(
2018-01-19)
Balasuriya, Sanjeeva; Ouellette, Nicholas T.; Rypina, Irina I.
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.
