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Field measurements of wind speed and reconfiguration in Arundo donax (Poaceae) with estimates of drag forces¹

Plant Biomechanics Group, Fakultät für Biologie, Albert-Ludwigs-Universität Freiburg, Schänzlestr. 1, D-79104 Freiburg, Germany

Received for publication November 14, 2002. Accepted for publication March 28, 2003.

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION LITERATURE CITED

 
The giant reed (Arundo donax) is well known as a species that can withstand high wind loads without mechanical damage. To examine wind impact, profiles of vertical wind speeds in the plant's natural habitat (southern France) were measured at the edge and within a stand in the main wind direction. Wind speed was recorded simultaneously at five heights. For 75 measurements of within-canopy wind speed profiles, the attenuation coefficient was 4.4 ± 0.5, a value typical for plant stands with very dense canopies. Video recordings proved that A. donax becomes streamlined with increasing wind speed, reducing the projected surface area of leaves and stem. The total projected surface area is a function of wind speed and can be characterized by a second-order polynomial regression curve. For small wind velocities up to 1 m/s, the calculated drag force is proportional to the square of the wind speed. However, when A. donax plants are subjected to higher wind speeds (1.5–10 m/s), the drag force becomes directly proportional to the wind speed. Streamlining is a potentially important adaptation for withstanding high wind loads, especially for individual plants and plants at the edge of stands, whereas in dense stands streamlining probably plays a minor role.

Key Words: Arundo donax • biomechanics • drag force • France • Poaceae • profiles of vertical wind speeds • projected surface area

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION LITERATURE CITED

 
Arundo donax L. plants grow in dense stands and are often planted in hedge rows to serve as wind shelter because the slender culms have a pronounced pliability and excellent wind resistance. Wind and gravity are the two basic forces that affect plants in a variety of ways (Fraser, 1962 ). Measurements of air movements, such as profiles of vertical wind speeds, are necessary to understand the biotic effects of wind (Grace, 1989 ). The shape of a vertical wind profile is characterized by the wind velocity, which changes with height above ground, surface roughness, and length of uniform surface over which the wind has blown (Campbell, 1977 ). Predictions of wind velocity within a canopy are complicated, but the wind velocity can be estimated by formulas suggested by Bussinger (1975) . Niklas and Spatz (2000) explored the effects of five different biologically realistic wind speed profiles on safety, wind-induced bending moments, and stresses generated in the stems of leafless cherry trees.

Overcritical wind loads may cause severe damage in forests, for example (cf. Gardiner and Quine, 1994 ; Coutts and Grace, 1995 ) but also, due to lodging, in crop plantings (cf. Crook and Ennos, 2000 ). While a plant is subjected to wind, it responds with streamlining, especially of its branches and leaves, a behavior that may significantly reduce the danger of mechanical damage caused by drag forces. Vogel (1989) has shown that the drag on leaves varies with wind speed, an effect caused by reconfiguration of the leaves. Daffodil flowers also change both shape and orientation in response to wind above 5 m/s, and both changes lead to reductions of their drag by 30% (Etnier and Vogel, 2000 ).

The ultimate aim of our studies on A. donax is to analyze how this plant avoids or reduces mechanical damage due to wind loads. To answer this question we have studied the plant's response to varying wind speeds and have quantified its oscillation and damping behavior (e.g., Spatz and Speck, 2002 ). Further, we examined the range and profiles of wind speeds with which these plants have to cope and the wind-induced streamlining of the plants. The objectives of this study were (1) to measure wind speed profiles and (2) to analyze the correlation between the drag force on the plant and the wind velocity.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION LITERATURE CITED

 
Field measurements were carried out in the natural habitat of A. donax in the Camargue (southern France).

Wind speed profile
Vertical wind speed profiles in an open area were measured at the edge of an approximately 4-m-high A. donax stand (0.5 m upwind in front of the stand) and at 9.0 m within this stand in the direction of the main wind (Fig. 1). Wind speed was recorded simultaneously at five heights on a mast. Four hot-wire anemometers were used to measure the wind speed at 1 m, 2 m (both custom-made devices), 3.52 m, and 5 m (both Tri-Sense Model No. 37000-00, Cole-Palmer, Niles, Illinois, USA) above ground. One lightweight three-cup anemometer (Casella, London, UK) was used to measure the average wind speed above the canopy (6.26 m high) during the experimental period. Seventy-five profiles of wind speeds within the canopy and 50 at the edge of the stand were measured. On average, a measurement was taken every 45 s.

View larger version (95K): [in this window] [in a new window]   Fig. 1. Shape of wind speed profiles at five heights above ground (1 m, 2 m, 3.52 m, 5 m, and 6.26 m), and the experimental setup at the edge of a stand of Arundo donax. Mean wind velocity and standard deviation are shown. The canopy averaged 4 m in height

where u_top is the wind speed at the top of the canopy, h the canopy height, a the attenuation coefficient, and z the height of measurement (0 z h). The attenuation coefficient ranges from 0 for very sparse canopies to 5 for very dense canopies (Niklas and Speck, 2001 ).

Projected surface area and wind speed
A side view of a typical A. donax plant (height: 3.3 m) was videotaped. The video camera (Sharp, Osaka, Japan, Model VL-C750S) was arranged in such a way that the connecting line between camcorder and plant was parallel to the main wind direction. The wind speed was measured with a hot-wire anemometer (Tri-Sense Model No 37000-00, Cole-Palmer), which records wind velocity only for the main wind direction. With a second camera (Sony, Japan, Model CCD-V800E), the display of the anemometer was videotaped. With a splitter (Panasonic, Osaka, Japan, Digital AV Mixer WJ-MX 20), the recordings of the bending plant and the corresponding wind speed were combined on one tape.

With the aid of Occulus frame grabber software (Computer Products, Inc.), selected video images were transferred onto the hard disk of a computer. Projected surface areas of individual images of stems and leaves were measured electronically with the software SECTION. This program was used to calculate the surface areas of specified regions of each image once the magnification of each image is set. For each image, the program was also used to measure the linear distance of markers fixed to the stem with respect to ground level (cf. Niklas and Spatz, 2000 ).

For individual objects in high Reynolds number flow, the drag force D_f(u) is related to the square of the ambient wind velocity and the projected surface area of stem and leaves of plants by the following equation:

where C_D is the drag coefficient, the density of air (1.29 kg/m³), and u the wind speed. Assuming that C_D = 1.0 (cf. Vogel, 1981 ; Niklas, 1994 ), the term 0.5 C_D equals 0.65. The projected surface area of stem and leaves, A_SL(u), depends on the wind speed. The drag force is proportional to the product of ambient wind speed squared times the total projected surface area of the plant [D_f(u) = 0.65 u² A_SL(u)].

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION LITERATURE CITED

 
Wind speed profile
Vertical wind speed profiles in an open area were measured at the edge of an A. donax stand (approximately 4 m high) and within this stand in the direction of the main wind. The mean wind velocity did not vary much during the 1 h, 35 min of the recording, except for individual gusts at different periods. Within the stand (Fig. 1), the average wind speeds ± SD of 75 recordings measured at four heights were 1.04 ± 0.23 m/s (1 m), 0.87 ± 0.16 m/s (2 m), 1.74 ± 0.39 m/s (3.52 m), and 6.43 ± 1.23 m/s (5 m), whereas above the canopy (6.26 m) an average wind speed of 6.01 m/s was found during the experimental period. At the edge of the stand, 50 measurements of wind speed averaged 2.42 ± 0.87 m/s (1 m), 3.56 ± 1.02 m/s (2 m), 3.22 ± 0.49 m/s (3.52 m), and 4.86 ± 0.66 m/s (5 m); above the canopy (6.26 m) an average wind speed of 4.92 m/s was measured. The average wind speed was considerably reduced within the vegetation compared to values found at the edge of the stand. In addition, the probability of wind peaks is considerably reduced in the stand, which is mirrored by the very small standard deviations of wind speeds within the stand. Both findings are a consequence of the "self-sheltering effect" caused by the dense stand growth. In both profiles, the wind velocity abruptly increased above the closed canopy. In the latter case, the values within the vegetation exceeded those measured at the edge.

For 75 profiles of wind speeds, the attenuation coefficient was calculated following Eq. 1 and yielded on average 4.4 ± 0.5. This value is typical for dense stands of plants with uniform shapes and heights (cf. Campbell, 1977 ).

Projected surface area and estimated drag
The video recording showed that A. donax streamlines and tends to reduce the projected surface area of leaves and stems with increasing wind speed. Even at relatively low wind speeds, the leaves start to orientate leeward and the apicalmost stem part begins to bend. At higher wind speeds, the leaves flutter and are entirely streamlined, and the stems curvilinearly bend with an acropetally increasing curvature. At the highest wind speed measured (10 m/s), the maximum height of the plant is reduced by 45%. The correlation of wind speed and total projected surface area can be characterized by a decreasing second-order polynomial (Fig. 2), mirroring the streamlining of the plant.

View larger version (21K): [in this window] [in a new window]   Fig. 2. The relationship between wind speed and total projected surface area of an individual plant of Arundo donax. The second-order polynomial regression curve has a coefficient of determination of R2 = 0.9742

View larger version (20K): [in this window] [in a new window]   Fig. 3. The relationship between wind speed and drag force of an individual plant of Arundo donax. The drag force is calculated using Eq. 2 (see text), where the projected surface area is a function of wind speed (see Fig. 2 ). For small wind velocities up to 1 m/s (see inset), the drag force is proportional to the square of the wind velocity (R2 = 0.994), whereas a linear proportionality results for higher wind speeds between 1.5 and 10 m/s (R2 = 0.988)

Streamlining seems to mainly benefit plants growing in isolation or at the edge of the stand. Within the stand, wind speeds are low (<1.7 m/s) and streamlining probably plays a minor role. However, at the edge, where wind velocities are up to 3.6 m/s, the drag force is significantly reduced due to streamlining. In addition, plants growing in stands interact and may form a drag-reducing aerodynamic unit, especially at high wind speeds, an effect well known from compound leaves (Vogel, 1989 ). Thus, streamlining may permit plants to survive at the edge and facilitate progressive growth of clonal stands. On the other hand, through "self-sheltering" stand growth apparently removes the threat of wind-damage for the great bulk of the plants.

	FOOTNOTES

 
¹ The author wishes to thank Prof. Dr. K. J. Niklas for fastidious measurements of the projected surface areas. I am grateful to Prof. Dr. T. Speck for his help with the field experiments and to Prof. Dr. H.-Ch. Spatz for helpful discussions. I also thank two anonymous reviewers for helpful criticism of the manuscript. This study was in part supported by the DaimlerChrysler AG and Alumni Freiburg.

² Phone: +49 (0)761-203-2803; FAX: +49 (0)761-203-2804; e-mail: olga.speck{at}biologie.uni-freiburg.de

	LITERATURE CITED

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION LITERATURE CITED

 
Bussinger J. A. 1975 Aerodynamics of vegetated surfaces. In D. A. DeVries and N. H. Afgan [eds.], Heat and mass transfer in the biosphere, 104–119. Wiley, New York, New York, USA

Campbell G. S. 1977 An introduction to environmental biophysics. Springer, Ulm, New York, New York, USA

Coutts M. P. J. Grace [eds.] 1995 Wind and trees. Cambridge University Press, Cambridge, UK

Crook M. A. R. Ennos 2000 A field based method of quantifying the lodging resistance of wheat cultivars. In H.-Ch. Spatz and T. Speck [eds.], Plant biomechanics 2000, 315–320. Thieme, Stuttgart, Germany

Etnier S. E. S. Vogel 2000 Reorientation of daffodil (Narcissus: Amaryllidaceae) flowers in wind: drag reduction and torsional flexibility. American Journal of Botany 87: 29-32[Abstract/Free Full Text]

Fraser A. I. 1962 Wind tunnel studies of the forces acting on the crown of small trees. Report on Forest Research 178–183

Gardiner B. A. C. P. Quine 1994 Wind damage to forests. Biomimetics 2: 139-147

Grace J. 1989 Measurements of wind speed near vegetation. In R. W. Pearcy, J. R. Ehleringer, H. A. Mooney, and P. W. Rundel [eds.], Plant physiological ecology, 57–73. Chapman and Hall, New York, New York, USA

Niklas K. J. 1992 Plant biomechanics: an engineering approach to plant form and function. University of Chicago Press, Chicago, Illinois, USA

Niklas K. J. 1994 Plant allometry: the scaling of form and process. University of Chicago Press, Chicago, Illinois, USA

Niklas K. J. H.-Ch. Spatz 2000 Wind-induced stresses in cherry trees: evidence against the hypothesis of constant stress levels. Trees 14: 230-237[CrossRef]

Niklas K. J. T. Speck 2001 Evolutionary trends in safety factors against wind-induced stem failure. American Journal of Botany 88: 1266-1278[Abstract/Free Full Text]

Spatz H.-Ch. O. Speck 2002 Oscillation frequencies of tapered plant stems. American Journal of Botany 89: 1-11[Abstract/Free Full Text]

Vogel S. 1981 Life in moving fluids. Willard Grant Press, Boston, Massachusetts, USA

Vogel S. 1989 Drag and reconfiguration of broad leaves in high winds. Journal of Experimental Botany 40: 941-948[Abstract/Free Full Text]

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