Reproducing size distributions of swarms of barchan dunes on Mars and Earth using a mean-field model

We apply a mean-field model of interactions between migrating barchan dunes, the CAFE model, which includes calving, aggregation, fragmentation, and mass-exchange, yielding a steady-state size distribution that can be resolved for different choices of interaction parameters. The CAFE model is applied to empirically measured distributions of dune sizes in two barchan swarms on Mars, three swarms in Morocco, and one in Mauritania, each containing 1000 bedforms, comparing the observed size distributions to the steady-states of the CAFE model. We find that the distributions in the Martian swarm are very similar to the swarm measured in Mauritania, suggesting that the two very different planetary environments however share similar dune interaction dynamics. Optimisation of the model parameters of three specific configurations of the CAFE model shows that the fit of the theoretical steady-state is often superior to the typically assumed log-normal. In all cases, the optimised parameters indicate that mass-exchange is the most frequent type of interaction. Calving is found to occur rarely in most of the swarms, with a highest rate of only 9% of events, showing that interactions between multiple dunes rather than spontaneous calving are the driver of barchan size distributions. Finally, the implementation of interaction parameters derived from 3D simulations of dune-pair collisions indicates that sand flux between dunes is more important in producing the size distributions of the Moroccan swarms than of those in Mauritania and on Mars. 1 ar X iv :2 11 0. 15 85 0v 1 [ ph ys ic s. ge oph ] 2 9 O ct 2 02 1

[1]  P. Claudin,et al.  Field evidence for surface-wave-induced instability of sand dunes , 2005, Nature.

[2]  H. Elbelrhiti,et al.  Initiation and early development of barchan dunes: A case study of the Moroccan Atlantic Sahara desert , 2012 .

[3]  Xiaoping Yang,et al.  Origin and morphology of barchan and linear clay dunes in the Shuhongtu Basin, Alashan Plateau, China , 2019, Geomorphology.

[4]  A. Goudie,et al.  Varieties of barchan form in the Namib Desert and on Mars , 2009 .

[5]  Bin Yang,et al.  Experimental study on the stable morphology and self-attraction effect of subaqueous barchan dunes , 2020 .

[6]  Hans J. Herrmann,et al.  A continuous model for sand dunes: Review, new developments and application to barchan dunes and barchan dune fields , 2010 .

[7]  X. Gong,et al.  Generalized simulated annealing algorithm and its application to the Thomson model , 1997 .

[8]  Erick de Moraes Franklin,et al.  Subaqueous barchan dunes in turbulent shear flow. Part 1. Dune motion , 2011, Journal of Fluid Mechanics.

[9]  Bruno Andreotti,et al.  Barchan dune corridors: Field characterization and investigation of control parameters , 2006, cond-mat/0609120.

[10]  P. Claudin,et al.  Selection of dune shapes and velocities Part 2: A two-dimensional modelling , 2002, cond-mat/0201105.

[11]  Yang Xiang,et al.  Generalized Simulated Annealing for Global Optimization: The GenSA Package , 2013, R J..

[12]  Clément Narteau,et al.  Morphodynamics of barchan and transverse dunes using a cellular automaton model , 2010 .

[13]  Z. Dong,et al.  Migration of barchan dunes in the western Quruq Desert, northwestern China , 2019, Earth Surface Processes and Landforms.

[14]  C. Tsallis Possible generalization of Boltzmann-Gibbs statistics , 1988 .

[15]  Alessia Annibale,et al.  A combined model of aggregation, fragmentation, and exchange processes: insights from analytical calculations , 2021 .

[16]  P. Vermeesch,et al.  Solitary wave behavior in sand dunes observed from space , 2011 .

[17]  G. Grégoire,et al.  Spatial structuring and size selection as collective behaviours in an agent-based model for barchan fields , 2013, The European Physical Journal B.

[18]  P. Hersen Flow effects on the morphology and dynamics of aeolian and subaqueous barchan dunes , 2005 .

[19]  K. Glasner,et al.  Long-time evolution of models of aeolian sand dune fields: Influence of dune formation and collision , 2010 .

[20]  A. Goudie Global barchans: A distributional analysis , 2020 .

[21]  M. Kikuchi,et al.  Cellular model for sand dunes with saltation, avalanche and strong erosion: collisional simulation of barchans , 2011 .

[22]  S. Redner,et al.  A Kinetic View of Statistical Physics , 2010 .

[23]  A. Refaat,et al.  Morphologic characteristics and migration rate assessment of barchan dunes in the Southeastern Western Desert of Egypt , 2016 .

[24]  M. Mézard,et al.  The Bethe lattice spin glass revisited , 2000, cond-mat/0009418.

[25]  K. H. Andersen,et al.  Corridors of barchan dunes: Stability and size selection. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Veit Schwämmle,et al.  Geomorphology: Solitary wave behaviour of sand dunes , 2003, Nature.

[27]  H. Herrmann,et al.  Minimal model for aeolian sand dunes. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  N. Endo,et al.  Observation of the whole process of interaction between barchans by flume experiments , 2004 .

[29]  P. Claudin,et al.  Modeling emergent large-scale structures of barchan dune fields , 2013 .

[30]  A. Barra,et al.  Immune networks: multitasking capabilities near saturation , 2013, 1305.5936.

[31]  A Comprehensive Picture for Binary Interactions of Subaqueous Barchans , 2020, Geophysical Research Letters.

[32]  E. Seif,et al.  Environmental Hazards of Sand Dunes, South Jeddah, Saudi Arabia: An Assessment and Mitigation Geotechnical Study , 2019, Earth Systems and Environment.

[33]  Pedro G. Lind,et al.  Size distribution and structure of Barchan dune fields , 2007 .

[34]  Mohamed H. El-Khashab,et al.  Desertification Risk Assessment of Sand Dunes in Middle Egypt: A Geotechnical Environmental Study , 2018, Arabian Journal for Science and Engineering.

[35]  H. J. Herrmann,et al.  Modelling a dune field , 2002 .

[36]  H. Heywood The Physics of Blown Sand and Desert Dunes , 1941, Nature.

[37]  C. Tsallis,et al.  Generalized simulated annealing , 1995, cond-mat/9501047.

[38]  H. Herrmann,et al.  Minimal size of a barchan dune. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  Xiang,et al.  Efficiency of generalized simulated annealing , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[40]  Joel Nothman,et al.  SciPy 1.0-Fundamental Algorithms for Scientific Computing in Python , 2019, ArXiv.

[41]  N. Vriend,et al.  Wake Induced Long Range Repulsion of Aqueous Dunes. , 2020, Physical review letters.