Integrated Computation of Finite Time Lyapunov Exponent During ...
Integrated Computation of Finite Time Lyapunov Exponent During ...
Integrated Computation of Finite Time Lyapunov Exponent During ...
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Double Gyre flow: [Solomon and Gollub, 1988]<br />
u = −πA sin(πf (x)) cos(πy) (10)<br />
v<br />
f<br />
a<br />
b<br />
= πA cos(πf (x)) sin(πy) ∂f<br />
∂x<br />
(x, t) = a(t)x 2 + b(t)x<br />
(t) = ɛ sin(ωt)<br />
(t) = 1 − 2ɛ sin(ωt)<br />
ɛ = 0.1, A = 0.1, ω = 2π<br />
10<br />
512 × 256 Cartesian grid:<br />
0 ≤ X ≤ 2, 0 ≤ Y ≤ 1<br />
(11)<br />
Eulerian and Lagrangian results are<br />
equivalent<br />
(g) Backward time Lagrangian<br />
(h) Forward time Lagrangian<br />
(i) Backward time Eulerian (j) Forward time Eulerian<br />
(k) Backward time relative<br />
error<br />
(l) Forward time relative<br />
error<br />
Finn & Apte FTLE & DNS Integration 16
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