Volume 83, Number 3, August 2008
Article Number 34001
Number of page(s) 6
Section Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics
Published online 11 July 2008
EPL, 83 (2008) 34001
DOI: 10.1209/0295-5075/83/34001

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

M. Giona, S. Cerbelli and F. Garofalo

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

received 13 March 2008; accepted in final form 9 June 2008; published August 2008
published online 11 July 2008

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, $-
\mu _{d}\sim Pe^{-\gamma }$ ($\gamma$ < 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.

PACS - Mixing enhancement.
47.61.Ne - Micromixing.
47.15.G- - Low-Reynolds-number (creeping) flows.

© EPLA 2008