April 2011

George Haller

Department of Mechanical Engineering, McGill University

Friday, April 15th 2011, 6 pm
McGill University
Otto Maass Building, Room OM-10

Lagrangian Coherent Structures: The Skeleton of Water

Lagrangian Coherent Structures (LCS) are dynamically evolving material surfaces that govern the evolution of complex material patterns in moving fluids and solids.Examples of such patterns include oil spills, ash clouds, plankton populations, schools of fish and moving crowds. Because of their finite lifetime and aperiodic nature,LCS have been challenging to locate, predict or control. At the same time, LCS promise to play a key role in the real-time assessment and short-term forecasting of a number of environmental conditions, including hazardous winds over airports and the spread of contaminants in coastal waters. In this talk, I describe a matehmatical theory that enables a mathematically rigorous extraction of LCS from observational flow data. In this approach, LCS are defined as invariant surfaces that extremize an appropriate finite-time normal repulsion or attraction measure in the governing dynamical system. Solving this variational problem leads to computable sufficient and necessary criteria for LCS. I will show recent applications to large scale oceanic and atmospheric flow problems.