Geostrophy
Even though the fluid is in motion, the nearly horizontal character of the fluid trajectories makes the vertical accelerations so small that the Archimedean principle for a static fluid is applicable. That is, the pressure difference between any two points on the same vertical line depends only on the weight of the fluid between those points, as if the fluid were at rest, though in fact it is in motion StratifiedFluid
SouthernOceanBath

In the Northern Hemisphere, looking downstream, warm water (lower density) is on the right-hand side of the current, while cold water (higher density) is on the left-hand side. In the Southern Hemisphere, it is the opposite.

There exists an anomalous low sea surface height surrounding Antarctica, this anomalous low sea surface height must correspond to an anomalous low Sea Surface Temperature (SST) region. Given the background of the Southern Hemisphere, it is easy to judge that there exists a large-scale vortex-like geostrophic circulation — this is the famous Antarctic Circumpolar Current.

Besides SST and sea surface height, it is also possible to use indicators such as chlorophyll concentration for judgment. These principles are interconnected and can be generalized.

1 Pedlosky, J. (1982). Geophysical Fluid Dynamics. Springer study edition. Springer, Berlin, Heidelberg.

2 Benoit Cushman-Roisin & Jean-Marie Beckers. Introduction to Geophysical Fluid Dynamics - Physical and Numerical Aspects. International Geophysics, Volume 101, 2011.

3 Armitage, Thomas & Kwok, Ronald & Thompson, Andrew & Cunningham, Glenn. (2018). Dynamic Topography and Sea Level Anomalies of the Southern Ocean: Variability and Teleconnections. Journal of Geophysical Research: Oceans. 123. 10.1002/2017JC013534.

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