On Ocean Currents with Constant Vorticity
Explicit Solutions and an Application to the ACC
Anna Geyer (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Ronald Quirchmayr (Interdisciplinary Research Institute on Bio-Nano-Science of Babes-Bolyai University)
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Abstract
We study the three-dimensional, divergence-free, incompressible Euler equations in the (Formula presented.) -plane approximation for off-equatorial oceanic flows of constant vorticity, where the fluid domain is bounded by a free surface and a flat bed. The major difference, compared to related earlier works, is that we refrain from any global restrictions on solutions with respect to the latitudinal coordinate (Formula presented.), which we justify by the (Formula presented.) -plane approximation's locality. The resulting flows are necessarily steady (despite the time dependence of the governing equations), zonal, independent of the zonal coordinate (Formula presented.), and fully explicit; the corresponding free surface exhibits a nontrivial parabolic structure in (Formula presented.). We also provide an application to the Antarctic Circumpolar Current (ACC) for which we compare the sea surface height predicted by our constant vorticity model with satellite altimetry measurements available in the literature.
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