Lagrangian coherent structures

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.

Unsteady swimming and flying flows

One of the most natural inspirations for modern underwater vehicle technology is the locomotion of fish and aquatic mammals, which have proven to be examples of exceedingly efficient, maneuverable, or high-powered swimming. By oscillating their fins and flukes, they create complicated, vortex-dominated wakes, and my current research uses an LCS description of these wakes to determine the underlying physics. I use trapezoidal pitching panels in my experiments as models of flapping caudal fins, and use techniques such as flow visualization by planar laser induced fluorescence (PLIF), digital particle image velocimetry (DPIV), and time-resolved pressure measurements on the panel surface. I am particularly interested in designing both active and passive control implementation on propulsive surfaces to enhance performance, and to better understand the interaction and potential benefits of multiple propulsive surfaces or multiple bodies (schooling and flocking).

In the video above, the trapezoidal panel is pitching, and the green surfaces show the positive vortices being shed once per cycle. The negative vortices shed in the second half of the cycle aren't shown here, just for clarity. The red and blue curves are the negative-time and positive-time LCS, respecitively. Not only do they track the same structures as the vorticity, they reveal dynamics the vorticity does not.

Suction cup whale tags

I have also been fortunate enough to start a collaboration with Dr. Susan Parks in the Biology Department of Syracuse University. Dr. Parks studies acoustic signaling in both marine and terrestrial species, and has recently been using hydroacoustic datalogging tags to record the communication of North Atlantic right whales. These tags use suction cups instead of piercing the skin because right whales are more susceptible to inflammation and infection.

There is a need, then, to characterize the fluid dynamics around these devices for a couple of different reasons. Although the tags are fairly streamlined, they're not perfect nor do they always attach aligned with the direction of flow. Separation will both increase the amount of force felt by the tag (possibly causing it to detach too early) or create extra noise that could be recorded by the hydrophones built into the tag. If this happens around the same frequencies of those studies by the scientists, it could cause problems with their data.

Top left image: four Acousonde hydroacoustic datalogging tags. The brightly colored portions are syntactic foam, which cause the tags to float to surface once they detach. At that point, the scientists can recover the tags and download the raw data. (credit: Top right: CFD simulation of an Acousonde tag at a 45 degree angle to the flow, with a GPS Fasttrack attached to the back. This is a common device that field biologists would like to add to tags to help them recover the hardware. Bottom: an Acousonde attached to a minke whale in Antartica - which lasted over 18 hours. (credit:

Turbulent combustion

Previous research has shown that chemical reactions in a compressible fluid flow interact strongly with the surrounding turbulence both in quantitative measures and qualitative character. In the case of a flame propagating through homogeneous isotropic turbulence, the rapid flow expansion generated in the reaction zone causes a significant attenuation in the vorticity. The suppression of the vorticity magnitude complicates the tracking of individual coherent structures using Eulerian methods. Instead, we use LCS to study the nature of the vortex dynamics, such as structure creation, destruction, and reorientation. It has also been shown that an increase in turbulence intensity increases wrinkling of the flame brush, which increases flame speed and enhances burning. Preliminary results show that as the vortices interact with the flame brush, the surface of the flame brush comes into alignment with the structure boundaries - that is, the flame appears to align with the incoming Lagrangian coherent structures. This understanding can lead to the design and optimization of upstream flow conditions to produce efficient burning and combustion.

In the video below, a flame produced by H2-air compustion propagates through a turbulent flow field. This data is from an implicit Large Eddy Simulation (LES), details of which can be found in this article. The flame is visualized using an isosurface of fuel mass fraction, and the turbulent structures are shown as isosurfaces of the Eulerian Q criterion.