Filament inclination effect on turbulent canopy flows

TL;DR

Six dense-canopy configurations with filament inclination θ ∈ [0°,90°] are studied using large-eddy simulations at $Re_b=6000$. An extended virtual-origin framework, incorporating turbulence origins, velocity-fluctuation origins, and a non-linear transpiration correction, is developed to predict drag changes across all inclinations. The results reveal a transition from canopy-dominated to sheltered outer-layer turbulence near $\theta \approx 84^{\circ}$, with a modest drag reduction at $\theta = 90^{\circ}$ and KH-like instabilities that diminish with increasing inclination. Spectral analysis shows distinct inner-canopy and outer-canopy structures whose prominence shifts with $\theta$, and the transpiration velocity at the canopy tip, $v_h'^+$, emerges as a robust predictor of drag changes within this extended framework.

Abstract

Inspired by the spontaneous behaviour observed in filamentous layers -- where the balance between flow-induced drag and structural elasticity dictates the filaments' equilibrium streamlined posture -- we perform a series of large-eddy simulations to investigate how filament inclination affects turbulent shear flows developing both above and within a canopy of filaments. We examine six distinct filament inclination angles ranging from 0°to 90°. The in-plane solid fraction and filament length are chosen to achieve a fully dense canopy at zero inclination, and these parameters remain constant throughout our study. By setting a nominal bulk Reynolds number of 6000, we provide a detailed statistical characterisation of the turbulent flow. Our findings illustrate distinct changes in the flow regime with varying filament inclination. At lower angles, the canopy remains dense and significantly influences the flow, conforming to a classical canopy-flow regime. However, as the inclination approaches 90°, the intra-canopy region progressively becomes shielded from the outer flow. Remarkably, at 90°inclination, the flow drag reduces significantly, and the total drag becomes lower than that typically seen in an open, filament-free flow. We document this transition from a canopy-dominated regime to a scenario where the canopy becomes largely sheltered from the outer turbulent flow, highlighting key alterations in intra-canopy dynamics as filament inclination increases. Our observations are substantiated by an analysis of the velocity spectra, providing deeper insight into the interactions between the canopy and the developing turbulent boundary layer.

Figures (14)

• Figure 1: Sketch of the geometrical parameters governing our inclined canopy, constituted by solid cylindrical filaments with diameter $d$ arranged in squared tiles of size $\Delta S$. Their shape is defined by the angle of inclination ($\theta$), the sheath region ($h_s$), the length of the inclined region ($l_i$) and the frontal projected height ($h$).
• Figure 2: RMS velocity fluctuations and Reynolds stress profiles for all canopy configurations. Profiles are normalised using wall units: $u'$, $v'$, $w'$ and $\langle u'v' \rangle$ are scaled by $u_\tau$; $y^+$ is defined either from the wall-based friction velocity (i.e. $u_{\tau,in}$) or from the total stress at the canopy tip ($u_{\tau,out}$). This change in scaling definition introduces a small gap in the $y^+$ coordinate between approximately 3 and 8, visible across all cases. Marker shapes indicate different inclination angles, as defined in Table I, and colours follow a monotonic colormap (increasing with $\theta$) to help track trends.
• Figure 3: (a) Variation of the effective canopy height $k_{\mathrm{eff}} = h_\perp - y_{vo}$ with the filament spacing $\Delta S$, illustrating the geometric control of the canopy penetration depth across inclination angles. (b) Corresponding variation of the drag offset $\Delta U^+$ with the effective aspect ratio $\Lambda_{\mathrm{eff}} = k_{\mathrm{eff}}/\Delta S$. The logarithmic trend in panel (b) aligns with classical roughness-function behaviour, while panel (a) highlights the direct geometric influence of spacing on the flow-perceived canopy height. Red and blue symbols represents the data extracted from monti2020genesis and nicholas2022, respectively.
• Figure 4: Root-mean-square (r.m.s.) velocity fluctuations of the streamwise ($u'$), wall-normal ($v'$), and spanwise ($w'$) components, normalised using both outer and local friction velocities (see bottom row), for all canopy configurations. Markers correspond to those defined in Table I. A curved arrow indicates the direction of increasing inclination angle $\theta$ across configurations.
• Figure 5: Conventional approach for turbulence statistics with the origin at the canopy tip: (a) mean velocity, (b) r.m.s. velocity fluctuations, (c) Reynolds shear stress. Black, blue, and red curves represent $Re_{\tau}=326$ smooth wall, $\theta=77.5^\circ$, and $\theta=90^\circ$, respectively. Solid, dashed, and dotted lines (in b,c) are the streamwise, wall-normal, and spanwise components.