Study of an Elliptic Partial Differential Equation Modeling the Ocean Flow in Arctic Gyres
Susanna V. Haziot
Abstract
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.
Topics & Concepts
Ocean gyreUniquenessMathematical analysisElliptic partial differential equationPartial differential equationMathematicsFlow (mathematics)Unit diskConformal mapProjection (relational algebra)Domain (mathematical analysis)GeometryFisherySubtropicsAlgorithmBiologyDifferential Equations and Numerical MethodsAdvanced Mathematical Modeling in EngineeringArctic and Antarctic ice dynamics