12 Pages
English
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Modelling of dune patterns by short range interactions

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12 Pages
English

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Niveau: Supérieur, Doctorat, Bac+8
Modelling of dune patterns by short range interactions Clement Narteau, Eric Lajeunesse, Franc¸ois Metivier & Olivier Rozier Equipe de Geomorphologie, Laboratoire de Dynamique des Systemes Geologiques, Institut de Physique du Globe de Paris, 75252 Paris cedex 05, France (). A 3D cellular automaton is disclosed that enables modelling the dynamics of bedform. The overall mechanism can be regarded as a Markov chain, a discrete system with a finite number of configurations and probabilities of transition between them. Physical processes such as erosion, deposition and transport are modelled at the elementary scale by nearest neighbour interactions. At larger length scales, topographic structures arise from internal relationships based upon these short range interactions. This article focuses on crescentic barchan dunes that are used as a benchmark for our numerical model of bedforms. Length and time scales of isolated barchan dunes are studied in order to constrain the parameters of the model. Then we discuss pattern selection and the evolution of a population of dunes over a wide range of initial and boundary conditions. We eventually show that our model can be generalized to bedforms through the increase of the sand availability. 1 Introduction There is a considerable variation within bedforms as they locally depend on the topography, the sed- iment load, and the flow. Such variability might be expressed by different relationships between erosion and deposition rates and the fluid velocity field.

  • fluid shear

  • permutation between

  • fluid states

  • fluid

  • following transitions

  • transition rate

  • sediment results

  • wall

  • dune


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ModellingofdunepatternsbyshortrangeinteractionsCle´mentNarteau,EricLajeunesse,Fran¸coisMe´tivier&OlivierRozierEquipedeGe´omorphologie,LaboratoiredeDynamiquedesSystemesGe´ologiques,InstitutdePhysiqueduGlobedeParis,75252Pariscedex05,France(narteau@ipgp.jussieu.fr).A3Dcellularautomatonisdisclosedthatenablesmodellingthedynamicsofbedform.TheoverallmechanismcanberegardedasaMarkovchain,adiscretesystemwithanitenumberofcongurationsandprobabilitiesoftransitionbetweenthem.Physicalprocessessuchaserosion,depositionandtransportaremodelledattheelementaryscalebynearestneighbourinteractions.Atlargerlengthscales,topographicstructuresarisefrominternalrelationshipsbasedupontheseshortrangeinteractions.Thisarticlefocusesoncrescenticbarchandunesthatareusedasabenchmarkforournumericalmodelofbedforms.Lengthandtimescalesofisolatedbarchandunesarestudiedinordertoconstraintheparametersofthemodel.Thenwediscusspatternselectionandtheevolutionofapopulationofdunesoverawiderangeofinitialandboundaryconditions.Weeventuallyshowthatourmodelcanbegeneralizedtobedformsthroughtheincreaseofthesandavailability.1Introductioncontinuityequationfortheheightprole∂h=∂q(1)Thereisaconsiderablevariationwithinbedformstxastheylocallydependonthetopography,thesed-whereqisdenedasavolumicsanduxperunitimentload,andtheow.Suchvariabilitymightbeoftimeandperunitoflengthperpendicularlytotheexpressedbydifferentrelationshipsbetweenerosionwinddirection.Thecapacityoftransporttakesthere-anddepositionratesandtheuidvelocityeld.Whileforetheformofasaturatedsanduxqs,andtheonlyempiricalrelationshipsestimatethesequantitiesforaparametersarethosewhicharerelevantforthemag-givenbedunderparticularconditions,theoreticalre-nitudeofqsaccordingtothetopography(Kroyetal.lationshipssimplifytheturbulenceproblemtomake2002a;Andreottietal.2002).Schematically,foraeasierthedescriptionofthesedimentcapacityofthestrongenoughwind,depositiondominatesifqap-ow.Inbothcases,itremainsextremelydifculttoproachesqs(i.exq<0),elseerosionoccurs(i.etackletheimpactofthesizedistributionofsedimentxq>0).Inallcases,therearedifferentwaystheparticles.Despitetheselimitations,thestudyofaeo-grainscanbeputintomovement.First,theycanbelianduneshassignicantlylledthegapbetweenob-dragged,liftedandacceleratedbytheexcessshearservationsandmodels(Bagnold1941;PyeandTsoarstressexertedbytheuidonthesurface.Thiscorre-1990;Lancaster1995).spondstosaltation.Second,theycanbereleasedbyimpactsoffallinggrainsandcrawlonthesurface.Underdryconditions,thetransportofsandgrainsThiscorrespondstoreptation.Thesetwotransportbythewindinvolvessimilarphysicalmechanismsmodesareobviouslyrelatedtooneanother,essen-thansedimenttransportinliquids.Howevertheab-tiallybecausesaltationimpliesanirregularhoppingsenceofcohesion,dissolutionandsedimentationlim-processthroughtheretroactionoftransportedgrainsitsthenumberofrelationsbetweenuidandsolidin-onwindvelocity.gredients.Then,inordertoinvestigatecouplingsbe-Inthispaper,weconcentrateontheformationandtweenwindandtopography,itissufcienttoformal-theevolutionofcrescenticbarchansdunesasabench-izethewindvelocityeldwithrespecttothesurfacemarkforanewmodelofsedimenttransport.Barchanproleaswellastheerosionanddepositionresponsesdunesareisolatedstructureswithhornsextendingtoshearstress(JacksonandHunt1975;Huntetal.downwindonbothsidesofansandpilecharacterized1988;Wengetal.1991).Inthisframework,theprin-byaslipfaceandawindwardface(Fig.1).Saltationcipleofmassconservationiscommonlyensuredbyaandreptationareactiveonthewindwardfaceandthe1