Complex spectral properties of non-Hermitian operators: An application to open-flow mixing systems

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)similar to Pe(-gamma) (gamma < 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., gamma = 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. Copyright (C) EPLA, 2008.