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Register a new userModeling the large-scale structure of a barchan dune field
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In nature, barchan dunes typically exist as members of larger fields that display striking, enigmatic structures that cannot be readily explained by examining the dynamics at the scale of single dunes, or by appealing to patterns in external forcing. To explore the possibility that observed structures emerge spontaneously as a collective result of many dunes interacting with each other, we built a numerical model that treats barchans as discrete entities that interact with one another according to simplified rules derived from theoretical and numerical work and from field observations: (1) Dunes exchange sand through the fluxes that leak from the downwind side of each dune and are captured on their upstream sides; (2) when dunes become sufficiently large, small dunes are born on their downwind sides (`calving); and (3) when dunes collide directly enough, they merge. Results show that these relatively simple interactions provide potential explanations for a range of field-scale phenomena including isolated patches of dunes and heterogeneous arrangements of similarly sized dunes in denser fields. The results also suggest that (1) dune field characteristics depend on the sand flux fed into the upwind boundary, although (2) moving downwind, the system approaches a common attracting state in which the memory of the upwind conditions vanishes. This work supports the hypothesis that calving exerts a first-order control on field-scale phenomena; it prevents individual dunes from growing without bound, as single-dune analyses suggest, and allows the formation of roughly realistic, persistent dune field patterns.
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Barchan dunes --- crescent-shaped dunes that form in areas of unidirectional winds and low sand availability --- commonly display an asymmetric shape, with one limb extended downwind. Several factors have been identified as potential causes for barchan dune asymmetry on Earth and Mars: asymmetric bimodal wind regime, topography, influx asymmetry and dune collision. However, the dynamics and potential range of barchan morphologies emerging under each specific scenario that leads to dune asymmetry are far from being understood. In the present work, we use dune modeling in order to investigate the formation and evolution of asymmetric barchans. We find that a bimodal wind regime causes limb extension when the divergence angle between primary and secondary winds is larger than $90^{circ}$, whereas the extended limb evolves into a seif dune if the ratio between secondary and primary transport rates is larger than 25%. Calculations of dune formation on an inclined surface under constant wind direction also lead to barchan asymmetry, however no seif dune is obtained from surface tilting alone. Asymmetric barchans migrating along a tilted surface move laterally, with transverse migration velocity proportional to the slope of the terrain. Limb elongation induced by topography can occur when a barchan crosses a topographic rise. Furthermore, transient asymmetric barchan shapes with extended limb also emerge during collisions between dunes or due to an asymmetric influx. Our findings can be useful for making quantitative inference on local wind regimes or spatial heterogeneities in transport conditions of planetary dune fields hosting asymmetric barchans.
Transverse dunes, which form under unidirectional winds and have fixed profile in the direction perpendicular to the wind, occur on all celestial objects of our solar system where dunes have been detected. Here we perform a numerical study of the average turbulent wind flow over a transverse dune by means of computational fluid dynamics simulations. We find that the length of the zone of recirculating flow at the dune lee --- the {em{separation bubble}} --- displays a surprisingly strong dependence on the wind shear velocity, $u_{ast}$: it is nearly independent of $u_{ast}$ for shear velocities within the range between $0.2,$m$$s and $0.8,$m$$s but increases linearly with $u_{ast}$ for larger shear velocities. Our calculations show that transport in the direction opposite to dune migration within the separation bubble can be sustained if $u_{ast}$ is larger than approximately $0.39,$m$$s, whereas a larger value of $u_{ast}$ (about $0.49,$m$$s) is required to initiate this reverse transport.
The next generation of galaxy surveys like the Dark Energy Spectroscopic Instrument (DESI) and Euclid will provide datasets orders of magnitude larger than anything available to date. Our ability to model nonlinear effects in late time matter perturbations will be a key to unlock the full potential of these datasets, and the area of initial condition reconstruction is attracting growing attention. Iterative reconstruction developed in Ref. [1] is a technique designed to reconstruct the displacement field from the observed galaxy distribution. The nonlinear displacement field and initial linear density field are highly correlated. Therefore, reconstructing the nonlinear displacement field enables us to extract the primordial cosmological information better than from the late time density field at the level of the two-point statistics. This paper will test to what extent the iterative reconstruction can recover the true displacement field and construct a perturbation theory model for the postreconstructed field. We model the iterative reconstruction process with Lagrangian perturbation theory~(LPT) up to third order for dark matter in real space and compare it with $N$-body simulations. We find that the simulated iterative reconstruction does not converge to the nonlinear displacement field, and the discrepancy mainly appears in the shift term, i.e., the term correlated directly with the linear density field. On the contrary, our 3LPT model predicts that the iterative reconstruction should converge to the nonlinear displacement field. We discuss the sources of discrepancy, including numerical noise/artifacts on small scales, and present an ad hoc phenomenological model that improves the agreement.
Corridors of size-selected crescent-shaped dunes, known as barchans, are commonly found in water, air, and other planetary environments. The growth of barchans results from the interplay between a fluid flow and a granular bed, but their size regulation involves intricate exchanges between different barchans within a field. One size-regulating mechanism is the binary interaction between nearby dunes, when two dunes exchange mass via the near flow field or by direct contact (collision). In a recent Letter (Assis and Franklin, Geophys. Res. Lett., 2020), we identified five different patterns arising from binary interactions of subaqueous barchans, and proposed classification maps. In this paper, we further inquire into binary exchanges by investigating the motion of individual grains while barchans interact with each other. The experiments were conducted in a water channel where the evolution of pairs of barchans in both aligned and off-centered configurations was recorded by conventional and high-speed cameras. Based on image processing, we obtained the morphology of dunes and motion of grains for all interaction patterns. We present the trajectories of individual grains, from which we show the origin and destination of moving grains, and their typical lengths and velocities. We also show that grains from the impacting dune spread with a diffusion-like component over the target barchan, and we propose a diffusion length. Our results provide new insights into the size-regulating mechanisms of barchans and barchanoid forms found on Earth and other planets.
Crescentic shape dunes, known as barchan dunes, are formed by the action of a fluid flow on a granular bed. These bedforms are common in many environments, existing under water or in air, and being formed from grains organized in different initial arrangements. Although they are frequently found in nature and industry, details about their development are still to be understood. In a recent paper [C. A. Alvarez and E. M. Franklin, Phys. Rev. E 96, 062906 (2017)], we proposed a timescale for the development and equilibrium of single barchans based on the growth of their horns. In the present Letter, we report measurements of the growth of horns at the grain scale. In our experiments, conical heaps were placed in a closed conduit and individual grains were tracked as each heap, under the action of a water flow, evolved to a barchan dune. We identified the trajectories of the grains that migrated to the growing horns, and found that most of them came from upstream regions on the periphery of the initial heap, with an average displacement of the order of the heap size. In addition, we show that individual grains had transverse displacements by rolling and sliding that are not negligible, with many of them going around the heap. The mechanism of horns formation revealed by our experiments contrasts with the general picture that barchan horns form from the advance of the lateral dune flanks due to the scaling of migration velocity with the inverse of dune size. Our results change the way in which the growth of subaqueous barchan dunes is explained.
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