Singular eigenvalue limit of advection-diffusion operators and properties of the strange eigenfunctions in globally chaotic flows

摘要: Enforcing the results developed by Gorodetskyi et al. [O. Gorodetskyi, M. Giona, P. Anderson, Phys. Fluids 24, 073603 (2012)] on application of mapping matrix formalism to simulate advective-diffusive transport, we investigate structure and properties strange eigenfunctions associated eigenvalues up values Peclet number Pe ~ 𝒪(108). Attention is focused possible occurrence a singular limit for second eigenvalue, ν2, advection-diffusion propagator as number, Pe, tends infinity, corresponding eigenfunction. Prototypical time-periodic flows two-torus are considered, which give rise toral twist maps with different hyperbolic character, encompassing Anosov, pseudo-Anosov, smooth nonuniformly systems possessing set full measure. We show that uniformly systems, dominant decay exponent occurs, log|ν2| → constant≠0 ∞, whereas log |ν2| 0 according power-law in non-uniformly not hyperbolic. The mere presence nonempty nonhyperbolic points (even if zero Lebesgue measure) thus found mark watershed between regular vs. behavior ν2 ∞.