Imagine a point source that releases particles that are carried away by the currents in various directions. You do this over a period of time to get a representative ensemble of particle trajectories from the point of release. The area that has been reached by the particles as a function of time can be expressed in terms of an evolving or expanding domain of occupation. This is a powerful Lagrangian tool for charting how stuff spreads out in the ocean.
The early years of the RAFOS float program illustrates this concept well, Beginning in 1984 (40 years ago!) and later in 1988 we released numerous isopycnal RAFOS floats in the center of the Gulf Stream just east of Cape Hatteras. We ballasted the floats for the 9-12°C range in the beginning and moved toward warmer 15°C water in later deployments. It was truly astounding what these slight differences in temperature made in terms of how far the floats would travel in 28 days. This seemed to contradict our view of the Gulf Stream as a well-defined current extending to great depths. The vertical separation between the cooler and warmer floats (9 to 15°C) is at most 250 m, a small fraction of the current’s vertical extent. Yet the warmer floats stayed in the stream to various distances as far as ~2000 km, floats in the intermediate range (~12°C, only 100+ m deeper) traveled perhaps half as far with more frequent expulsions from the stream. And the coldest ones were expelled almost immediately from the current! See figure 3 in Rossby (2016). The shallower floats remain trapped in the stream whereas at depth floats can wander from side-to-side. On warm (shallow) surfaces the stream is acting as a barrier; on cooler deeper surfaces it acts as a blender. The shallow domain of occupation is narrow and extended, the deep one is more limited but wider.
This form of point-release sampling has been used effectively to study the spread of Mediterranean water from south of Portugal (Bower et al., 1995), and the spread of North Atlantic waters in the Norwegian Sea (Rossby et al., 2009).
Suppose you released isopycnal RAFOS floats in the middle of the Florida Current, do you think they would make it to Cape Hatteras?
Rossby, T. (2016), Visualizing and quantifying oceanic motion. Ann. Rev. Mar. Sci. 8:7.1–7.23. 10.1146/annurev-marine-122414-033849
Bower, A. S., L. Armi, and I. Ambar (1995) Direct evidence of meddy formation off the southwestern coast of Portugal. Deep-Sea Res, 42(9), l621-1630. 1995
Rossby, T., M. Prater and H. Søiland, 2009. Pathways of inflow and dispersion of warm waters in the Nordic Seas. J. Geophys Res.. 114, C04011, doi:10.1029/2008JC005073