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

Dipartimento di Ingegneria Chimica, Università di Roma ”La Sapienza” - via Eudossiana 18, 00184 Roma, Italy, EU

Corresponding author: max@giona.ing.uniroma1.it

Received: 13 March 2008
Accepted: 9 June 2008

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, (γ < 1) of the real part of the dominant eigenvalue, , vs. Pe. Among these regimes, a Pe-independent scaling = 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.