Environmental Engineering Reference
In-Depth Information
is referenced to a seven-year (1993-1999) mean, obtained from the combined
processing of data collected by altimeters on the constellation of available satellites
(Le Traon et al.
1998
).
To obtain the flow map,
F
, we integrated Eq. (
1
) with the altimetric veloc-
ity field (
11
) for initial positions,
x
0
, on a regular 0.5-km-width grid covering the
domain of interest. This was done using a stepsize-adapting fourth-order Runge-
Kutta method with interpolations obtained using a cubic scheme. The derivative of
the flowmap, D
F
(
x
0
)
, was computed using finite differences on an auxiliary 0.1-km-
width grid of four points neighboring each point in the above grid. Explicit formulas
were used for the eigenvalues and eigenvectors of the Cauchy-Green strain tensor,
C
(
x
0
)
. Finally, to obtain squeezelines (resp., stretchlines), we integrated, using a
stepsize-adapting fourth-order Runge-Kutta method and cubic interpolation,
(
x
0
)
r
=
r
(
sign
s
−
ʔ), ʾ
i
(
r
)
ʾ
i
(
r
),
i
=
1
[
resp.,
i
=
2
]
.
(A.1)
The factor multiplying
ʾ
i
(
arising
from the lack of global orientation of an eigenvector field (Haller and Beron-Vera
2012
).
r
)
removes orientational discontinuities in
ʾ
i
(
r
)
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