ContinentalShelfResearch21(2001)1331–1360 Wave-currentinteractionsinshallowwaters andshore-connectedridges JuanMarioRestrepo Department of Mathematics and Program in Applied Mathematics, University of Arizona, Tuscon, AZ 85721, USA Received16June2000;receivedinrevisedform16February2001;accepted16April2001 Abstract Aformalismisdevelopedfortheinteractionsofwavesandcurrentsonlongtimescales.Theresulting hydrodynamicequationsareapplicabletoavarietyofbarotropicflows.ItspecificallyidentifiestheStokes driftvelocityduetothegravitywavesasthecontributingeffectofthewavestothegeneralcirculation.The Stokesdriftplaysaroleonthelong-timedynamicsofthemeanEulerianvelocity,bycouplingtothemean vorticity.Iftracersarepresentintheflow,thisStokesdriftalsoaffectsthedynamicsofthemeantracerfield bymodifyingitsadvectionduetocurrentsalone.Thetheorymaybeusedtostudythedynamicsoflarge scaleerodiblebedscomposedofloosesedimentsubjectedtointeractingstorm-andtidal-drivenflows.One suchproblemistheoriginandevolutionofcertainshore-obliquesandridges.Anhypothesisisthattheyare generatedbyinstabilitiesintheerodiblebedduetothepassageofsteadycurrents.Byapplyingthetheory weshowhowsuchanhypothesisismodifiedwhentheunsteadinessassumptionisliftedandwhenboth wavesandcurrentsarepresent. r 2001ElsevierScienceLtd.Allrightsreserved. Keywords: Waves–currentinteractions;Sandridges;Shore-connectedridges 1. Introduction SurfacegravitywavesarecapableofgeneratingacurrentcalledtheStokesdrift(Stokes,1847). TheStokesdriftcanaffecttheseastateinasometimesdramaticway(someexamplesappearin Longuet-Higgins and Stewart, 1960, 1961; Hasselmann, 1971). It also influences the ocean currents. Hasselmann (1970) shows that the Stokes drift is capable of inducing, in conjunction withtheCoriolisforce,anopposingmeanEuleriancurrentandinertialoscillations.Craikand Leibovich(1976)showthattheinteractionoftheStokesdriftwiththemeanflowcouldgiveriseto Langmuircirculationcells.Webber ð1983Þ andWebberandMelsom(1993)analyzethetransferof E-mail address: restrepo@math.arizona.edu(J.M.Restrepo). 0278-4343/01/$-seefrontmatter r 2001ElsevierScienceLtd.Allrightsreserved. PII:S0278-4343(01)00016-4