Study of an Elliptic Partial Differential Equation Modeling the Ocean Flow in Arctic Gyres

Susanna V Haziot

doi:10.1007/s00021-021-00584-0

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.

Highlights

The shape of our coasts and the mixing and transportation of temperature, chemicals, and nutrients are largely due to oceanic currents: these currents sometimes link up to form large-scale spiraling circulations called gyres
The waters move in the direction of the winds on small scales but on large-scales they are deflected by the second major force, due to the rotation of the Earth
Haziot ice, surrounded by land, the Antarctic is a landmass surrounded by a very powerful current known as the antarctic circumpolar current (ACC)

Summary

Introduction

The shape of our coasts and the mixing and transportation of temperature, chemicals, and nutrients are largely due to oceanic currents: these currents sometimes link up to form large-scale spiraling circulations called gyres. The movements of gyres drive the “ocean conveyor belt”, which in turn circulates ocean water around the entire planet. The waters move in the direction of the winds on small scales but on large-scales they are deflected by the second major force, due to the rotation of the Earth. This force, commonly referred to as the Coriolis force, produces clockwise circular motions in the Northern hemisphere and counterclockwise ones in the Southern hemisphere. We have the subtropical gyres, situated between the Equator and the polar regions Since they lie beneath areas of high atmospheric pressure, they are gigantic placid ocean areas with thousands of kilometers of diameter.

48 Page 2 of 9

The Arctic Gyres

48 Page 4 of 9

The Conformal Mapping

Constant Vorticity

Linear Vorticity

Physical Relevance of the Results