Generalized Lagrangian coherent structures

• Published in: Physica. D 2018-06, Vol.372, p.31-51
• Main Authors: Balasuriya, Sanjeeva, Ouellette, Nicholas T., Rypina, Irina I.
• Format: Article
• Language: English
• Subjects: Atmospheric vortices; Flow barriers; Fluid flow; Lagrangian Coherent Structures; Ocean eddies
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/j.physd.2018.01.011

The notion of a Lagrangian Coherent Structure (LCS) is by now well established as a way to capture transient coherent transport dynamics in unsteady and aperiodic fluid flows that are known over finite time. We show that the concept of an LCS can be generalized to capture coherence in other quantities of interest that are transported by, but not fully locked to, the fluid. Such quantities include those with dynamic, biological, chemical, or thermodynamic relevance, such as temperature, pollutant concentration, vorticity, kinetic energy, plankton density, and so on. We provide a conceptual framework for identifying the Generalized Lagrangian Coherent Structures (GLCSs) associated with such evolving quantities. We show how LCSs can be seen as a special case within this framework, and provide an overarching discussion of various methods for identifying LCSs. The utility of this more general viewpoint is highlighted through a variety of examples. We also show that although LCSs approximate GLCSs in certain limiting situations under restrictive assumptions on how the velocity field affects the additional quantities of interest, LCSs are not in general sufficient to describe their coherent transport. •Comprehensively surveys Lagrangian Coherent Structure (LCS) methods.•Highlights that each LCS method provides different information, and has limitations.•Argues the need for generalizing LCS methods, and provides a general framework.•Provides examples from advecting and diffusing fluids, oceanography and microfluidics.•Discusses overarching issues relevant to LCSs and their generalizations.