To investigate fluid flows I primarily use a Lagrangian Coherent Structure (LCS) analysis, which has enjoyed increasing popularity in the fluid dynamics community as a method of coherent structure identification. Whereas vorticity shows those regions where the vorticity magnitude is highest (vortex cores), LCS shows the vortex boundaries, those regions where the dynamics occur that dictate structure creation, destruction, and interaction. As with all new tools, it is my belief that there are many more uses of LCS that have not yet been explored, and I am particularly intrigued by the idea of deriving quantities such as averaged structure size and speed and statistical measures from FTLE fields of fully turbulent fluid flows.
I also believe that a similar approach can inform a much more general problem, which is the interpretation and analysis of vast amounts of data. Fluid dynamics is not the only area in which structures and patterns are educed from large data sets, and I would like to take the experience of identifying and describing coherent structures in fluid flows and apply it to other natural systems governed by partial differential equations. I am curious to see how the methods I use in my research could be extended to such areas, thereby addressing the problems facing the entire scientific community as the scale and scope of computations advance to include more and more physics.
The figure above shows the coherent structure composition of a fully turbulent channel flow using data from Direct Numerical Simulation (DNS). The top left image shows the structures visualized using the Eulerian Q-criterion. The panels lined with red, yellow, and blue show the negative-time FTLE field in the corresponding planes. Ridges of this field (white) are the nLCS.