Study of an Elliptic Partial Differential Equation Modeling the Ocean Flow in Arctic Gyres
We study the ocean flow in Arctic gyres using a recent model for gyres derived in spherical coordinates on the rotating sphere. By projecting this model onto the plane using the Mercator projection, we obtain a semi-linear elliptic partial differential equation in an unbounded domain, difficulty whi...
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| Published in | Journal of mathematical fluid mechanics Vol. 23; no. 2 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
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Springer International Publishing
01.05.2021
Springer Nature B.V |
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| Abstract | We study the ocean flow in Arctic gyres using a recent model for gyres derived in spherical coordinates on the rotating sphere. By projecting this model onto the plane using the Mercator projection, we obtain a semi-linear elliptic partial differential equation in an unbounded domain, difficulty which is then overcome by projecting the PDE onto the unit disk via a conformal map. We then study existence, regularity and uniqueness of solutions for constant and linear vorticity functions. |
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| AbstractList | We study the ocean flow in Arctic gyres using a recent model for gyres derived in spherical coordinates on the rotating sphere. By projecting this model onto the plane using the Mercator projection, we obtain a semi-linear elliptic partial differential equation in an unbounded domain, difficulty which is then overcome by projecting the PDE onto the unit disk via a conformal map. We then study existence, regularity and uniqueness of solutions for constant and linear vorticity functions. Abstract We study the ocean flow in Arctic gyres using a recent model for gyres derived in spherical coordinates on the rotating sphere. By projecting this model onto the plane using the Mercator projection, we obtain a semi-linear elliptic partial differential equation in an unbounded domain, difficulty which is then overcome by projecting the PDE onto the unit disk via a conformal map. We then study existence, regularity and uniqueness of solutions for constant and linear vorticity functions. |
| ArticleNumber | 48 |
| Author | Haziot, Susanna V. |
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| References | ConstantinAJohnsonRSEkman-type solutions for shallow-water flows on a rotating sphere: a new perspective on a classical problemPhys. Fluids201910.1063/1.5083088 KamkeEDifferentialgleichungen: Lösungensmethoden und Lösungen1967LeipzigAkademische Verlagsgesellschaft HaziotSVExplicit two-dimensional solutions for the ocean flow in arctic gyresMonatshefte Math.2018189429440397667310.1007/s00605-018-1198-31420.35425 QuirchmayrRA steady, purely azimuthal flow model for the Antarctic Circumpolar CurrentMonatshefte Math.2018187565572385843210.1007/s00605-017-1097-z1400.86003 AbramowitzMStegunIHandbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables1965New YorkDover Publications, INC.0171.38503 VallisGKAtmosphere and Ocean Fluid Dynamics2006CambridgeCambridge University Press10.1017/CBO9780511790447 AsplinMGLukovichJVBarberDGAtmospheric forcing of the Beaufort Sea ice gyre: surface pressure climatology and sea ice motionJ. Geophys. Res.200910.1029/2008JC005127 DanersDThe Mercator and stereographic projections, and many in betweenAm. Math. Mon.2012119199210291143610.4169/amer.math.monthly.119.03.199 AndrewsGEAskeyRRoyRSpecial Functions1999CambridgeCambridge University Press10.1017/CBO9781107325937 HaziotSVStudy of an elliptic partial differential equation modelling the Antarctic Circumpolar CurrentDiscrete Contin. Dyn. Sys. A201939844154427398629410.3934/dcds.2019179 BrézisHFunctional Analysis, Sobolev Spaces and Partial Differential Equations2011BerlinSpringer1220.46002 HsuH-CMartinCIOn the existence of solutions and the pressure function related to the Antarctic Circumpolar CurrentNonlinear Anal.2017155285293363175510.1016/j.na.2017.02.021 StuartJTOn finite amplitude oscillations in laminar mixing layersJ. Fluid Mech.1967294174401967JFM....29..417S10.1017/S0022112067000941 ConstantinAJohnsonRSLarge gyres as a shallow-water asymptotic solution of Euler’s equation in spherical coordinatesProc. R. Soc. Lond. Ser. A2017473201700632017RSPSA.47370063C36505911404.86015 CrowdyDGStuart vortices on a sphereJ. Fluid Mech.20043983814022004JFM...498..381C225692410.1017/S0022112003007043 ProtterMHWeinbergerHFMaximum Principles in Differential Equations1984New YorkSpringer10.1007/978-1-4612-5282-5 GilbargDTrudingerNSElliptic Partial Differential Equations of Second Order1983BerlinSpringer10.1007/978-3-642-61798-0 ConstantinAJohnsonRSAn exact, steady, purely azimuthal flow as a model for the Antarctic Circumpolar CurrentJ. Phys. Oceanogr.201646358535942016JPO....46.3585C10.1175/JPO-D-16-0121.1 ConstantinAKrishnamurthyVStuart-type vortices on a rotating sphereJ. Fluid Mech.2019865107210842019JFM...865.1072C391834810.1017/jfm.2019.109 EvansLawrence CPartial Differential Equations20102ProvidenceAmerican Mathematical Society1194.35001 MarynetsKTwo-point boundary problem for modeling the jet flow of the Antarctic Circumpolar CurrentElectron. J. Differ. Equ.20185611237811711387.34037 DG Crowdy (584_CR9) 2004; 398 M Abramowitz (584_CR1) 1965 GE Andrews (584_CR2) 1999 SV Haziot (584_CR14) 2019; 39 MH Protter (584_CR18) 1984 D Daners (584_CR10) 2012; 119 R Quirchmayr (584_CR19) 2018; 187 E Kamke (584_CR16) 1967 JT Stuart (584_CR20) 1967; 29 D Gilbarg (584_CR12) 1983 A Constantin (584_CR7) 2019 K Marynets (584_CR17) 2018; 56 A Constantin (584_CR6) 2016; 46 H-C Hsu (584_CR15) 2017; 155 Lawrence C Evans (584_CR11) 2010 SV Haziot (584_CR13) 2018; 189 GK Vallis (584_CR21) 2006 H Brézis (584_CR4) 2011 MG Asplin (584_CR3) 2009 A Constantin (584_CR5) 2017; 473 A Constantin (584_CR8) 2019; 865 |
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| Snippet | We study the ocean flow in Arctic gyres using a recent model for gyres derived in spherical coordinates on the rotating sphere. By projecting this model onto... Abstract We study the ocean flow in Arctic gyres using a recent model for gyres derived in spherical coordinates on the rotating sphere. By projecting this... |
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| SubjectTerms | Classical and Continuum Physics Conformal mapping Fluid mechanics Fluid- and Aerodynamics Gyres Mathematical Methods in Physics Mercator projection Ocean models Partial differential equations Physics Physics and Astronomy Rotating spheres Spherical coordinates Theoretical mathematics Vorticity |
| Title | Study of an Elliptic Partial Differential Equation Modeling the Ocean Flow in Arctic Gyres |
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