Surface layer response to heterogeneous tree canopy distributions: roughness regime regulates secondary flow polarity

Abstract

Large-eddy simulation was used to model turbulent atmospheric surface layer (ASL) flow over canopies composed of streamwise-aligned rows of synthetic trees of height, $h$, and systematically arranged to quantify the response to variable streamwise spacing, $\delta _1$, and spanwise spacing, $\delta _2$, between adjacent trees. The response to spanwise and streamwise heterogeneity has, indeed, been the topic of a sustained research effort: the former resulting in formation of Reynolds-averaged counter-rotating secondary cells, the latter associated with the $k$- and $d$-type response. No study has addressed the confluence of both, and results herein show secondary flow polarity reversal across ‘critical’ values of $\delta _1$ and $\delta _2$. For $\delta _2/\delta \lesssim 1$ and $\gtrsim 2$, where $\delta$ is the flow depth, the counter-rotating secondary cells are aligned such that upwelling and downwelling, respectively, occurs above the elements. The streamwise spacing $\delta _1$ regulates this transition, with secondary cell reversal occurring first for the largest $k$-type cases, as elevated turbulence production within the canopy necessitates entrainment of fluid from aloft. The results are interpreted through the lens of a benchmark prognostic closure for effective aerodynamic roughness, $z_{0,{Eff.}} = \alpha \sigma _h$, where $\alpha$ is a proportionality constant and $\sigma _h$ is height root mean square. We report $\alpha \approx 10^{-1}$, the value reported over many decades for a broad range of rough surfaces, for $k$-type cases at small $\delta _2$, whereas the transition to $d$-type arrangements necessitates larger $\delta _2$. Though preliminary, results highlight the non-trivial response to variation of streamwise and spanwise spacing.