Abstract
We construct an explicit steady stratified purely azimuthal flow for the governing equations of geophysical fluid dynamics. These equations are considered in a setting that applies to the Antarctic Circumpolar Current, accounting for eddy viscosity and forcing terms.
Highlights
Thorough analytical investigations of exact solutions to the fully nonlinear governing equations of geophysical fluid dynamics (GFD) represent an extensive and active research area, which was initiated by Constantin [1,2,3,4] and Constantin and Johnson [5,6,7,8]
We construct a unidirectional flow satisfying GFD considered in the so-called f -plane at the 45th parallel south, enhanced with an eddy viscosity term and a forcing term, and equipped with appropriate boundary conditions
We propose this specific flow for representing the gross dynamics of the Antarctic Circumpolar Current (ACC)—the World’s longest and strongest Ocean current
Summary
Thorough analytical investigations of exact solutions to the fully nonlinear governing equations of geophysical fluid dynamics (GFD) represent an extensive and active research area, which was initiated by Constantin [1,2,3,4] and Constantin and Johnson [5,6,7,8] Following this approach, we construct a unidirectional flow satisfying GFD considered in the so-called f -plane at the 45th parallel south, enhanced with an eddy viscosity term and a forcing term, and equipped with appropriate boundary conditions. To account for the transportation effects of mesoscale eddies we equip the system with an eddy viscosity term; we include a forcing term to ensure the dynamical balance of the flow Both pressure and wind stress are prescribed on the ocean surface; a no-slip boundary condition is assumed for the ocean bed. A collection of numerous recent analytical studies concerning the dynamics of ACC can be found in [7,17,18,22,26,27,28,31] and the references therein
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