Airflow and roughness characteristics over partially vegetated linear dunes in the southwest Kalahari Desertкод для вставкиСкачать
EARTH SURFACE PROCESSES AND LANDFORMS, VOL. 21, 19-34 (1996) AIRFLOW A N D ROUGHNESS CHARACTERISTICS OVER PARTIALLY VEGETATED LINEAR DUNES IN THE SOUTHWEST KALAHARI DESERT GILES F. S. WIGGS: Shefield Centre for International Drylands Research, Department of Geography, The University, Western Bank, Shefield, SlO 2TN, U.K. IAN LIVINGSTONE: School of Environmental Science, Nene College, Northampton "2 7AL, U.K. DAVID s. G. THOMAS AND JOANNA E. BULLARD~ Shefield Centre for International Drylands Research, Department of Geography, The University. Western Bank, Shefield, S10 ZTN, U.K. Received 1 September 1993 Accepted 15 August 1994 ABSTRACT There is little understanding of the flow-field surrounding semi-vegetatedlinear dunes, and predictions of dune mobility are hampered by a lack of empirical data concerning windflow. In an attempt to characterize the near-surface airflow upwind of and over partially vegetated linear dunes in the southwest Kalahari Desert, this study presents measurements of vertical and horizontal wind velocity profiles across cross-sectional transects of seven partially vegetated linear dunes. Vegetation surveys combined with velocity measurements from vertical arrays of cup-anemometers, placed up to 2.3 m above the ground surface, were used to gain information concerning the modification of airflow structure caused by the intrusion of the dunes into the atmospheric boundary layer and to predict the variability of aerodynamic roughness (zo) from interdune to crest. The results suggest an acceleration of flow up the windward slopes of the dunes and, as such, the data correspond to classical theory concerning flow over low hills (essentially Jackson and Hunt (1975) principles). Where the theory is incapable of explaining the airflow structure and acceleration characteristics, this is explained, in part, by the presence of a spatially variable vegetation cover over the dunes. The vegetation is important both in terms of the varying aerodynamic roughness (20) and problems concerning the definition of a zero-plane displacement ( d ) .It is considered that any attempts to characterize surface shear stress over the Kalahari linear dunes, in order to predict sand transport and dune mobility, will be hampered by two problems. These are the progressively non-log-linear nature of the velocity profiles over the dunes caused by flow acceleration, and the production of thin near-surface boundary layers caused by areally variable aerodynamic roughness as a result of the partially vegetated nature of the dunes. KEY WORDS Kalahari Desert; linear dunes; vegetation; airflow; aerodynamic roughness; zero-plane displacement; shear stress; velocity profiles INTRODUCTION In the past 10 to 15 years, several studies have investigated dune movement and windflow at the scale of the individual dune (e.g. Knott, 1979; Livingstone, 1986; Mulligan, 1988; Tsoar, 1978, 1983; Warren and Kay, 1987; Wiggs, 1992). The value of studying dune dynamics at this scale is that it is possible to examine the local effect of the intrusion of a dune into the atmospheric boundary layer. The feedback processes between airflow and dune morphology have been the focus of attention for several investigators (Burkinshaw et al., * Formerly at: School of Natural and Environmental Sciences, Division of Geography,Coventry University, Coventry,CVl 5FB, U.K. 'Currently at: Department of Geography, University of Keele, Keele, STS SBG, U.K. CCC 0 197-9377/96/0 100 19- 16 0 1996 by John Wiley & Sons, Ltd. 20 G. F. S. WIGGS, I. LIVINGSTONE, D. S. G. THOMAS AND J. E. BULLARD 1993; Howard et af.,1977; Tsoar, 1978, 1983). However, there is still much debate as to the character of the flow-field surrounding sand dunes (Lancaster, 1985, 1987; Livingstone, 1986; Watson, 1987; Wiggs, 1992, 1993). In particular, despite some broader scale studies concerning the stabilizing effect of vegetation on sand dunes (Ash and Wasson, 1983) and more detailed investigations of the protective role of sparse vegetation on flat surfaces (Wolfe and Nickling, 1993), there has been no investigation of the effect of a partial vegetation cover on linear dune aerodynamics. This is important because linear dunes, which are the most areally extensive dune form on a global scale, commonly support a vegetation cover. This paper is concerned with characterizing the near-surface airflow upwind of and over partially vegetated linear dunes in the southwest Kalahari Desert. The study was carried out as part of a larger project to examine the dynamics and palaeoenvironmental significance of the Kalahari dunes; data concerning the patterns of erosion and deposition on the dune surfaces are presented by Wiggs et af. (1995). The aim of the part of the project presented in this paper was to measure vertical and horizontal wind velocity profiles across cross-sectional transects of linear dunes, with the intention of broadening our understanding of the modification of airflow structure caused by the intrusion of a dune into the atmospheric boundary layer. The air/dune interface is complicated in this study by the presence of vegetation on the linear dune surfaces in varying degress of cover. A further aim was to characterize the effect of this partial vegetation cover on airflow over the dunes in terms of the aerodynamic roughness (zo) and zero-plane displacement ( d ) , both of which are highly important to any assessment of shear stress and predictions of sand transport on the dune surfaces. VEGETATION CHARACTERISTICS AND AIRFLOW STRUCTURE: MEASUREMENT TECHNIQUES As part of a wider study, seven dune sites were selected in the southwest Kalahari for aerodynamic measurements during October and November 1992 (Figure 1). The dunes, which were surveyed with a theodolite and EDM, were all partially vegetated and of linear type, varying in the height from 3 to 13m. The vegetation characteristics at each of the sites varied markedly, and were assessed in the field using a combination of a quadrat analysis to determine ground cover and mean plant height (h), and transect measurements to assess plant spacing. At each dune site, the vegetation cover was measured on each of the visually determined morphological units (i.e. interdune, slope, crest, etc.). Further details concerning this procedure are reported by Wiggs et al. (1995). In studying the relationships between airflow and sand dune morphology it is important to measure wind velocity within the inner layer ( I ) , defined in Figure 2, because it is within this region of flow, close to the surface, where turbulent transfer processes become dynamically significant (Jackson and Hunt, 1975). Taylor et al. (1987) describe it as the depth of flow where changes in shear stress and turbulent structure caused by the intrusion of the dune into the airflow are greatest, and where feedback mechanisms between the airflow and the dune surface can be assumed to be important. The depth of the inner layer (0 is generally assumed to be governed by the half-length of the dune (L)and the upwind roughness (zo), as defined by Jackson and Hunt (1975): where I = inner-layer depth, L = dune half-length (upwind length at half-height), zo = aerodynamic surface roughness and R = von Karman’s constant (0-4). The operation of equation 1 has been examined by Rasmussen et al. (1985) and others (see Taylor et af. (1987) for a review). It has been noted that the equation overestimates the value of 1 by about one-third. Preference has therefore been given to an alternative relationship presented by Jensen et al. (1984): where f1 = inner-layer depth. 21 SEMI-VEGETATED LINEAR DUNES jji 26Q30' 920 -- =s=,-=-- River A, Site - 0 Road m902 Spot Height (m) krn 20 Figure 1. Map of the southwest Kalahari and Kalahari and Kalahari Gemsbok National Park showing experimental sites 22 G . F. S. WIGGS, I. LIVINGSTONE, D. S. G . THOMAS AND J. E. BULLARD i Upper Layer er Layer Figure 2. Schematic showing and structural zones of airflow over sand dunes and important length scales (from Jackson and Hunt, 1975). L is dune half-length; H is maximum dune height; I is inner layer depth The validity of the calculations for the depth of the inner layer on sand dunes is uncertain as few have been empirically tested (although see Wiggs (1992)). Nevertheless, the dunes in the present study were chosen for investigation partly because their size suggested that they would support an inner-layer of the order of 1 to 2m, using either Equation 1 or 2. Such a depth of flow is measurable with the use of rotating-cup anemometers, as used in this investigation. Anemometers were arranged in vertical arrays at heights of 0 5 0 . 8 , 1.0, 1.3, 1.8 and 2.3 m. The upper limit of the anemometer heights was determined by practical limitations, although it was also of sufficient distance from the surface to encompass a wide range of inner-layer depths. Furthermore, it was sufficiently close to the surface to negate the need to account for airflow instability induced by excessive surface heating. Rasmussen et af. (1985) found that at near-surface heights, such as those used in this study, the effect of buoyancy in the production of shear stress was not significant. A lower anemometer height limit of 0.5 m was imposed by the height of the vegetation canopies, which were of the order of 0.3-0.6 m. The anemometers were positioned upwind, on the windward slopes and on the downwind flanks and interdunes of the dune sites on cross-sectional transects perpendicular to the crests of the dunes from interdune to interdune. Aidow measurement at any one site was only carried out when the wind direction was concordant with the anemometer transect. The horizontal distance between vertical anemometer arrays varied according to individual circumstances at each of the sites. In most cases, however, the arrays were spaced between 15 and 20 m apart on the windward slopes, and up to 30 m apart on the downwind interdunes. The anemometers were connected to electronic loggers, and data were downloaded to computer at the end of each measurement sequence. Each recording was of windspeed averaged over a period of 1 min. However, each individual array was left in position for between 30 and 60 min. Two anemometer arrays were erected at any one time, each array consisting of six anemometers. It was therefore necessary to use one set of anemometers as a 'mobile' array, moving it every 30 to 60min to a new measurement position on the transect, and one set as a reference array. At each site the reference array was positioned at the crest of the dune and all data measured by the mobile array were normalized by the reference measurements. This is common practice where associated measurements have been taken at different times (e.g. Lancaster, 1989; Livingstone, 1986; Mulligan, 1988; Wiggs, 1992). Such a technique has been substantiated by Bradley (1980), who noted that the variability in windspeed had little effect on the shape of a normalized profile. The normalizing procedure adopted in this study was similar to that used by Jackson and Hunt (1975) and Tsoar (1985). It involved the calculation of a perturbation in velocity from the reference measurement (termed 'fractional speed-up ratio' by Jackson and Hunt (1975)): where 6, =velocity perturbation, u, = velocity at height z and u, = reference velocity at height z. 23 SEMI-VEGETATED LINEAR DUNES The result occurs as a fraction which is analogous to the percentage speed-up (e.g. 6,= 0.1 5 represents an increase in speed compared to the reference of 15 per cent). The winds during the 10 week study period, measured by a meteorological station at a height of 3.5 m at Twee Rivieren (Figure l), were mostly southwesterly (reaching maximum strength between 10 am and 3 pm), with a mean hourly maximum of 7.54 m s-’ and mean of 2.29 m s-l. UPWIND VELOCITY PROFILES AND ROUGHNESS (zO) CALCULATIONS At each of the sites, vertical velocity profiles were measured on the upwind interdunes in order to assess the relationships between upwind roughness characteristics and vegetation geometry. The upwind velocity profiles are shown to correspond to the Kirmin-Prandtl logarithmic velocity profile law: where u, = shear velocity (m s-’), K, = von Karmin’s constant (0.4), zo = aerodynamic roughness (m) and d = zero-plane displacement (m). An example is shown in Figure 3, which presents upwind velocity profiles measured on the interdune at site F, where the mean height of vegetation upwind of the anemometer array was 0.5m. the six profiles shown here result from 5 min means of windspeed, and are seen to display near log-linear profiles. Similar profiles were apparent at each of the other sites. Extrapolation of the profiles to the ‘surface’ (i.e. where windspeed approaches zero) gives an assessment of the aerodynamic roughness of the surface (zo). The aerodynamic roughness is a function of the height, density and porosity of the roughness elements (i.e. the vegetation characteristics). The velocity extrapolations to the y-axis intercept, shown in Figure 3, are based on regression analysis of the form: y=mx+c where U, = tw~and zo = exp(-c/m) after Wilkinson (1983/84). In Figure 3 the mean zo is 0.024m, a fairly typical value for low-lying shrubs in this environment (Lee, 0.0 0.5 1 .o 1.5 2.0 Wlndspeed 2.5 3.0 3.5 4.0 (mls) Figure 3. Velocity profiles measured on the upwind surface at site F. The six profiles shown here result from 5 min means of windspeed. Mean aerodynamic roughness (zo) is estimated from the extrapolation of the velocity profiles onto the y-axis 24 G. F. S. WIGGS, I. LIVINGSTONE, D. S. G. THOMAS AND J. E. BULLARD 1991; Wiggs, 1992). An approach such as this is commonly used to calculate the near-surface shear velocity (u,) on unvegetated sand dunes, from which Bagnold-type sand transport rate equations are used to deter- mine the sand flux and hence dune dynamics (Howard et al., 1977; Lancaster, 1985; Wiggs, 1992). However, in the case of partially vegetated dunes the process is considerably complicated because u, is highly dependent upon the values of zo and d (see Equation 4), and both of these important parameters are principally determined by the vegetation characteristics on the dune. Furthermore, the magnitude of zo is highly dependent upon the chosen value for the zero-plane displacement (4.The question therefore arises as to the magnitude of variations in zo and d across dune slopes consequent upon changes in vegetation density and cover. A common definition of the zero-plane displacement height is the level which would be obtained by flattening out all the roughness elements into a smooth surface (Jackson, 1981). it is the height to which the velocity profile should be referenced, so all height measurements taken from the surface should have d subtracted from them (see Equation 4). Some research, however, suggests that d is the level of the mean momentum sink (Thom, 1971), with zo being the length scale which expresses the magnitude of the forces that act on the surface, and d related to the distribution of these forces. It is therefore at an elevation d at which the mean drag appears to act. For a large range of flows, the approximation d f h = 0.7 is considered reasonably good (Jackson, 1981), where h is defined as the mean vegetation canopy height. Nevertheless, there is a complex relationship between d, zo and roughness element geometry, which has yet to be fully understood (Lee, 1991). Where roughness elements are relatively widely spaced, one would expect the zo to be determined by the geometry of the roughness elements and d to be small, having a value just above the base of the roughness elements. At the opposite extreme, where the roughness elements are so dense that their tops are touching, the flow would skim across the gaps, the apparent zo would decrease (being controlled only by the roughness of the tops of the canopies), d would approach the scale of the roughness elements, and u, in the fluid trapped beneath the canopy would be zero (Jackson, 1981). So, zo is small for both very wide and very closely spaced objects. Some studies (Lee, 1991) have found d lying above the tops of shrubs with a very small zo. Lee considered that this was due to the flow responding to an apparent drag created by turbulent eddies between (and extending above) the shrubs, not just drag from flow contact with the shrubs themselves. Within this domain of uncertainty, the upwind d value for each of the sites in this investigation was determined by subtracting a value from the height data of the measured vertical velocity profiles which resulted in the greatest improvement in the regression analysis correlation statistic (i.e. d was considered to be the value which improved the log-linearity of the upwind velocity profile to the greatest degree). This is a typical method of d determination (Cook, 1977; Stearns, 1970; Wiggs, 1992). Table I presents values for mean upwind vegetation height (h),zero-plane displacement (d), upwind aerodynamic roughness (zo) and mean shear velocity (u,) during the measurement periods for all the dune sites. From Table I it can be seen that a d value could not be determined for two of the sites. At sites D1 and E, burning and grazing, respectively, had destroyed the vegetation canopy to such an extent that the roughness Table I. Aerodynamic parameters of the upwind interdune areas at each site (m) d (m) 10 (m) zo/h dlh u, (ms-'1 na. not available A B C 0.6 0.12 0.032 0.054 0.2 0.298 0.5 0.3 0.023 0.046 0.6 0.356 0.5 0.3 0.036 0.072 0.6 0.346 D1 0.3 na 0.006 0.022 na 0.463 D2 E F 0.5 0.3 0.046 0.093 0.6 0.572 na 0.5 0.15 0.024 0.048 0.3 0.266 na 0.012 na na 0.283 25 SEMI-VEGETATED LINEAR DUNES elements were acting in isolation from each other. The roughness was therefore not acting as a single unit in exerting a drag on the airflow and so no zero-plane displacement (responding to vegetation) could be identified. For those sites where a d value could be determined, it can be seen from Table I that d / h varied between 0.3 and 0.6, with a median value of 0.6. This corresponds well with the value of 0.7 suggested by Jackson (1 98 1). The zo values shown in Table I, ranging from 0.006 to 0-046m, are of the expected order of magnitude. The sites where vegetation had largely been destroyed (sites D1 and E) exhibit the smallest values of zo, and those where vegetation was visually perceived to be quite dense (sites A and D2) show the highest values of zo. The relationship between zo and vegetation characteristics can be examined by calculating the roughness element concentration (A), after Raupach et al. (1980): X = hw/D2 (5) where hw = mean silhouette area of vegetation (mean height x mean width) and D =mean distance between plants. The roughness element concentration in this investigation was calculated from the site vegetation surveys (see Wiggs et af. (1995) for details). Figure 4 shows the relationship noted in this investigation between upwind zo and upwind A. As found by Lee (1991), the relationship in this investigation is a positive one (r2 = 0.82), significant at the 0.02 significance level. Figure 4 does not include data from site D1. Due to a data collection error, the vegetation survey and velocity profile measurements were acquired from different parts of the interdune and so the analyses of roughness element concentration and aerodynamic roughness did not match. On this basis, the results from site D2 were discarded from further analysis. VARIATIONS IN AERODYNAMIC ROUGHNESS ACROSS DUNE TRANSECTS Using the regression equation presented in Figure 4,describing the relationship between upwind zo (aerodynamic roughness) and A, it is possible to estimate zo for each of the geomorphological units on the dune transects from the apparent roughness element concentration determined from the vegetation surveys. It is necessary to estimate aerodynamic roughness in this way, rather than from measured velocity profiles, because velocity profiles on dune slopes are non-log-linear (Mulligan, 1988; Wiggs, 1992) and hence it is very difficult to extrapolate zo from them. Three examples of the results from sites A, C and D2 are shown in Figures 5A, B and C, respectively. From Figures 5A and B it is apparent that minima in estimated zo occur at crests while maxima occur on the interdunes or plinths. However, such relationships are not universal in the Kalahari dunefield. For example, the estimated zo for site D2 (Figure 5C) shows a maximum value on the interdune and a minimum of the plinth. 0 0.05 0.1 0.15 0.2 0.25 Roughness element concentration (1) Figure 4. Relationship between upwind aerodynamic roughness (zo) and roughness element concentration (A) at each of the experimental sites 26 G. F. S. WIGGS, I. LIVINGSTONE, D. S. G . THOMAS AND J. E. BULLARD It is also noticeable from Figure 5C that the two interdune estimates of zo are widely disparate (from 0.028 m on one side to nearly 0.049 m on the other). The range in zo across a single dune transect is also apparent. At site A (Figure 5A) the estimated zo ranges from 0.021 m at the crest to 0.032 m at the plinth. From the estimates of zo shown in Figures 5A, B and C , several important considerations arise. First, the apparent upwind zo, which in part determines the configuration of any approaching velocity profile, is highly dependent upon the direction of the prevailing wind. This is because the interdune regions within a partially vegetated dune system do not have a uniform value of zo (Figure 5C). Secondly, the intradune variation in zo makes the successful assessment of near-surface shear velocity (u,) from Equation 4 very difficult. This is because at each step-change in zo, as the wind flows across a dune transect, an internal boundary layer will be propagated which will not have grown to a measurable depth (at least 0.5 to 1.0 m) before a further internal boundary layer is created, of differing turbulent characteristics. Furthermore, as zo alters in relation to the vegetation characteristics, so too does the zero-plane displacement ( d ) . This means that different portions of a velocity profile at a single measurement point on a dune surface are responding to different surface characteristics. The upper part of a velocity profile will reflect A 0.028 0.026 0.024 0.022 4 V ~ 1 interdune 0.02 crest plinth I plinth interdune Geomorphological Unit 0.015 int. 0.05 plinth crest plinth int. plinth crest Geomorphological unit plinth slope pan - c ’gE g 0.045 .. 8 - 9 % 8 Y 0.04 .. 0.035 .. I 0.02 4 interdune plinth crest plinth interdune Geomorphological Unit Figure 5 . Cross-sectional transects of estimated aerodynamic roughness (20) at sites A (A), C (B) and D2 (C) SEMI-VEGETATED LINEAR DUNES 27 surface conditions somewhere upwind of the measurement point, whilst the lower part will be responding to conditions closer to the measurement point. AIRFLOW STRUCTURE OVER THE DUNES In the following discussion, only the results from site A are presented in graphical form. Results of a similar nature are apparent at each of the other sites and are summarized in the relevant tables. Figure 6 shows the fractional speed-up ratio (&), calculated from Equation 3, at six constant heights above the surface of site A. The data presented in this figure were initially normalized by the reference array at the crest of the dune. However, for ease of analysis, the data were then transformed by assuming a constant 10ms-’ approach flow, and subsequently normalized (using Equation 3) with reference to the upwind array. In general terms, Figure 6 indicates an increase in wind velocity, compared to upwind values, along the windward slope of the dune at all measured heights. The maximum velocity is found within the crest region whilst donwnwind of this, in the lee region, the velocity is retarded to below upwind values (measured downwind of the visually determined leeside separation vortex). At a distance lOOm downwind from the crest, the velocity at the majority of measured heights has recovered to equal upwind magnitudes. The trend in the horizontal fractional speed-up ratio cross-section noted in Figure 6 is similar to that found by Howard et al. (1977), Livingstone (1986), Wiggs (1992) and Burkinshaw et al. (1993) over sand dunes, and demonstrated over fixed hills by Walmsley and Salmon (1984), Jensen and Zeman (1985), Taylor et al. (1987) and Hunt et al. (1988). It conforms to the expected pressure gradient over the dune. A decline in pressure as the streamlines converge on the windward face of the dune results in the wind being accelerated to a maximum near the crest. The erratic nature of the results at 0.5m is likely to be due to the local effects of vegetation interference and for this reason these results are discarded from further analysis. A notable difference from the results of Howard et al. (1977) and Wiggs (1992), however, is the absence of a clear region of airflow deceleration upwind and at the toe of the dune. Such a reduction in wind velocity may be expected as the approach flow is retarded by the presence of the dune mass, resulting in an increasing pressure gradient. The absence of such a ‘low-flowzone’ in the current investigation may be due to the coarse resolution of the measurements. The degree of velocity reduction would be expected to reach a maximum perturbation of only about -0-10 to -0.15, and to be more pronounced closer to the surface (Wiggs, 1992). It is possible that the large positive perturbations apparent in the present investigation (shown in Figure 6), coupled with the relatively large measurement heights, may have resulted in the low-velocity zone not being recognized. The maximum fractional speed-up ratio (S%,,) apparent at the crest ranges from 0.69 at 0.8 m height to 1.28 at 1.8m height (representing a 128 per cent increase in windspeed compared to upwind values. This range covers the value of 0.75 calculated by the Jackson and Hunt (1975) approximate formula. where Ss,, =maximum fractional speed-up, H =maximum dune or hill height and L = dune or hill halflength. The measured range, however, is still of a larger magnitude than might be expected. A possible explanation for this contrast may be that whilst the ratios H / L for the dunes in this study were within the critical range required for Jackson and Hunt type analysis (critical range between 0.1 and 0-7; contrast with Table 11), the ratios of Lizo were outside the range typical in previous investigations concerning flow over low hills (range from 0.8 x lo4 to 5 x lo4; contrast with Table 11). and values calculated A further possible explanation for the mismatch between measured values of from 2HIL (shown in Table 11) is that the Jackson and Hunt formula assumes a zo and d constancy across the whole windward slope. Such an assumption is inapplicable to the slopes of the dunes in the southwest Kalahari, where a strong gradient in vegetation characteristics is evident, as discussed above. 28 G. F. S . WIGGS, 1. LIVINGSTONE, D. S. G. THOMAS AND J. E. BULLARD 0 0 (u tttttt - 0 Lo c C r 0 0 i: N 0 Lo T 4 .-- E O 0 - 0 m c m al n 0 C Lo U C " 4 9 7 0 29 SEMI-VEGETATED LINEAR DUNES Table 11. Site length scales and maximum acceleration values A ~~ H (m) L( 4 H IL LIZ0 2HfL &",. B C Dl D2 E F 10.38 32.8 0.32 1426 0.63 0.50 10.43 27.70 0.38 769 0.75 0.80 5.03 26.65 0.19 444 1 0.38 0.78 3.14 19.60 0.16 426 0.32 0.45 8.43 46.9 0.18 3908 0.36 0.41 10.20 30.20 0.34 1258 0.68 0.68 ~ 12-51 33.45 0.37 514 0.75 1.28 H =maximum dune height; L = dune half-length; 4., = maximum measured fractional speed-up ratio The variation in height of SSmax as the flow crosses the windward slope of site A is more easily distinguished in Figure 7. This figure shows vertical profiles of fractional speed-up ratio at five selected points on the dune cross-section. The perturbations are calculated using Equation 3 and are normalized using the upwind velocity profile (dashed lines at zero perturbation shown in Figure 7). In both profiles B and D in Figure 7 the height of maximum flow acceleration is at the lowest measurement height of 0.5 m, although some acceleration is apparent throughout the length of the measured vertical profiles. However, as discussed above, the velocity results measured at a height of 0.5 m are subject to local interference from vegetation and are therefore liable to error. At the crest of the dune (Ref profiles in Figure 7), the 6, profile has become curved, showing a maximum at a height of 1.8 m. This height is lower than that predicted by the Jackson and Hunt inner-layer depth calculation of 2.24m (from Equation l), but higher than that predicted by the Jensen et al. (1984) formula (Equation 2) of 1.25m. However, these formulae provide 'order-of-magnitude' estimates at best, and in the past they have been tested on hills with much larger inner layers (10 to 20m in depth). Furthermore, in the calculations shown here, constant values of zo and d have been assumed (based on the upwind velocity profile characteristics). Such an assumption is an over-simplification (as discussed above). The results presented here are therefore considered to be in reasonable agreement with the theory. for the other study dunes are compared to the calculated results apparent The measured heights of hsrnax from Equations 1 and 2 in Table 111. In a similar manner to the site A results, the measured heights of dhaX at the remaining sites are of the same order of magnitude as predicted by Equations 1 and 2. The 6,profiles measured downwind of the crest of site A (profiles e and g in Figure 7) reveal that beyond the leeside separation vortex, the velocity at all measured heights is retarded below upwind values (profile e). The height of maximum deceleration is 1.8 m, the same as the height of maximum acceleration at the crest. Profile g in Figure 7 (on the downwind interdune) shows that at all measured heights except 0.5m, the velocity has returned to upwind magnitudes. The non-uniform nature of the vertical profiles of fractional speed-up shown in Figure 7 is also apparent at each of the other study sites. Figure 8 presents crest vertical profiles of 6, (normalized by upwind values using Equation 3) for the other sites, and clearly shows non-uniform flow acceleration. It is also noticeable from Figure 8 that each of the 6, profiles at the crest of the different dune sites are of a different shape. Table 111. Inner-layer depths and measured heights of maximum acceleration at each site (all measurements in metres) ~ MJW MJen) k*Ft ~~ ~ A B C D1 D2 F E 2.09 0.99 1.80 1.98 0.87 1.so 1.78 0.90 1.50 1.45 0.50 0.80 1.34 0.78 0.20 2.55 0.88 2.30 1.85 0.84 1.15 Is(JH) = inner-layer depth from Equation 1; Is(Jen) = inner-layer depth from Equation 2; &maxHt =height of maximum fractional speed-up ratio as measured at the crest 30 G. F. S. WIGGS, I. LIVINGSTONE, D. S. G. THOMAS AND J. E. BULLARD -1 -1 -1 4 4 4 -1 4 4 . 4 31 SEMI-VEGETATED LINEAR DUNES -1 0 1 Fractional Speed-up Ratio 2.5 1 -1 0 1 1 0 1 1 0 1 1 0 1 Site 0 2 -1 0 1 Fractional Speed-up Ratio Figure 8. Vertical profiles of fractional speed-up ratio (6,) measured at the crest of each of the sites. Dashed lines represent respective upwind values Some appear convex whilst others are concave. The shapes of the profiles are governed principally by the length scales of the dunes, because it is these which determine the depth of the inner layer and the height of the tisma,.However, close to the surface the effects of local vegetation interference also have an influence. The non-uniform acceleration (shown in Figures 7 and 8) has an important effect on the structure of the vertical velocity profile. An example of this is displayed in Figure 9, which shows vertical velocity profiles (normalized by the reference array measurement at a height of 2.3 m) measured upwind and at the crest of site A. The upwind profile is seen to be of a log-linear nature. However, the acceleration of flow up the windward slope of the dune results in a distinctly non-log-linear velocity profile at the crest. Similar non-log-linear profiles have been found over sand dunes by Burkinshaw et al. (1993), Butterfield (1991), Mulligan (1988) and Wiggs (1992, 1993). The increasingly non-log-linear nature of the vertical velocity profiles on the windward slopes of the dunes has important implications for the calculation of surface shear velocity, because Equation 4 relies on a log-linear velocity profile in order to operate. CONCLUSIONS From measurements of aerodynamic roughness and airflow structure on several partially vegetated dunes in 32 G. F. S. WIGGS, I. LIVINGSTONE, D. S. G. THOMAS AND J . E. BULLARD crest E =-rn 1 - 0 X . l 0.2 l . . . , 0.4 . . . , 0.6 Normalised . . . , . 0.8 . . , . . 1 .o . l 1.2 Velocity Figure 9. Normalized vertical velocity profiles measured upwind and at the crest of site A. Note the non-log-linear nature of the crest profile. Data normalized by windspeed at 2.3 m on the crest the southwest Kalahari Desert, a number of conclusions can be drawn. 1, The partially vegetated dunes display a wide range of aerodynamic roughness (zo) values which are highly variable across a single dune transect. Generally, the plinth and interdune regions comprise higher aerodynamic roughness values than the crests. This variation in both zo and zero-plane displacement ( d ) , caused by the irregularity of the vegetation cover across a transect, has implications for the successful calculation of near-surface shear velocity (u~).This is because the step-changes in zo and d are likely to lead to the growth of very thin internal boundary layers which are of insufficient depth to enable easy measurement of flow parameters. 2. Airflow over the dunes broadly corresponds to Jackson and Hunt (1975) principles and, as such, the study is analogous to investigations of airflow over low hills (see Taylor et al. (1987) for a review of the most prominent engineering papers). However, all the dunes studied in this investigation display acceleration of near-surface flow up their windward slopes, reaching a maximum within the crest region. This acceleration results in vertical velocity profiles becoming non-log-linear on the windward slope and at the crests of the dunes. Furthermore, the shapes of the vertical velocity profiles on the windward slopes and at the crests of the dunes are highly variable and strongly dependent on the dune length scales. Where the velocity profiles do not correspond to the KarmamPrandtl logarithimic Profile law, it is not possible to calculate shear velocity and sand transport rates from velocity data. The final conclusion confirms that of Mulligan (1988), who suggested that wind velocity should be measured within 0.2 m of dune surfaces in order to overcome the problem of non-log-linear velocity profiles. However, in the case of the Kalahari dunes, this was not possible because of the local interference of surface vegetation. Furthermore, above-canopy velocity measurements respond to the highly variable aerodynamic roughness presented by the vegetation canopy and hence have little coupling to sand movement on the surface. Before any estimation of sand transport rates on partially vegetated dunes can be carried out it is necessary to gain an improved understanding of both the magnitude of surface roughness variations across the dunes, and also the effect that the vegetation has on partitioning the shear stress SEMI-VEGETATED LINEAR DUNES 33 between that absorbed by the canopy and that transferred to the surface. The implication of these conclusions is that there is no simple method of gaining data concerning surface shear velocity on vegetated sand dunes from above-canopy velocity measurements. ACKNOWLEDGEMENTS This research is funded by NERC grant GR3/7541. Considerable help has been received from officials at the Kalahari-Gemsbok National Park, South Africa, particularly from Mr E. LeRiche. 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