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Double gyre velocity field
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This time-dependent double gyre velocity field has become a common test problem for techniques involving Lagrangian coherent structures (LCS). The flow was first analyzed using LCS by Shadden et al. and consists of two counter-rotating gyres with a time dependent perturbation. The velocity field is shown in the first video. In the absence of the perturbation, a heteroclinic connection exists between the points (1,0) and (1,1), preventing any exchange of fluid between the left and right gyres. The perturbation breaks this connection, forming a heteroclinic tangle that enables transport between the two gyres.
LCS are commonly defined as ridges of the finite time Lyapunov exponent (FTLE) field. By this definition, LCS act as repelling or attracting structures in the flow. Additionally, LCS act as transport barriers and are in many ways analogous to the stable and unstable manifolds of traditional dynamical systems. The second video shows the attracting (red) and repelling (blue) LCS in the double gyre system. The closed "lobes" formed by the interaction of the LCS reveal the mechanisms of transport between the two gyres.
Swimming jellyfish
These videos show the Lagrangian coherent structures from a numerical simulation of a swimming jellyfish. This jellyfish, Sarsia tubulosa, ejects a single energetic vortex during each swimming period. For details of the CFD, see Sahin and Mohseni, JEB 2009.
The Lagrangian coherent structures were computed using the swirl free axisymmetric velocity data and are shown in the first video. The red curves represent attracting structures in the flow and would also be seen in dye-visualization experiments. The blue curves represent repelling structures which are otherwise not easily visualized. Together, these structures define the skeleton of transport in the flow including the ejected vortices and fluid intake into the bell.
The second video shows the full three-dimensional LCS in this flow. The LCS were computed using a ridge tracking algorithm that only performs computations near the LCS surfaces, providing large computational savings. For more information see "A 3D fast algorithm for computing Lagrangian coherent structures via ridge tracking".
LCS in the Gulf of Mexico
The fluid transport and currents in the Gulf of Mexico have direct and significant impacts on the weather in much of the eastern United States. Influxes of moist air from the Gulf create intense storms and tornados over the plains and the warm water can feed and intensify hurricanes. Despite it's importance, few modern studies exist on the three-dimensional transport in the Gulf. This video shows a single near-surface plane of the three-dimensional LCS in the Gulf during 2010. The LCS were computed from the publicly available ECCO2 dataset using the ridge tracking algorithm mentioned above. The most prominent features reveal the loop current and its accompanying warm-core rings that are periodically shed in the eastern Gulf. These rings drift gradually to the west under the influences of the beta effect and the underlying bathymetry, eventually disipating in the western Gulf.
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image: Jet Propulsion Laboratory
At least one potentially dire consequence of climate change predicted by some models doesn't appear to be happening yet: BBC News reports that though it made for semi-compelling cinema in The Day After Tomorrow, according to research published in Geophysical Research Letters the Gulf Stream does not appear to be slowing down. Scientists from NASA's Jet Propulsion Laboratory say that new measurements of the Atlantic Meridional Overturning Circulation "show no significant slowing over the past 15 years." In fact, at least in a short time scale, recently it appears that things have even sped up a bit.
NASA oceanography Josh Willis says that though the latest climate models predict a slow down in the overturning circulation as the planet warms and more freshwater enters the system, at least for now that isn't happening.
Willis adds, "The changes we're seeing in overturning strength are probably part of a natural cycle. The slight increase in overturning since 1993 coincides with a decades-long natural pattern of Atlantic heating and cooling."
Last Ice Age Brought About by Changes in This Circulation
Why is this important? NASA describes it:
Without the heat carried by this circulation system, the climate around the North Atlantic--in Europe, North America and North Africa--would likely be much colder. Scientists hypothesize that rapid cooling 12,000 years ago at the end of the last ice age was triggered when freshwater from melting glaciers altered the ocean's salinity and slowed the overturning rate. That reduced the amount of heat carried northward as a result.
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