A Fourier approach to Lagrangian vortex detection.

We study the transport properties of coherent vortices over a finite-time duration. Here, we reveal that such vortices can be identified based on the frequency-domain representation of Lagrangian trajectories. We use Fourier analysis to convert particles' trajectories from their time domain to a presentation in the frequency domain. We then identify and extract coherent vortices as material surfaces along which particles' trajectories share similar frequencies. Our method identifies all coherent vortices in an automatic manner, showing high vortices' monitoring capacity. We illustrate our new method by identifying and extracting Lagrangian coherent vortices in different two- and three-dimensional flows.