^{\prime\prime} > 0$ in much of the lower canopy levels (about 0.75 h _c ) while ${\bar{w}}^{\prime\prime} < 0$ in the upper canopy levels.