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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 April 10, 2026
Lift and drag forces on a moving intruder in granular shear flow
Lift and drag forces on moving intruders in flowing granular materials are of fundamental interest but have not yet been fully characterized. Drag on an intruder in granular shear flow has been studied almost exclusively for the intruder moving across flow streamlines, and the few studies of the lift explore a relatively limited range of parameters. Here, we use discrete element method simulations to measure the lift force,$$F_{{L}}$$, and the drag force on a spherical intruder in a uniformly sheared bed of smaller spheres for a range of streamwise intruder slip velocities,$$u_{{s}}$$. The streamwise drag matches the previously characterized Stokes-like cross-flow drag. However,$$F_{{L}}$$in granular shear flow acts in the opposite direction to the Saffman lift in a sheared fluid at low$$u_{{s}}$$, reaches a maximum value and then decreases with increasing$$u_{{s}}$$, eventually reversing direction. This non-monotonic response holds over a range of flow conditions, and the$$F_{{L}}$$versus$$u_{{s}}$$data collapse when both quantities are scaled using the particle size, shear rate and overburden pressure. Analogous fluid simulations demonstrate that the flow around the intruder particle is similar in the granular and fluid cases. However, the shear stress on the granular intruder is notably less than that in a fluid shear flow. This difference, combined with a void behind the intruder in granular flow in which the stresses are zero, significantly changes the lift-force-inducing stresses acting on the intruder between the granular and fluid cases.
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- Award ID(s):
- 1929265
- PAR ID:
- 10588087
- Publisher / Repository:
- Cambridge University Press
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 1008
- ISSN:
- 0022-1120
- Page Range / eLocation ID:
- A5
- Subject(s) / Keyword(s):
- dry granular material granular materials
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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