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Color flood contour of Reynolds-averaged vertical vorticity, ˜ ω z t (x, y, z/ h = 0.5), at wall-normal elevation, z/ h = 0.5, for Cases S1 (a); S2 (b); S3 (c); S4 (d); S3 (e); and S4 (f) (see Table I for topography details). Included on the color floods are low-pass filtered datapoints for the wake, emanating from the small and large dunes, δ s (x s ; z/ h = 0.5) and δ l (x l ; z/ h = 0.5), respectively. Low-pass filtered wake profiles emanating from large and small dunes, δ l (x l ; z/ h = 0.5) (Panel g) and δ s (x s ; z/ h = 0.5) (Panel h), respectively, where local coordinate originates at respective dune crest, where Fig. 2 graphically illustrates the local axes, x s and x l. Black, gray, and light gray solid lines correspond with Cases S2, S3, and S4, respectively, dashed blue and dotted red lines correspond with S3 and S4 , respectively, while cyan circles and dash-dot magenta line correspond with S5 and S6, respectively.

Color flood contour of Reynolds-averaged vertical vorticity, ˜ ω z t (x, y, z/ h = 0.5), at wall-normal elevation, z/ h = 0.5, for Cases S1 (a); S2 (b); S3 (c); S4 (d); S3 (e); and S4 (f) (see Table I for topography details). Included on the color floods are low-pass filtered datapoints for the wake, emanating from the small and large dunes, δ s (x s ; z/ h = 0.5) and δ l (x l ; z/ h = 0.5), respectively. Low-pass filtered wake profiles emanating from large and small dunes, δ l (x l ; z/ h = 0.5) (Panel g) and δ s (x s ; z/ h = 0.5) (Panel h), respectively, where local coordinate originates at respective dune crest, where Fig. 2 graphically illustrates the local axes, x s and x l. Black, gray, and light gray solid lines correspond with Cases S2, S3, and S4, respectively, dashed blue and dotted red lines correspond with S3 and S4 , respectively, while cyan circles and dash-dot magenta line correspond with S5 and S6, respectively.

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The coupling between turbulent flow physics and barchan dune geometry is important to dune migration, morphology of individual dunes, and the morphodynamics of merging and separating proximal dunes. Large-eddy simulation was used to model turbulent, inertial-dominated flow over a series of static barchan dune configurations. The dune configurations...

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... s x /h, Fig. 4(h)] exhibits a distinct veering, relative to Case ...
Context 2
... Fig. 1). At the elevation considered in Fig. 4, z/ h = 0.5, the small dune wake is far more sensitive to changing attributes of the topography, relative to the large dune. Recall, however, that the small dune height is equivalent to z/ h = 0.5, and when the same contours are generated at z/ h = 1, the large dune wake responds more to s x /h, etc., but we have excluded these figures ...
Context 3
... from stretching. Figure 9 was used to conclude that stretching provides the largest gain to sustenance of the interdune roller, although this argument was predicated only upon a profile from a discrete location. To further the argument, we have prepared Fig. 10: a horizontal contour of the stretching term, with the wake pro- files from Fig. 4 superimposed for generality. For the isolated case [ Fig. 10(a)], the magnitude of the stretching term is equal and opposite on the dune stoss face, and the wake exhibits no veering. With introduction of the upflow dune, however, an additional location of stretching is introduced [Figs. 10(b) to 10(f)], and the magnitude of this grows ...

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Citations

... Because of the compression of the streamline on the windward slope of a dune, the airflow was accelerated and gradually increased along the stoss slope and reached the maximum at the crest, leading to the capacity of wind erosion (Lancaster et al., 1996;Baddock et al., 2011;Faria et al., 2011;Dong et al., 2014). After the separation of airflow from the crest, flow expansion occurs and recycles back up the leeward slope above the point of reattachment (Frank and Kocurek, 1996;Walker and Nickling, 2002;Walker and Shugar, 2013;Jiang et al., 2017;Wang and Anderson, 2018). The reversed flow above the point of reattachment can influence sediment transport and aeolian bedform development (Baddock et al., 2011;Palmer et al 2012;Araújo et al., 2013;Walker and Shugar, 2013;Jiang et al., 2017). ...
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The interactions between wind flow and sand transport on the leeward side of dunes are complex due to highly turbulent fluctuations. Most models of turbulent flow on the individual barchan dunes have recognized the flow structure of recirculation cell and shear stress within the Inner Boundary Layer (IBL) on the leeward side, however these models neglected the processes of aeolian erosion caused by the recovering flow and reversed flow. Here, we investigated the airflow and aeolian erosion processes of an erodible surface on the leeward side of a barchan dune in a scaled wind tunnel simulation. Results show that the recovering flow triggered the wind erosion on the leeward side of barchan dunes through the unsaturated flux. The length of the wind erosion zone ranged from 4.5 to ~16H (H is the dune height). Under the condition of abundant sand supply, the length of wind erosion zone decreases slightly. However, abundant sand supply has notably weakened the wind erosion rate, and individual barchan dunes link into sinuous-crested ridges. As confirmed by field observations, this study provides empirical evidence for aeolian erosion on the leeward side of barchan dunes and suggests that airflow recovery length and sand supply collectively determine the spatial distribution patterns of barchan dunes on Earth.
... Barchan collisions, and bedform interactions more generally, have been studied both numerically (e.g. Katsuki et al. 2011;Omidyeganeh et al. 2013;Parteli et al. 2014;Wang & Anderson 2018) and experimentally (e.g. Endo, Taniguchi & Katsuki 2004;Hersen & Douady 2005;Fernandez, Best & López 2006;Palmer et al. 2012;Bristow et al. 2018;Assis & Franklin 2020). ...
... Recent studies have increasingly shown that the morphodynamics of interactions between dunes in close proximity is linked to enhanced turbulence produced in the wake of an upstream bedform impinging on a downstream bedform (Fernandez et al. 2006;Wang et al. 2017;Bristow et al. 2018;Wang & Anderson 2018Bristow et al. 2019Bristow et al. , 2020Assis & Franklin 2020;Bacik et al. 2020;Khosronejad et al. 2020). Bacik et al. (2020) showed for transverse dunes that the turbulent wake of the upstream bedform influences the migration speed of the downstream bedform by enhancing downstream sediment flux. ...
... Studies that focus on flow over barchans in particular (i.e. capturing the relevant aspect ratio H/W, where W is dune spanwise length), and which have also modelled bedforms at this scaling within the boundary layer, however, are relatively few (Palmer et al. 2012;Wang et al. 2017;Bristow et al. 2018;Wang & Anderson 2018Bristow et al. 2019Bristow et al. , 2020. Moreover, these studies have generally not focused on how the boundary layer structure interacts with, and possibly modulates, the flow perturbations from the bedform itself. ...
... Airflow over static beds with Computational Fluid Dynamics-As reviewed by Smyth (2016), more tractable Computational Fluid Dynamic (CFD) models have been thus deployed to obtain an approximate solution of the associated partial differential equations (Navier-Stokes equations). One of these models is the Large Eddy Simulation (LES), which applies a low-pass filtering that suitably averages the flow fields at small time-and length-scales (Omidyeganeh et al., 2013;Bristow et al., 2018;Wang and Anderson, 2018;Bristow et al., 2019Bristow et al., , 2020. Alternatively, the time-averaged shear stress distribution over the complex dune topography is estimated by solving the Reynolds-averaged Navier Stokes (RANS) equations (Fig. 11), which are obtained by applying a decomposition of the flow fields into their respective mean and fluctuating quantities Parsons et al., 2004a,b;Herrmann et al., 2005; Wakes et al., 2010;Liu et al., 2011;Araújo et al., 2013;Bruno and Fransos, 2015;Jackson et al., 2013Jackson et al., , 2015Jackson et al., , 2020Michelsen et al., 2015). ...
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... Several studies have attempted observations via satellite imagery (e.g., Elbelrhiti et al., 2005;Hugenholtz & Barchyn, 2012) and shown that morphological changes in the DBD start before the barchans come into contact, suggesting that proximity triggers these early interaction processes which must be driven by interdune flow. Recent studies have proposed that it is the turbulent nature of the interdune flow that may drive the observed morphodynamics (Bristow et al., 2018Omidyeganeh et al., 2013;Palmer et al., 2012;Wang et al., 2016;Wang & Anderson, 2018), although numerical models that do not embody dynamic feedback between the flow and morphology fail to capture these phenomena. In this regard, it is increasingly accepted that the physics governing morphodynamic interactions involves a While much is known concerning flow over 2-D transverse dunes (e.g., Best, 2005a;Nezu & Nakagawa, 1993), and recent studies have begun to uncover the flow physics of barchan dune interactions (Baddock et al., 2007;Bristow et al., 2018Bristow et al., , 2019Omidyeganeh et al., 2013;Smith et al., 2017;Palmer et al., 2012;Wang et al., 2016;Wang & Anderson, 2018), relatively little is known concerning the secondary flows that result from the three-dimensional, crescentic morphology of a barchan dune. ...
... Recent studies have proposed that it is the turbulent nature of the interdune flow that may drive the observed morphodynamics (Bristow et al., 2018Omidyeganeh et al., 2013;Palmer et al., 2012;Wang et al., 2016;Wang & Anderson, 2018), although numerical models that do not embody dynamic feedback between the flow and morphology fail to capture these phenomena. In this regard, it is increasingly accepted that the physics governing morphodynamic interactions involves a While much is known concerning flow over 2-D transverse dunes (e.g., Best, 2005a;Nezu & Nakagawa, 1993), and recent studies have begun to uncover the flow physics of barchan dune interactions (Baddock et al., 2007;Bristow et al., 2018Bristow et al., , 2019Omidyeganeh et al., 2013;Smith et al., 2017;Palmer et al., 2012;Wang et al., 2016;Wang & Anderson, 2018), relatively little is known concerning the secondary flows that result from the three-dimensional, crescentic morphology of a barchan dune. Studies have focused on the stoss-side flow structure (Charru & Franklin, 2012;Lancaster et al., 1996;Weaver & Wiggs, 2011;Wiggs et al., 1996), flow along the centerline (Baddock et al., 2011;Palmer et al., 2012), or on sediment transport patterns alone (Alvarez & Franklin, 2018), without a strong consideration of the three-dimensionality of flow in the wake region. ...
... However, an important caveat of these simulations was the periodic boundary conditions, which meant that these flow structures could not be attributed to an individual barchan, but rather a long train of barchans. More recently, Wang and Anderson (2018) used LES to resolve flow around a number of colliding barchan dunes and performed conditional calculations of differential helicity to investigate secondary flow structures. For a laterally offset collision configuration, they observed the formation of a persistent streamwise roller in the interdune region, although strong evidence of such rollers was not clearly shown downstream of the horns of an isolated barchan. ...
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... There has been increased interest in turbulent flow processes above fields of dunes in aquatic and aeolian environments, where efforts have focused on large-scale flow processes (Livingstone et al. 2006;Claudin et al. 2013), mixing processes (Fröhlich et al. 2005;Piomelli 2011, 2013a, b;Palmer et al. 2012b;Omidyeganeh et al. 2013;Anderson and Chamecki 2014;Wang et al. 2016;Wang and Anderson 2018;Bristow et al. 2018Bristow et al. , 2019, and coupled morphodynamics (Ortiz and Smolarkiewicz 2009;Sotiropoulos 2014, 2017;Zgheib et al. 2018a, b). In addition, substantial efforts have been devoted to the underlying mechanisms of self assembly exhibited by complex dune fields-see, for example, work based upon aeolian dune fields in complex environments (Hersen et al. 2004;Hersen and Douady 2005;Kocurek et al. 2007;Ewing and Kocurek 2010a;Durán et al. 2010) and prognostic morphodynamic schemes based upon cellular automata (Werner 1995;Jerolmack and Mohrig 2005;Narteau et al. 2009). ...
... In addition, substantial efforts have been devoted to the underlying mechanisms of self assembly exhibited by complex dune fields-see, for example, work based upon aeolian dune fields in complex environments (Hersen et al. 2004;Hersen and Douady 2005;Kocurek et al. 2007;Ewing and Kocurek 2010a;Durán et al. 2010) and prognostic morphodynamic schemes based upon cellular automata (Werner 1995;Jerolmack and Mohrig 2005;Narteau et al. 2009). Wang and Anderson (2018) used large-eddy simulation (LES) to model flow over an idealized barchan dune arrangement replicating the so-called 'offset interaction' merger (Hersen and Douady 2005;Ewing and Kocurek 2010a). For this arrangement, a relatively smaller dune is placed upflow and spanwise offset a relatively larger dune, thereby guaranteeing collision, or interaction, since the relatively smaller dune migrates faster (see also Fig. 1c-e, as this arrangement was encompassed as part of the present research effort). ...
... This is assured, since dune migration represents cumulative grain transport: the smaller dune has a relatively lesser number of gains, and is placed upflow of the large dune, thus absorbing aerodynamic momentum fluxes first. Results from Wang and Anderson (2018) reveal the presence of a persistent roller in the region between the interacting dunes, the interdune space. Vorticity dynamics analysis confirmed that sustenance of the roller is derived from the simultaneous supply of streamwise vorticity and channeling flow in the interdune space-i.e., vortex stretching ( Fig. 1c-e features annotation of channeling flow). ...
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... Various studies have been done to understand the relation between turbulent coherence and morphodynamics, some of which are focusing on sediment saltation based on local dune morphological conversion under turbulent aerodynamic loading (Khosronejad and Sotiropoulos, 2017;Pähtz et al., 2012;Kok et al., 2012;Ortiz and Smolarkiewicz, 2009;Bagnold, 1956;Shao, 2008). While turbulent coherence study associated with different dune-field arrangements have also been dictated (Palmer et al., 2012b;Piomelli, 2011a, 2013a,b;Omidyeganeh et al., 2013;Wang and Anderson, 2018b;Bristow et al., 2017Bristow et al., , 2019Anderson and Chamecki, 2014;Wang and Anderson, 2018a,b, 2017, 2019a. These works ideographically provide plenty of numerical and experimental datasets for dune field analysis and indeed have helped us to achieve the full understanding of dune field. ...
... In this arrangement, the small dune will eventually merge with the large dune while, simultaneously, a small dune will be ejected from the large dune (Ewing and Kocurek, 2010a;Kocurek et al., 2007;Frank and Kocurek, 1996;Kocurek and Ewing, 2005;. To capture the aero-and hydrodynamic effects during the interaction, tow of the configurations featured downflow dunes with significant asymmetry (S3, S4, S3 l , S4 l ) (Wang and Anderson, 2018b). In the interest of generality, White Sands National Monument (WSNM) aeolian dune field in southern New Mexico has been used as realistic study case. ...
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... To list but a few examples, Refs. [1][2][3][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] investigated the problem analytically, experimentally or numerically. However, given the high complexity of grain-fluid interactions and the different scales involved, the problem is still open and several aspects need to be understood before a complete understanding is achieved. ...
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Many complex aspects are involved in the morphodynamics of crescent-shaped dunes, known as barchans. One of them concerns the trajectories of individual grains over the dune, and how they affect its shape. In the case of subaqueous barchans, we proposed in Alvarez and Franklin [Phys. Rev. Lett. 121, 164503 (2018)] that their extremities, called horns, are formed mainly by grains migrating from upstream regions of the initial pile, and that they exhibit significant transverse displacements. Here, we extend our previous work to address the dynamics of grains migrating to horns after the dune has reached its crescentic shape, and present new aspects of the problem. In our experiments, single barchans evolve, under the action of a water turbulent flow, from heaps of conical shape formed from glass beads poured on the bottom wall of a rectangular channel. Both for evolving and developed barchans, the horns are fed up with grains coming from upstream regions of the bedform and traveling with significant transverse components, differently from the dynamics usually described for the aeolian case. For these grains, irrespective of their size and strength of water flow, the distributions of transverse and streamwise components of velocities are well described by exponential functions, with the probability density functions of their magnitudes being similar to results obtained from previous studies on flat beds. Focusing on moving grains whose initial positions were on the horns, we show that their residence time and traveled distance are related following a quasi-linear relation. Our results provide new insights into the physical mechanisms underlying the shape of barchan dunes.
... However, the dynamic coupling between form and flow renders predictive modeling of nonisolated barchans very challenging, since the local flow is continuously modified as the spatial distribution of bedforms changes. Research has shown that as bedforms move into close proximity, they begin to interact, displaying mass exchange (Endo et al., 2004;Hersen & Douady, 2005;Kocurek et al., 2010;Zhang et al., 2010) as well as significantly changing local flow (Bristow et al., 2018;Omidyeganeh et al., 2013;Palmer et al., 2012;Wang et al., 2016;Wang & Anderson, 2018). Studies based upon idealized fixed-bed models have speculated that highly turbulent shear layers shedding from an upstream barchan may be responsible for the deviation from the simplified behavior of an isolated barchan (Palmer et al., 2012;Omidyeganeh et al., 2013;Wang et al., 2016;Bristow et al., 2018). ...
... Studies based upon idealized fixed-bed models have speculated that highly turbulent shear layers shedding from an upstream barchan may be responsible for the deviation from the simplified behavior of an isolated barchan (Palmer et al., 2012;Omidyeganeh et al., 2013;Wang et al., 2016;Bristow et al., 2018). However, while this hypothesis can best Recent numerical simulations (Omidyeganeh et al., 2013;Wang et al., 2016;Wang & Anderson, 2018) and laboratory experiments (Bristow et al., 2018;Palmer et al., 2012) of idealized barchans have begun to uncover the flow dynamics associated with barchan-barchan interactions. The fixed-bed experiments of Palmer et al. (2012) were the first to investigate quantitatively how the proximity and volume ratio between tandem barchans modifies the structure of the turbulent flow. ...
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