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dc.contributor.authorTanios, Ramy
dc.contributor.authorMohtar, Samah El
dc.contributor.authorKnio, Omar
dc.contributor.authorLakkis, Issam
dc.date.accessioned2019-12-23T07:41:24Z
dc.date.available2019-12-23T07:41:24Z
dc.date.issued2019-11-21
dc.identifier.urihttp://hdl.handle.net/10754/660746
dc.description.abstractIn geophysical fluid dynamics, the screened Poisson equation appears in the shallow-water, quasi geostrophic equations. Recently, many attempts have been made to solve those equations on the sphere using different numerical methods. These include vortex methods, which solve a Poisson equation to compute the stream-function from the (relative) vorticity. Alternatively, the stream-function can be computed directly from potential vorticity (PV), which would offer the possibility of constructing more attractive vortex methods because PV is conserved along material trajectories in the inviscid case. On the spherical shell, however, the screened Poisson equation does not admit a known Green's function, which limits the extension of such approaches to the case of a sphere. In this paper, we derive an expression of Green's function for the screened Poisson equation on the spherical shell in series form and in integral form. A proof of convergence of the series representation is then given. As the series is slowly convergent, a robust and efficient approximation is obtained using a split form which isolates the singular behavior. The solutions are illustrated and analyzed for different values of the screening constant.
dc.description.sponsorshipThis work is supported by the University Research Board of the American University of Beirut. The authors would like to acknowledge Professor Leila Issa of the Lebanese American University-Beirut for her insightful feedback on the mathematical derivation of the convergence of the Green’s Function.
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/1911.10944
dc.rightsArchived with thanks to arXiv
dc.titleGreen's function of the screened Poisson's equation on the sphere
dc.typePreprint
dc.contributor.departmentKing Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.eprint.versionPre-print
dc.contributor.institutionAmerican University of Beirut, Beirut, Lebanon
dc.contributor.institutionDuke University, Durham, NC 27708, USA
dc.identifier.arxivid1911.10944
kaust.personMohtar, Samah El
kaust.personKnio, Omar
refterms.dateFOA2019-12-23T07:42:03Z


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