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

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.

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Journal of Fluid Mechanics
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Journal of Fluid Mechanics
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National Science Foundation
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    The following summarizes the main results proved under suitable partition hypotheses.

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