Flow Coherence: Distinguishing Cause from Effect - Selected Topics of Computational and Experimental Fluid Mechanics - page 84

ridges, particularly at initial times. Indeed, at initial times patch centerline LCS and
nearby FTLE ridges run transversal, almost orthogonal, to each other. At later times,
FTLE ridges run closer to the LCS, but this is not a consequence of the LCS being
attracted by the FTLE ridges. Rather, it is a consequence of the LCS organizing the
flow into ordered patterns, which place their imprints in any scalar that is transported
by the flow or flow diagnostic that is constructed from fluid trajectories, such as the
FTLE. For instance, the reason for the peculiar pattern shapes in the FTLE field
on t 0 = 22 September 2012 is attributed to attracting LCS over t 0 = 12 September
2012 through t = 22 September 2012. Because of the duality between backward
squeezelines and forward stretchlines, these LCS are given by images under the flow
map of stretchlines on t 0 = 12 September 2012 computed in forward time out to
t = 22 September 2012 or, equivalently, squeezelines on t 0 = 22 September 2012
computed in backward time out to t = 12 September 2012.

5 Final Remarks

The geodesic transport theory seeks to reveal the fundamental cause of coherence
in flow datasets, manifested by the emergence of ordered patterns in the distribution
of any transported scalar. The fundamental cause of flow coherence is found in
the existence of special material lines, known as LCS, which control the evolution
of neighboring fluid trajectories. In this note we have illustrated the ability of the
geodesic transport theory to reveal LCS by analyzing an oceanic flow dataset. Using
the same dataset, we showed that while the FTLE, by far the most popular flow
diagnostic, tends to carry flow coherence imprints, it is not successful in revealing
the LCS that dictate the evolution of the fluid transported. We emphasized that the
ability of the FTLE to carry flow coherence imprints is a direct effect of being
constructed from fluid trajectories, whose evolution is tied to LCS. Similar tendency
to carry flow coherence imprints by other flow diagnostics constructed from fluid
trajectories is expected for the same reason.

Acknowledgments The altimeter dataset is distributed by AVISO ( http://www.aviso.oceanobs.
com ) . Work supported by a BP/The Gulf of Mexico Research Initiative grant; NSF grant
CMG0825547; and NASA grant NX10AE99G.

A Altimetry Data and Numerical Details

The sea surface elevation field, ʷ( x , t ) , consists of background and perturbation com-

ponents. The background ʷ( component is steady, given by a mean dynamic

topography constructed from satellite altimetry data, in-situ measurements, and a
geoid model (Rio and Hernandez 2004 ). The perturbation ʷ(

x , t )

component is tran-
sient, given by altimetric sea surface elevation anomaly measurements provided
weekly on a 0.25 ⓦ -resolution longitude-latitude grid. This perturbation component

x , t )