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The backward phase flow method for the Eulerian finite time Lyapunov exponent computations
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10.1063/1.4847175
/content/aip/journal/chaos/23/4/10.1063/1.4847175
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/4/10.1063/1.4847175
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Lagrangian and Eulerian interpretations of the function . (a) Lagrangian ray tracing from a given grid location x at  0. Note that y might be a non-grid point. (b) Eulerian values of at a given grid location gives the corresponding take-off location at  = 0. Note the take-off location might not be a mesh point.

Image of FIG. 2.
FIG. 2.

(Section IV A with  = 0.0) The scaled forward FTLE using the proposed backward phase flow method, i.e., :  = 1/256, * = 0.1. We apply the backward phase flow method to obtain the scaled FTLE at (a)–(c) * (215 – 25 ) for  1, 2, and 3 with *25 k. (d) Once we have obtained 3276.8 3276.8(x, 0), we propagate the solution to obtain 3276.8 3276.8(x, 3276.8).

Image of FIG. 3.
FIG. 3.

(Section IV A with  = 0.0) Trajectories of several particles corresponding to Figure 2(a) . Initial locations are plotted in (red) square, and final locations are plotted in (blue) circle.

Image of FIG. 4.
FIG. 4.

(Section IV A with  0.1) The scaled forward FTLE at  0 using the Lagrangian approach, i.e., :  320,  = 1/64, and 1/128, respectively.

Image of FIG. 5.
FIG. 5.

(Section IV A with  = 0.1) The scaled forward FTLE using the proposed backward phase flow method, i.e., :  1/256, * 10. (a)–(c) We apply the backward phase flow method to obtain the scaled FTLE's (x, 0) for * • 25 and  = 1, 2, and 5. (d) Once we have obtained 320 (x, 0), we propagate it to obtain 320 320(x, 320).

Image of FIG. 6.
FIG. 6.

(Section IV A with an aperiodic perturbation (8) ) The scale backward FTLE for an aperiodic flow using the proposed backward phase flow method, i.e., :  =   1/256,  10/128, and * = 10/212. We iterate the obtained flow map for (a) 3, (b) 6, (c) 9, and (d) 12 times to obtain the scaled backward FTLE (a) 23 (x, 10), (b) 26 (x, 10), (c) 29 (x, 10), and (d) 212 (x, 10).

Image of FIG. 7.
FIG. 7.

(Section IV B ) The scaled backward FTLE using the proposed backward phase flow method, i.e., −T:  3/128, * = 0.0625. We apply the backward phase flow method to obtain the scaled FTLE's 64 −64(x, 64).

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/content/aip/journal/chaos/23/4/10.1063/1.4847175
2013-12-12
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The backward phase flow method for the Eulerian finite time Lyapunov exponent computations
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/4/10.1063/1.4847175
10.1063/1.4847175
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