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Spatio-Temporal Surface Shear-Stress Variability in Live Plant Canopies and Cube Arrays


This study presents spatiotemporally-resolved measurements of surface shear-stress τ s in live plant canopies and rigid wooden cube arrays to identify the sheltering capability against sediment erosion of these different roughness elements. Live plants have highly irregular structures that can be extremely flexible and porous resulting in considerable changes to the drag and flow regimes relative to rigid imitations mainly used in other wind-tunnel studies. Mean velocity and kinematic Reynolds stress profiles show that well-developed natural boundary layers were generated above the 8 m long wind-tunnel test section covered with the roughness elements at four different roughness densities (λ = 0, 0.017, 0.08, 0.18). Speed-up around the cubes caused higher peak surface shear stress than in experiments with plants at all roughness densities, demonstrating the more effective sheltering ability of the plants. The sheltered areas in the lee of the plants are significantly narrower with higher surface shear stress than those found in the lee of the cubes, and are dependent on the wind speed due to the plants ability to streamline with the flow. This streamlining behaviour results in a decreasing sheltering effect at increasing wind speeds and in lower net turbulence production than in experiments with cubes. Turbulence intensity distributions suggest a suppression of horseshoe vortices in the plant case. Comparison of the surface shear-stress measurements with sediment erosion patterns shows that the fraction of time a threshold skin friction velocity is exceeded can be used to assess erosion of, and deposition on, that surface.

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A f :

Roughness element frontal area

D :

Average roughness element diameter

Q :

Mass transport rate

Re h = U δ h/ν :

Roughness element Reynolds number

S :

Ground area per roughness element

U δ :

Free-stream velocity

U s :

Wind speed at Irwin sensor-tube height

c 1 and c 2 :


d :

Sand grain diameter

f = 20 kHz:

Hot-film sampling frequency

f c :

Cut-off frequency

h :

Roughness element height

h s :

Irwin sensor tube height

m :

Parameter relating \({\tau_{\rm s}^{\prime \prime}}\) to τ s

Δp :

Pressure difference measured by Irwin sensor


Fluctuations over pressure signal

u :

Mean streamwise wind velocity


Fluctuations in mean streamwise wind velocity

\({u_\ast=(\tau/\rho)^{1/2}}\) :

Friction velocity

u *t :

Fluid threshold friction velocity

\({u_{\tau}=(\tau_{\rm s}/\rho)^{1/2}}\) :

Skin friction velocity

u τ t :

Fluid threshold skin friction velocity

\({\overline {{u}^{\prime}{w}^{\prime}}}\) :

Kinematic Reynolds stress


Fluctuations in mean vertical wind velocity

β c :

Irwin sensor calibration constant

β :

Ratio of roughness element to surface drag coefficient

λ :

Roughness density

ν :

Kinematic viscosity of air

\({\psi}\) :

Percentage of time that threshold skin friction velocity is exceeded

ρ :

Air density

σ :

Ratio of roughness element basal to frontal area

σ u :

Standard deviation of wind speed U s

\({\tau=\rho u_\ast^2 }\) :

Total shear stress averaged over whole canopy

τ R :

Shear stress acting on roughness elements

τ s(t, x, y):

Shear stress acting on surface

\({\tau_{\rm s}^{\prime \prime}}\) :

Spatial peak of temporally-averaged surface shear-stress distribution

τ s0 :

Spatiotemporally-averaged surface shear stress in the absence of roughness elements

\({\xi}\) :

Normalized turbulence intensity


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Correspondence to Benjamin Walter.

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Walter, B., Gromke, C., Leonard, K.C. et al. Spatio-Temporal Surface Shear-Stress Variability in Live Plant Canopies and Cube Arrays. Boundary-Layer Meteorol 143, 337–356 (2012).

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  • Aeolian processes
  • Drag partitioning
  • Particle erosion
  • Surface shear-stress
  • Turbulent boundary-layer
  • Vegetation aerodynamics