Environmental Engineering Reference
In-Depth Information
Flow Coherence: Distinguishing
Cause from Effect
F.J. Beron Vera
Abstract The geodesic transport theory unveils the especial fluid trajectory sets,
referred to as Lagrangian Coherent Structures (LCS), that cause a flow to organize
into ordered patterns. This is illustrated through the analysis of an oceanic flowdataset
and contrasted with the tendency of a widely used flow diagnostic to carry coherence
imprints as an effect of the influence of LCS on neighboring fluid trajectories.
1 Introduction
Flowcoherence ismanifested by the appearance of ordered patterns in the distribution
of any transported scalar. The fundamental cause of flow coherence is attributed to the
existence of especial sets of fluid trajectories that dictate the evolution of neighboring
ones. In two-space dimensions, time slices of these especial fluid trajectory sets form
material lines which are widely referred to as Lagrangian Coherent Structures (LCS),
a terminology introduced by Haller and Yuan ( 2000 ); cf. Haller ( 2015 ) for a recent
review.
Since the introduction of the LCS notion, a considerable effort has been devoted to
devising techniques capable of diagnosing flow coherence from time-aperiodic flows
defined over finite-time intervals that is not obvious from the inspection of velocity
snapshots. One such flow diagnostic is the Finite-Time Lyapunov Exponent (FTLE),
which characterizes the amount of stretching about fluid trajectories in an objective
(i.e., frame-independent) manner. Constructed fromfluid trajectories, the FTLE tends
to carry flow coherence imprints as an effect of the underlying LCS, which have been
heuristically associated with locally extremizing FTLE curves. For a recent review
on the wide range of FTLE applications, cf. Peacock and Dabiri ( 2010 ). Similar
tendency to carry flow coherence imprints has been noted with other flow diagnostics
constructed from fluid trajectories. These include objective flow diagnostics, such
as relative dispersion (Provenzale 1999 ), Finite-Size Lyapunov Exponents (FSLE)
 
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