Shear-Stress Partitioning in Live Plant Canopies and Modifications to Raupach’s Model

Abstract

The spatial peak surface shear stress \({\tau _S^{\prime\prime}}\) on the ground beneath vegetation canopies is responsible for the onset of particle entrainment and its precise and accurate prediction is essential when modelling soil, snow or sand erosion. This study investigates shear-stress partitioning, i.e. the fraction of the total fluid stress on the entire canopy that acts directly on the surface, for live vegetation canopies (plant species: Lolium perenne) using measurements in a controlled wind-tunnel environment. Rigid, non-porous wooden blocks instead of the plants were additionally tested for the purpose of comparison since previous wind-tunnel studies used exclusively artificial plant imitations for their experiments on shear-stress partitioning. The drag partitioning model presented by Raupach (Boundary-Layer Meteorol 60:375–395, 1992) and Raupach et al. (J Geophys Res 98:3023–3029, 1993), which allows the prediction of the total shear stress τ on the entire canopy as well as the peak \({(\tau _S ^{\prime\prime}/\tau )^{1/2}}\) and the average \({(\tau _S^{\prime}/\tau )^{1/2}}\) shear-stress ratios, is tested against measurements to determine the model parameters and the model’s ability to account for shape differences of various roughness elements. It was found that the constant c, needed to determine the total stress τ and which was unspecified to date, can be assumed a value of about c = 0.27. Values for the model parameter m, which accounts for the difference between the spatial surface average \({\tau _S^{\prime}}\) and the peak \({\tau _S ^{\prime\prime}}\) shear stress, are difficult to determine because m is a function of the roughness density, the wind velocity and the roughness element shape. A new definition for a parameter a is suggested as a substitute for m. This a parameter is found to be more closely universal and solely a function of the roughness element shape. It is able to predict the peak surface shear stress accurately. Finally, a method is presented to determine the new a parameter for different kinds of roughness elements.

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Abbreviations

A f :

Roughness element frontal area

A :

Effective shelter area

C R :

Roughness element drag coefficient

C S :

Surface drag coefficient

R 2 :

Coefficient of determination

Re h  = U h h/ν:

Roughness element Reynolds number

S :

Total surface area per roughness element

S′:

Exposed surface area per roughness element

U δ :

Free stream velocity

\({\langle U_i \rangle}\) :

Spatiotemporally-averaged velocity inside the canopy

U h :

Mean velocity at top of roughness elements

V :

Effective shelter volume

a :

\({\tau _S ^{\prime\prime}/\tau _S^{\prime}}\) peak mean stress ratio

a i :

Fit parameters

b :

Roughness element width

b i :

Fit parameters

c, c i , c′ and c′′:

Constants of proportionality

h :

Roughness element height

m :

Parameter defining relation between \({\tau _S ^{\prime\prime}}\) and \({\tau _S^{\prime}}\)

u * = (τ /ρ)1/2 :

Friction velocity

u τ :

Skin friction velocity

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

Kinematic Reynolds stress

z 0 :

Aerodynamic roughness length

βC R /C S :

Roughness element to surface drag coefficient ratio

λA f /S :

Roughness density

\({\nu \approx 1.5\times 10^{-5} {m}^{2} {s}^{-1}}\) :

Kinematic viscosity of air

\({\Phi}\) :

Force on single roughness element

ρ :

Air density

σ :

Ratio of roughness element basal to frontal area

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

Total shear stress on entire canopy

τ R :

Shear stress acting on roughness elements

τ S :

Spatial average surface shear stress on area S

τ S (x, y):

Local surface shear stress

\({\tau _S^{\prime}}\) :

Spatial average surface shear stress on area S

\({\tau _S ^{\prime\prime}}\) :

Spatial peak surface shear stress

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Correspondence to Benjamin Walter.

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Walter, B., Gromke, C. & Lehning, M. Shear-Stress Partitioning in Live Plant Canopies and Modifications to Raupach’s Model. Boundary-Layer Meteorol 144, 217–241 (2012). https://doi.org/10.1007/s10546-012-9719-4

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Keywords

  • Boundary-layer flow
  • Drag partitioning
  • Irwin sensor
  • Shear-stress ratio
  • Vegetation canopy
  • Wind tunnel