Environmental Engineering Reference
In-Depth Information
and pressure gradient forces with the latter entirely due to differences in sea surface
elevation. Specifically,
f ʷ(
v(
x
,
t
) =
x
,
t
),
(11)
where ʷ(
is the sea surface elevation; f is the Coriolis parameter (twice the local
vertical component of the Earth's angular velocity); and g denotes gravity. Oceanic
flow data of this type are commonly used to monitor mesoscale variability, i.e., with
length and time scales of the order of tens of kilometers and weeks, respectively. For
a recent application in the Gulf of Mexico, cf. Olascoaga et al. ( 2013 ).
We begin by illustrating in Fig. 2 the role of LCS geodesically extracted from
the altimetric velocity data in revealing the cause of coherence in the resulting flow.
This figure specifically shows snapshots of the evolution of three fluid patches (blue)
along with those of the corresponding centerpiece LCS (red). Such attracting LCS
snapshots are images under the flow map of stretchlines on t 0 = 12 September 2012
computed in forward time out to t = 22 September 2012. More specifically, out
of the entire stretchli ne foli ation, the most stretching stretchline, i.e., that one with
the largest average ʻ 2 (
x
,
t
)
, through each patch is considered. Note that each patch
stretches and folds, acquiring a shape dictated by its centerpiece LCS.
We now turn to the FTLE analysis of the altimetric velocity data. The FTLE is
defined by
r
)
log ʻ 2 (
1
ʛ(
x 0 ) :=
x 0 ).
(12)
|
t
t 0 |
The FTLE, more precisely the backward FTLE, has a well-documented tendency
to carry ordered flow pattern imprints (cf. Peacock and Dabiri 2010 , for a recent
survey). This is illustrated in left panel of Fig. 3 , which shows the patches on t 0 =
22 September 2012 overlaid on a field of FTLE computed in backward time out to
t = 12 September 2012. Normalized by its maximum value attained in the domain,
the FTLE ranges from 0 (white) to 1 (black). Note the similarity between the shapes
acquired by the patches and those evident in the FTLE distribution, particularly as
15-Sep-12
17-S ep -12
22-Se p -12
28:0 o N
28:0 o N
28:0 o N
26:5 o N
26:5 o N
26:5 o N
25:0 o N
25:0 o N
25:0 o N
23:5 o N
23:5 o N
23:5 o N
22:0 o N
22:0 o N
22:0 o N
92:0 o W : o W : o W : o W : o W
92:0 o W : o W : o W 87:5 o W 86:0 o W
92:0 o W 90:5 o W 89:0 o W 87:5 o W 86:0 o W
Fig. 2 Selected snapshots of the evolution of fluid patches ( blue ) and corresponding centerpiece
LCS ( red ), all computed based on satellite altimetry flow data in a selected region of the Gulf
of Mexico ( inset ). Centerpiece LCS correspond to images under the flow map of most stretching
stretchlines obtained from forward integration
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