{"title":"Flux atop an advancing slip face and the brink line curvature of barchan dunes","authors":"Jakob Leck","doi":"10.1007/s10035-024-01464-w","DOIUrl":null,"url":null,"abstract":"<p>A two-dimensional argument by Bagnold for the flux over the brink line of a shape-invariantly moving dune is generalized to three dimensions. This is achieved by describing the slip face as the solution to an eikonal equation with an unusual Dirichlet boundary condition where part of the boundary is to be determined. With the assumption of potential flow the flux over a heap is obtained based on kinematics, by solving a Poisson equation and without making reference to the wind profile or sand flux laws. Matching it with the brink line flux can be used in the results of field observations by Sauermann et al. (Geomorphology 36:47–62, 2000) to explain one of the five measured shape parameters of a barchan, the brink line curvature, from the other four. More generally the brink line flux formula proposed here could serve as an evolution equation for the brink line position in a given height and flux profile, in the limit that the avalanching processes are much faster than the rest of the surface evolution.</p>","PeriodicalId":49323,"journal":{"name":"Granular Matter","volume":"26 4","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Granular Matter","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10035-024-01464-w","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
A two-dimensional argument by Bagnold for the flux over the brink line of a shape-invariantly moving dune is generalized to three dimensions. This is achieved by describing the slip face as the solution to an eikonal equation with an unusual Dirichlet boundary condition where part of the boundary is to be determined. With the assumption of potential flow the flux over a heap is obtained based on kinematics, by solving a Poisson equation and without making reference to the wind profile or sand flux laws. Matching it with the brink line flux can be used in the results of field observations by Sauermann et al. (Geomorphology 36:47–62, 2000) to explain one of the five measured shape parameters of a barchan, the brink line curvature, from the other four. More generally the brink line flux formula proposed here could serve as an evolution equation for the brink line position in a given height and flux profile, in the limit that the avalanching processes are much faster than the rest of the surface evolution.
期刊介绍：
Although many phenomena observed in granular materials are still not yet fully understood, important contributions have been made to further our understanding using modern tools from statistical mechanics, micro-mechanics, and computational science.
These modern tools apply to disordered systems, phase transitions, instabilities or intermittent behavior and the performance of discrete particle simulations.
>> Until now, however, many of these results were only to be found scattered throughout the literature. Physicists are often unaware of the theories and results published by engineers or other fields - and vice versa.
The journal Granular Matter thus serves as an interdisciplinary platform of communication among researchers of various disciplines who are involved in the basic research on granular media. It helps to establish a common language and gather articles under one single roof that up to now have been spread over many journals in a variety of fields. Notwithstanding, highly applied or technical work is beyond the scope of this journal.
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