| Abstract
| - We study the spectral properties of the advection-diffusion operator associated with a non-chaotic 3d Stokes flow defined in the annular region between counter-rotating cylinders of finite length. The focus is on the dependence of the eigenvalue-eigenfunction spectrum on the Peclet number Pe. Several convection-enhanced mixing regimes are identified, each characterized by a power law scaling, $- \mu _{d}\sim Pe^{-\gamma }$ ( γ< 1) of the real part of the dominant eigenvalue, $-\mu _{d}$, vs. Pe. Among these regimes, a Pe-independent scaling $- \mu _{d}$= const ( i.e., γ = 0), qualitatively similar to the asymptotic regime of globally chaotic flows, is observed. This regime arises as the consequence of different eigenvalues branches interchanging dominance at increasing Pe. A combination of perturbation analysis and functional-theoretical arguments is used to explain the occurrence and the range of existence of each regime.
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