Outlook

Results (Model Modification)

Results (Model Parameters and Performance)

Application and Improvement of Raupach’s Shear Stress Partitioning Model (EP41E-0842)

Benjamin Walter1, C. Gromke1,2, M. Lehning1,3

1 WSL Institute for Snow and Avalanche Research SLF, Davos Dorf, Switzerland2 Unit Building Physics and Systems, Eindhoven University of Technology, Eindhoven, Netherlands

3 CRYOS, Civil and Environmental Engineering, École Polytechnique Fédéral de Lausanne, Switzerland

- Aeolian processes like the entrainment, transport and redeposition of sand, soil or snow can have strong implications on our environment (land degradation, desertification, dust storms, … ).

- Reliable predictions of the sheltering effect of vegetation canopies against wind erosion are necessary e.g. to identify suitable and sustainable counteractive measures and for modeling aeolian processes.

- The model of Raupach (1992 and 1993) is a useful tool to quantify the sheltering effect of vegetation. However, the model includes parameters that are still relatively unspecified for vegetation canopies, and some of them are difficult to determine experimentally.

- We present an improvement of the model by specifying the parameters for a live plant canopy and by slightly modifying the model to improve its applicability.

Fig. 1: Exemplary surface shear stress τs(x,y) measurements using Irwin sensors. (a) and (c) for a live plant canopy and (b) and (d) for a wooden block array

References & Acknowledgments

Summary & Discussion Introduction

Methods

• Raupach MR (1992) Drag and Drag Partition on Rough Surfaces. Boundary-Layer Meteorology 60:375-395

• Raupach MR, Gillette DA, Leys JF (1993) The Effect of Roughness Elements on Wind erosion Threshold. Journal of Geophysical Research 98:3023-3029

This poster is based on the work presented in:

• Walter B, Gromke C, Lehning M (2012) Shear stress partitioning in live plant canopies and modifications to Raupach’s model. Boundary-Layer Meteorology, doi:10.1007/s10546-012-9719-4

We would like to thank the Vontobel foundation and the Swiss National Science Foundation (SNF) for financing this project.

- Results are based on spatially resolved surface shear stress τs(x,y) measurements in live plant canopies under controlled wind tunnel conditions (Fig. 1).

- Similar measurements in block arrays for comparison.

- 3 different plant/block densities: λ ≈ 0.017, 0.09, 0.2

- Data used to investigate the influence of the plants flexibility and porosity on the sheltering effect.

1. The c - parameter:

- Relates the size of an effective shelter area/volume to flow parameters. Important for the total stress prediction:

- So far: c was poorly specified; Now: c ≈ 0.27 ± 0.2

- c = 0.27 allows for more accurate predictions of the total stress τ = ρu*

2 on a canopy of interest (Fig. 2).

Fig. 2: Normalized friction velocity u* against roughness density λ

3. The m - parameter:

- Original definition to relate the peak stress τs'' with τs' :

Fig. 4: m-parameter against λ for the plants and the blocks at different free stream velocities Uδ

4. Modification: the a - parameter:

- New definition: the peak-mean stress ratio:

2. The average surface shear stress τs' :

- τs' is the key when quantifying particle mass fluxes.

- New: Model predicts difference in τs' between two different roughness elements (plants / blocks) correctly (Fig. 3).

- Reversal in the sheltering effect from low to high roughness densities (relative to the block results). This can be explained by the plants flexibility and porosity.

Fig. 3: Normalized τs' against roughness density λ.

Fig. 5: Peak stress τs'' against average stress τs'.

- m is a function of λ, the Reynolds number Re or Uδ and the roughness element shape (Fig. 4)

Difficult to determine m experimentally

- Strong linearity found between τs'' and τs' for all setups

- a is found to be independent of λ and Re and solely a function of the roughness element shape (Fig. 5)

a is experimentally much easier to determine than m

- Goal: determine m for various plant morphologies

1. The so far unspecified model parameter c is found to be c = 0.27.

2. Characteristics such as the porosity, the flexibility and the shape of the roughness elements can have complex influences on the stress partition and its dependency on λ (Fig. 3).

3. The empirical model parameter m is found to be impracticably defined in Raupach’s model (Fig. 4). A new, more physically-based definition of a peak-mean stress ratio, the a - parameter is suggested.

4. Our plant canopies partly differ from natural vegetation canopies, however, they are far closer to natural canopies than any roughness array used in previous wind-tunnel investigations.

5. The results may be similar for other plant species with similar morphology.

Potential future model improvements:

1. Quantifying the flexibility of the plants: The flexibility results in a higher horizontal coverage of the surface and a strong fluttering capability of the plants at higher wind speeds.

2. Determine the model parameters σ, β and a for a range of different plant species with variations in morphology, flexibility and porosity. Such a dataset can then be used by modelers and practitioners.

λ = 0.087 λ = 0.078

λ = 0.017 λ = 0.017