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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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This content will become publicly available on November 25, 2025
Towards a new roughness parametrization through the effective distribution function
Turbulent flows over rough surfaces can be encountered in a wide range of engineering applications. Despite the progress made after several decades of studies, the prediction of drag and roughness function from the surface geometrical parameters remains an open question. Several methods have shown encouraging results. However, they lack generality and present some scatter in the data. In this paper we propose a new parameter, the effective distribution ($$ED$$), which lays foundation on the effective slope with some changes to take into account the sheltering effect of large roughness elements and the drag induced by pinnacles higher than the average roughness elements. To develop this new correlation between geometrical features of the wall and the drag, we performed a set of simulations of the turbulent flow over a rough surface made of triangular elements varying their height and spatial distribution. The$$ED$$correlates quite well both with the drag and the roughness function for a wide range of cases having different mean roughness height, skewness and kurtosis. To further validate the$$ED$$, and assessing how it can be generalized to real rough wall, an irregular wall made from the superposition of random sinusoidal function was considered. Results were consistent with the correlation here presented.
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- Award ID(s):
- 2202710
- PAR ID:
- 10598220
- Publisher / Repository:
- Cambridge University Press
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 999
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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