EAPSI: Identification of Transport Barriers in Two-Dimensional Turbulence

Faber Benjamin J, Madison WI

Investigators

Abstract

Knowing the location and evolution of transport barriers within a fluid provides an important tool in predicting how particles disperse, a prime example being how an oil spill spreads on the ocean surface. A turbulent, two-dimensional fluid, like the surface of the ocean, can have distinct regions where the fluid does and does not mix, which determines how particles are transported across the surface of the fluid. Those non-mixing regions are known as transport barriers, as particles outside cannot move into or across the transport barrier. This project will use laboratory-produced two-dimensional turbulence to experimentally test and refine recently developed, novel mathematical methods for identifying transport barriers. This research will be conducted in collaboration with Dr. Hua Xia, an expert in experimental two-dimensional fluid turbulence, at Australian National University in Canberra, Australia. Historically, identifying coherent structures (transport barriers) in a fluid by way of finite time Lyapunov exponents is an intensive task that requires detailed resolution of the fluid velocity field. Recently, mathematical methods for identifying coherent structures based on braid theory have been developed and applied to several test cases. These methods are advantageous as they can identify coherent structures from a small number of surface particle trajectories, decreasing the computational cost and increasing the method applicability. This research will implement and improve the braid-theoretic identification scheme by testing the algorithms with surface particle trajectories taken from experiments in which turbulence is driven by Faraday waves. This project aims to develop a computational framework that can then be applied in situ to surface particle trajectories both inside and outside of laboratory experiments. This NSF EAPSI award is funded in collaboration with the Australian Academy of Science.