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Abstract:
The finite-time Lyapunov exponent (FTLE) has become a standard tool
for analyzing unsteady flow phenomena, partly since its ridges can
be interpreted as Lagrangian coherent structures (LCS). While there
are several definitions for ridges, a particular one called second
derivative ridges has been introduced in the context of LCS, but
subsequently received criticism from several researchers for being
over-constrained. Among the critics are Norgard and Bremer [Physica
D 2012.05.006], who suggest furthermore that the widely used definition
of height ridges was a part of the definition of second derivative
ridges, and that topological separatrices were ill-suited for describing
ridges. We show that (a) the definitions of height ridges and second
derivative ridges are not directly related, and (b) there is an interdisciplinary
consensus throughout the literature that topological separatrices
describe ridges. Furthermore, we provide pointers to practically
feasible and numerically stable ridge extraction schemes for FTLE
fields.
