Wind tunnel simulation of the three-dimensional airflow patterns behind cuboid obstacles at different angles of wind incidence, and their significance for the formation of sand shadows

Abstract

Sand shadows commonly form downwind of obstacles in arid and semi-arid regions. Understanding their dynamics requires insights into the airflow patterns behind the obstacles under different wind regimes. Here, we studied models of cuboid obstacles to characterize the three-dimensional responses of airflow behind obstacles with different shape ratios to variations in the incident flow in a wind-tunnel simulation. Wind velocity was measured using particle image velocimetry (PIV). The flow patterns behind cuboid obstacles were complicated by changes in the incidence angle of the approaching flow and in the obstacle's shape ratio. The flows separated both horizontally and vertically, creating reverse-flow cells downwind of the obstacles. The horizontal cells were characterized by two asymmetrical, opposing reverse vortices at flow incidence angles greater than 60 to 65°, whereas the vertical cells formed a single vortex at all angles. The cells shifted position in response to changes in the incidence angle and shape ratio, reflecting the interaction between outer and reverse flows. The parameters of the horizontal and vertical reverse cells depended on the shape ratios and incidence angles but not on the wind velocity. The sizes of the horizontal and vertical reverse cells were correlated, reflecting their interactions. The low-velocity “shadow” behind the obstacle caused sand deposition and determined the sand shadow's evolution. Field experiments will be required to relate these airflow patterns to sand shadow development.

Introduction

Sand shadows (also called shadow dunes) form in the lee of obstacles, and are widely distributed in arid and semi-arid regions and in some coastal regions around the world. The most frequently reported obstacles that create such sediment deposits are topographic obstacles such as hills and rocks, human structures such as cairns or buildings, and sediments trapped by vegetation (e.g., Karcz, 1968, Carter, 1978, Hesp, 1981, Clemmensen, 1986, Wilson, 1988, Gunatilaka and Mwango, 1989). Consequently, sand shadows have received much attention from eolian geomorphologists (Bagnold, 1941, Clemmensen, 1986, Hesp and McLachlan, 2000, Hesp et al., 2005, Dong et al., 2008). During the formation and subsequent evolution of sand shadows, there is an iterative interaction between the obstacle's geometry, the characteristics of the secondary airflow fields created by that geometry combined with the direction of the incident wind, the morphology of the sand shadow, and the interaction between neighboring dunes or obstacles (Cooke et al., 1993, Livingstone and Warren, 1996). Understanding the dynamics of these dunes thus requires insights into the airflow fields behind obstacles.

As the name implies, sand shadows represent sediment accumulations that form in the shelter (wind shadow) of, and immediately behind, an obstacle. Bagnold (1941) first used this name to describe the accumulation of eolian sand in the lee of an obstacle that reduces the local wind velocity. Similar structures, associated with both wind and water, have subsequently been recognized in a variety of depositional environments (e.g., Wilson, 1988). Allen (1982) suggested the less specific term current shadow for such features in both eolian and aqueous environments. However, related terms such as lee dune, shadow dune and coppice dune are more widely used in the eolian literature to describe such deposits (Hesp, 1981, Pye and Tsoar, 1990, Cooke et al., 1993).

Although sand shadows have attracted research attention because of their occurrence outside Martian craters, they are the least well-understood of anchored dunes (Greeley and Iversen, 1985). The literature suggests that these deposits cannot survive large changes in wind direction, such as the ones that occur where the wind regime is highly variable in direction, and can only grow to meso- or mega-size under constant wind regimes (Cooke et al., 1993, Livingstone and Warren, 1996). Obstacles generate different sand shadows depending on the sand supply, wind regime, and the geometry of the obstacle, and can generate double or single sand shadows. The eolian literature on sand shadows mainly concerns their internal sedimentary structures and morphological descriptions (Clemmensen, 1986, Gunatilaka and Mwango, 1989), and little attention has been paid to the aerodynamic processes that govern their development. Although there is an obvious association with turbulence patterns in the lee of an obstacle, there is still much to learn about sand shadows.

The wind pattern around the solid cuboid obstacle has been studied intensively in the field of civil engineering through experimental and numerical simulation (Castro, 1979, Hunt et al., 1979, Hunt, 1982, Castro and Dianat, 1984, Martinuzzi and Tropea, 1993, Lamb, 1994, Chou and Chao, 2000). There exists a considerable amount of published data for flows around obstacles. However, most literature is concerned with the flow structure upstream of surface-mounted rectangular cylinders in channel flow, there are few studies concerning the three-dimensional phenomena in the lee of an obstacle with different shapes and, in particular, the sedimentological process involved are still unclear. When a sufficiently strong wind flows around a rectilinear obstacle, flow separation occurs in the lee of the obstacle. The nature and significance of this and related secondary flows are controlled by the interaction of at least two factors: the obstacle's shape and the angle of incidence of the flow (Sweet and Kocurek, 1990, Cooke et al., 1993). Sand shadows can form after a storm or can be created by a weaker wind that exceeds the threshold frictional velocity required to entrain sand particles (Bagnold, 1941, Clemmensen, 1986, Pye and Tsoar, 1990, Cooke et al., 1993, Livingstone and Warren, 1996).

The morphology and evolution of a sand shadow are sensitive to the angle of the incident wind and the shape of the obstacle, which strongly affects the secondary flow patterns in its lee (Bagnold, 1941, Gunatilaka and Mwango, 1989, Dong et al., 2008). Wind tunnel studies have shown that the shear stress exerted on the sand bed in the wake of an obstacle is a function of the obstacle's dimensions and the friction wind velocity (Greeley and Iversen, 1985). Iversen et al. (1990) found that the intensity of turbulence and erosion was related to the obstacle's aspect ratio (the ratio of its height to its width perpendicular to the flow). Dong et al. (2008) wind tunnel simulation revealed that the flow patterns around shrubs were complicated by the presence of bleed flows (which pass through the obstacle) and displaced flows (which flow around the obstacle) when the shrub density equals or exceeds a critical density (which ranged between 0.05 and 0.08). Thus, sand shadows develop behind dense shrubs when the dominant reversed flow leads to sediment accumulation on the lee side. If the obstacle's shape varies in three dimensions, some of its facets will be oblique to the flow direction.

Bagnold (1941) illustrated the ideal stages in the evolution of sand shadows (Fig. 1), and noted that the size of the sand shadow is very sensitive to the shape of the bottom of the obstacle. However, the characteristics of the wakes that develop behind angular bodies, and especially the secondary airflow patterns behind these bodies, and their relationship with their shape and changes in the angle of incidence of the wind are not yet fully understood. To investigate the mechanisms responsible for the formation and evolution of sand shadows under complicated secondary airflows, we performed a scaled wind-tunnel simulation. Our goal was to improve understanding of the three-dimensional airflow patterns behind cuboid obstacles using models with different shapes and under different angles of incidence of the wind. We characterized the airflow fields using particle image velocimetry (PIV), and used the results to define the horizontal and vertical variations in airflow patterns as a function of the wind incidence angle and the obstacle's shape ratio, taking advantage of the ability of PIV to provide non-intrusive velocity measurements within the whole field of the target area. Based on our results, we discuss the geomorphological significance of the lee vortex and wake.