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1 Environmental Modelling & Software xxx (2009) 1 6 Contents lists available at ScienceDirect Environmental Modelling & Software journal homepage: Short communication Computational simulations of blown sand fluxes over the surfaces of complex microtopography Shi Feng a, Huang Ning a,b, * a Key Laboratory of Mechanics on Disaster and Environment in Western China, Lanzhou University, Lanzhou , Gansu Province, China b Minqin National Studies Station for Desert Steppe Ecosystem, Wuwei , Gansu Province, China article info abstract Article history: Received 1 December 2008 Received in revised form 11 June 2009 Accepted 1 September 2009 Available online xxx Keywords: Computational simulation Friction velocity Sand transport Wind field modeling Sand flux Studies of sand saltation are currently concentrating on wind tunnel experiments, theoretical analyses and numerical simulations under ideal as well as controllable conditions. These theoretical analyses and numerical simulations cannot accurately predict sand movements in field environments. In this paper, we simulate wind field patterns for two different surfaces of complex microtopography using the computational fluid dynamic model, FLUENT. To demonstrate that the model can successfully reproduce wind patterns in complex microtopography, we first simulate a well-studied mesquite bush and coppice dune field from the Chihuahuan Desert. This is then followed by an analysis of the wind field pattern around a large barchan dune that is complex in shape. For this case, the wind pattern was linked with a sediment transport equation to estimate sediment flux and transport. Finally, as shown by the simulation results, the sand flux, from the right horn to the left horn of the dune, first increased then decreased after reaching its maximum at the intersection of the brink and the longitudinal centreline of the dune. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction Studies of sand saltation are currently concentrating on wind tunnel experiments, theoretical analyses and numerical simulations under ideal as well as controllable conditions, such as under time-invariant wind speed and flat sand bed (Bauer et al., 1998; Huang et al., 2007; Leenders et al., 2005; Shao, 2000; van Boxel et al., 1999, 2004; Zheng et al., 2004; Zhou et al., 2002; Zou et al., 2001). However, these somehow idealized theoretical analyses and numerical simulations cannot accurately predict sand movements in field environments, which are generally composed of surface obstacles including dunes and bushes. Therefore, further study about the wind fields and sand saltation flux over the surfaces of complex microtopography is necessary. Many field measurements have been conducted to investigate the characteristics of blown sand flux over the surfaces of complex microtopology (Bauer et al., 1998; van Boxel et al., 2004; Leenders et al., 2005; Bowker et al., 2006, 2007), including the numerous field measurements of sand dunes (Frank and Kocurek, 1996a,b; Lancaster et al., 1996; Neuman et al., 2000; Tsoar, 1983; Wiggs et al., 1996a) and a limited number * Corresponding author. address: huangn@lzu.edu.cn (Huang, N.). of wind tunnel studies of airflows over Aeolian bedforms (Howard et al., 1977; White,1996; Wiggs, 1993; Wiggs et al., 1996b) that have been summarized by Wiggs (2001). Zheng et al. (2009) proposed a scale-coupled method for the formation and evolution of Aeolian sand dune fields, which successfully reproduces various dune patterns and the whole development process of a dune field of several square kilometers during several decades. Some computational fluid dynamics studies, including some using FLUENT, concentrated on simulating the wind profiles over barchan and transverse dunes (Herrmann et al., 2005; Parsons et al., 2004). However, few simulations dealt with the sand flux profile over the dunes although it has been pointed out that the dune studies will be focused on the dynamics of sediment transfers at the dune and inter-dune scales in the future (Livingstone et al., 2007). Based on the field measurement results of the wind speed and sand flux in Chihuahuan Desert (Gillette et al., 2006; Gillette and Pitchford, 2004), Bowker et al. (2006) simulated the wind speed over a surface of complex microtopography using QUIC 3.5 (Quick Urban & Industrial Complex), which is a fast-processing, massconsistent, and semi-empirical wind field model developed by Los Alamos National Laboratory (Williams et al., 2004). However, there are still deviations between the simulated and measured results at low wind speeds (Bowker et al., 2006). In this paper, we simulate wind field patterns for two different surfaces of complex microtopography using the computational fluid dynamic model, FLUENT /$ see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi: /j.envsoft

2 2 Shi, F., Huang, N. / Environmental Modelling & Software xxx (2009) 1 6 To demonstrate that the model can successfully reproduce wind patterns in complex microtopography, we first simulate a well-studied mesquite bush and coppice dune field from the Chihuahuan Desert. This is then followed by an analysis of the wind field pattern around a large barchan dune that is complex in shape. For this case, the wind pattern was linked with a sediment transport equation to estimate sediment flux and transport. 2. Measurement and simulation of wind speeds and sand fluxes 2.1. Simulation objects The complex microtopography in the Chihuahuan Desert is schematically shown in Fig. 1, which is extracted from Bowker et al. (2006). Specifically, Fig. 1a shows the location and extent of the Fig. 2. The plan view of the barchan dune. Fig. 1. Schematic of complex microtopography in the Chihuahuan Desert (extracted from Bowker et al., 2006). (a) Original flow field. (b) Modularized flow field. simulation domain in which mesquite bushes and coppice dunes are marked by green circles. In addition, the mast positions and the 15 m tower are denoted by blue diamonds labeled with a capital letter (B, C, D, M, N, Q, and Tower). Fig. 1b shows the actual simulation domain in which the bushes and coppice dunes are simplified as rectangular or cylindrical objects according to Bowker et al. (2006). In addition, the object color is related to its height (red 2 m, orange 1.5 m, yellow/green 1.25 m, light blue/green 1 m, medium blue 0.75 m, dark blue 0.5 m). To compare our simulation results with those of Bowker et al. (2006), the wind field of an object that is the same as that studied by Bowker et al. (2006) has been simulated in this work. The second simulation object is a barchan dune shown in Fig. 2 (location, N and E) near the meteorological tower of Integrated Desert Control Experimental Station in Minqin, a county in Gansu Province, China. This county is located at the intersection between the Badain Jaran Desert and the Tengger Desert. We used a High Precision GPS to measure the shape of the dune. The barchan dune is m in height and m in horn to horn width. The windward slope is m long and with an inclination of 10.12, while the leeward slope is m long with an inclination of The direction of the longitudinal centerline of the dune is to the east. The six white diamonds in Fig. 2 denote the sand flux measuring spots, while the two black diamonds represent the wind speed measuring spots A and B. In addition, there are six long-averaging-time collectors (BSNE, Big Spring Number Eight) used to measure horizontal mass flux (Fryrear, 1986) whose overall sampling efficiency varies between 86% and 95% (Shao et al., 1993). A vane and four lightweight fastresponding cup anemometers that are voltage-generating units (R.M. Young Model 03001) with a threshold speed of about 0.5 m s 1 were mounted on a straight and metallic bar along the gravity direction (Richards, 2005; Stout and Zobeck, 1997; Weaver, 1990). The cup anemometers and the vane sampled at a frequency of 1 Hz. The data were synchronously recorded by a Datalogger (Campbell Scientific CR 3000). The four anemometers at the spots A and B were 0.08, 0.43, 0.93, 1.92 m and 0.12, 0.45, 0.89, 1.92 m above the dune surface, respectively. The 0 value of vane indicated the North direction. Finally, the inflow direction of the specific sand storm studied here was northwest, specifically, in a range from 280 to 340. The velocity U(z) within a fully developed atmospheric turbulent boundary layer over a flat surface increases logarithmically with the distance z above the surface. Therefore, the inlet velocity profile can be described by (Shao, 2000):

3 Shi, F., Huang, N. / Environmental Modelling & Software xxx (2009) UðzÞ ¼ u * z ln k z 0 in which z 0 is the aerodynamic roughness length of the surface. The method to get the roughness length value in the Chihuahuan model described according to Bowker et al. (2006). We used the same method to gain the optimal roughness length value (¼0.465 m) in the barchan dune model. k ¼ 0.4 is the von Karman coefficient, and u * is the friction velocity whose value is specified by the value of reference velocity U ref. Here, U ref was taken as the velocity at the topmost measurement point of the meteorological tower where the velocity was presumably the least affected by the lower level flow disturbances resulting from the interactions between wind and obstacles. In addition, the direction of reference velocity U ref was assumed to be the same as the inflow direction. For the first object, 18 groups of the wind speed and direction at the height of 14.9 m were taken as the reference velocities that were measured on the meteorological tower in the Chihuahuan Desert (Gillette et al., 2006), as shown in Fig. 3a. While, for the second object, 33 groups of the wind speed and direction at the height of 49 m, which is the topmost measurement point of the meteorological tower ( N and E) near the barchan dune, were taken (1) as the reference velocities, as shown in Fig. 3b. In addition, the sand fluxes, wind speeds and directions on the windward slope of the dune were all measured during a 5.5 h sand storm (14:00 19:30) on March 17, Methodology Both objects have been simulated by the same method. The inflow velocity profile along the direction perpendicular to the flat surface follows the logarithmic law in a fully developed boundary layer (Eq. (1)). At the outlet profile, the flow was assumed as a fully developed flow, the outflow boundary condition was applied, and, thus, the conditions of the outlet plane were extrapolated from the domain and had no impact on the upstream (FLUENT, 2006). In addition, because the top boundary was sufficiently away from the ground surface, the symmetrical boundary conditions were applied to enforce a parallel flow by forcing the velocity component normal to the boundary to vanish and prescribing zero normal derivatives for all other flow variables. Finally, the non-slip boundary conditions were applied on the surface of obstacles. In this study, the three-dimensional and unstructured grid was generated using the grid generator GAMBIT and the microtopography in the Chihuahuan Desert to be simulated was represented by about tetrahedral cells and nodes, corresponding a domain of 150 (length) 130 (width) 12 m (height), while the barchans dune was gridded into tetrahedral cells and nodes, representing a domain of 360 (length) 280 (width) 60 m (height). The shear-stress transport (SST) k-u turbulence model enhancements cover a modified near wall treatment of the equations, which allows for a more flexible grid generation process and a zonal detached eddy simulation (DES) formulation, which reduces the problem of grid induced separation for flow simulations (Menter et al., 2003). So the SST k-u turbulence model was adopted to simulate the flow and turbulence in the study area. 3. Results and discussion 3.1. Wind speeds in Chihuahuan Desert The difference between the measured wind speeds and those simulated by QUIC (Bowker et al., 2006) as well as those calculated by FLUENT in this paper is shown in Fig. 4. As shown in Fig. 4, the simulation results of FLUENT are deviated less from the measured results than those of QUIC, particularly for the results when wind directions are between 220 and 240. The differences in wind speeds between the measured and the simulated results by FLUENT were all within 1.0 m s 1 under various inflow boundary conditions, which suggests that FLUENT software is reasonable in the simulation of wind field over these surfaces Wind field around the dune in Minqin Fig. 3. Wind speed and direction measured from the on-site meteorological tower. (a) 18 groups of the wind speed and direction in the Chihuahuan Desert (Gillette et al., 2006). (b) 33 groups of the wind speed and direction in the barchan dune. The major streamlines around the barchan dune as well as the streamwise velocity field of both longitudinal and transverse section of the dune under the wind blowing from 321 are shown in Fig. 5a and b. The longitudinal section was cut through the dune apex and was parallel to the wind flow direction. The transverse section was taken at 10 m above ground level. As shown in Fig. 5a, flow separation occurred at the top of the dune and a large eddy formed in the wake of the dune. It is consistent with the results reported in the literature (Neuman et al., 2000; Walker and Nickling, 2002; Wiggs et al., 1996b). In addition, there were two unsymmetrical vortices in the wake of the dune in Fig. 5b. The

4 4 Shi, F., Huang, N. / Environmental Modelling & Software xxx (2009) 1 6 Fig. 4. Difference between the measured wind speeds and those simulated by QUIC (Bowker et al., 2006) as well as those simulated by FLUENT in this paper. vortices were affected by the shape of the dune, the wind speed and direction of inflow. Fig. 6 shows the measured as well as the simulated wind speeds at 1.92 m above the dune surface at spots A and B at 33 different inflow conditions. It can be seen from Fig. 6 that the differences between the measured and simulated wind speeds are mostly within 2.5 m s 1, and the correlation coefficients of the regression equation of the simulated and measured wind speeds are and , respectively. In this case, the correlation between measured and predicted is poorer than in the Chihuahuan Desert. It may be caused by the assumption that the inlet wind velocity obeys the logarithm for the vegetation and sand dunes around this barchan dune may affect the inlet wind velocity although the surrounding surface of the barchan is relatively flat Sand flux over the dune in Minqin To calculate sand flux, Owen (1964) model is adopted in this work:! r G 1 ¼ c 0 g u3 * 1 u2 *t u 2 (2) * Fig. 5. Streamwise velocity field over the barchan dune. (a) Vertical section. (b) Transverse section. where G is sand flux, c 0 is an empirical coefficient, r ¼ kg 3 is the air density, g is the acceleration of gravity, u * and u *t are the friction velocity and threshold friction velocity, respectively. The velocity gradient of the wind velocity is usually assumed to be logarithmic above the saltation layer and the roughness length of the gradient does not vary with the locations during the sand flux simulations (Owen, 1964). Thus in these simulations, we assumed that the velocity was directly proportional to the friction velocity, and the threshold velocity above which the sands start to move can be found based on the threshold friction velocity. Therefore, Eq. (2) can be rewritten as: G 2 ¼ A 1 u 1 3 u2 t u 2 (3)

5 Shi, F., Huang, N. / Environmental Modelling & Software xxx (2009) Fig. 8. The simulated sand fluxes at thirteen positions of the dune brink under 298 and 321 wind directions. Fig. 6. Simulated and measured wind speeds at spots A and B. in which A 1 is an empirical coefficient, u and u t are the wind speed and the threshold wind speed 0.6 m above the dune surface, respectively. To calculate the sand flux, we need to know the values of A 1 and u t. Both A 1 and u t are related to the local surface conditions and can be determined by fitting the measurement results of BSNE collectors to the total simulated time-integrated fluxes at six sediment collector locations calculated from Eq. (3), as proposed by Bowker et al. (2007). Using the simulated wind velocity values from a height of 0.6 m, the value of A 1 and u t were found to be kg s 2 m 4 and 5.1 m s 1. The simulated total sand fluxes together with the measured results at six spots during a 5.5 h sand storm (March 17, 2008) are shown in Fig. 7. As shown in Fig. 7, the differences between the simulated and measured results are smaller than 10% in 5 spots, and the correlation coefficient of the regression equation is , indicating that the technique developed in this paper can be used to simulate the sand fluxes over a surface of complex microtopography. Fig. 8 shows the simulation results of the sand flux at 13 positions of the dune brink under the winds blowing from 298 to 321. In Fig. 2, the 13 positions are marked sequentially by the nodes from left to right along the dune brink. As shown in Fig. 8, from the right horn to the left horn of the dune, the sand flux first increased and then decreased after reaching its maximum at the intersection of the brink and the longitudinal centerline of the dune, then decreased. These results suggest that the sand transport over a dune by first going upwards across the gentle windward slope through saltation and surface creep, then arriving at the brink of barchans dune followed by depositing on the lee slope through avalanche (Bagnold, 1941). Particularly, the sand fluxes under the wind blowing from 321 were larger than those under the wind blowing from 298 due to the difference in the angle between the dune transverse section and the wind direction, which explains why the area of right horn of the dune is larger than that of the left horn. In addition, the simulated sand fluxes varied similarly along the dune brink under the winds blowing from both directions. 4. Conclusions Fig. 7. The simulated and measured total sand fluxes at six spots. In this work, the wind flows in Chihuahuan Desert have been simulated using FLUENT at 18 flow boundary conditions. The simulation results have been compared with the corresponding results of Bowker et al. (2006). In addition, the wind flows over a dune in Minqin have also been simulated at 33 flow boundary conditions. Based on the simulated wind flow, we calculated the

6 6 Shi, F., Huang, N. / Environmental Modelling & Software xxx (2009) 1 6 sand fluxes at six spots on the dune using Owen (1964) model. The calculated results have been compared with the measured sand fluxes and several conclusions can be summarized as follows: The simulated results of the wind fields in Chihuahuan Desert under 18 flow boundary conditions indicate that the simulation results of wind fields using FLUENT agree well with the measured wind speeds. Therefore it can be concluded that FLUENT can accurately simulate the wind fields over these surfaces. The simulation results of the sand fluxes at 6 spots agree with the measured sand fluxes, which indicates that the sand flux over a surface of complex microtopography can be accurately calculated using Owen model. From the right horn to the left horn of the dune, the sand flux first increased, and then decreased after reaching the maximum at the intersectionpoint of the brink and longitudinal centreline of the dune. Acknowledgements This research work was supported by a grant of the National Key Project for basic research (2009CB421304) and the Natural Science Foundation of China (Grant No ; ), and the Science Fund of the Ministry of Education of China for PhD Program (Grant No ). The authors sincerely appreciate this support. The authors also thank the anonymous reviewers and editors for their thoughtful comments which helped to improve and clarify the manuscript. References Bagnold, R.A., The Physics of Blown Sand and Desert Dunes. William Morrow & Company, New York. Bauer, B.O., Yi, J.C., Namikas, S.L., Sherman, D.J., Event detection and conditional averaging in unsteady Aeolian systems. Journal of Arid Environments 39 (3), Bowker, G.E., Gillette, D.A., Bergametti, G., Marticorena, B., Modelingflow patterns in a small vegetated area in the northern Chihuahuan Desert using QUIC (Quick Urban & Industrial Complex). 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