Journal
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
Volume 226, Issue 10, Pages 2247-2262Publisher
SPRINGER HEIDELBERG
DOI: 10.1140/epjst/e2017-70068-6
Keywords
-
Categories
Ask authors/readers for more resources
Enforcing the results developed by Gorodetskyi et al. [O. Gorodetskyi, M. Giona, P. Anderson, Phys. Fluids 24, 073603 (2012)] on the application of the mapping matrix formalism to simulate advective-diffusive transport, we investigate the structure and the properties of strange eigenfunctions and of the associated eigenvalues up to values of the P,clet number Pe similar to oe'(10(8)). Attention is focused on the possible occurrence of a singular limit for the second eigenvalue, nu(2), of the advection-diffusion propagator as the P,clet number, Pe, tends to infinity, and on the structure of the corresponding eigenfunction. Prototypical time-periodic flows on the two-torus are considered, which give rise to toral twist maps with different hyperbolic character, encompassing Anosov, pseudo-Anosov, and smooth nonuniformly hyperbolic systems possessing a hyperbolic set of full measure. We show that for uniformly hyperbolic systems, a singular limit of the dominant decay exponent occurs, log|nu(2)| -> constant not equal 0 for Pe -> a, whereas log |nu(2)| -> 0 according to a power-law in smooth non-uniformly hyperbolic systems that are not uniformly hyperbolic. The mere presence of a nonempty set of nonhyperbolic points (even if of zero Lebesgue measure) is thus found to mark the watershed between regular vs. singular behavior of nu(2) with Pe as Pe -> a.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available