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

Giona, M. ; Cerbelli, S. and Garofalo, F. LU (2008) In Europhysics Letters 83(3).
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, -μd∼Pe-γ (γd, vs.Pe. Among these regimes, a Pe-independent scaling -μd=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... (More)

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, -μd∼Pe-γ (γd, vs.Pe. Among these regimes, a Pe-independent scaling -μd=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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author
; and
publishing date
type
Contribution to journal
publication status
published
subject
in
Europhysics Letters
volume
83
issue
3
article number
34001
publisher
EDP Sciences
external identifiers
  • scopus:78951496047
ISSN
0295-5075
DOI
10.1209/0295-5075/83/34001
language
English
LU publication?
no
id
9cbaffc9-0b12-48b5-9f88-62d30786600f
date added to LUP
2016-06-27 10:11:17
date last changed
2022-03-16 06:49:51
@article{9cbaffc9-0b12-48b5-9f88-62d30786600f,
  abstract     = {{<p>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, -μ<sub>d</sub>∼Pe<sup>-γ</sup> (γd, vs.Pe. Among these regimes, a Pe-independent scaling -μ<sub>d</sub>=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.</p>}},
  author       = {{Giona, M. and Cerbelli, S. and Garofalo, F.}},
  issn         = {{0295-5075}},
  language     = {{eng}},
  month        = {{08}},
  number       = {{3}},
  publisher    = {{EDP Sciences}},
  series       = {{Europhysics Letters}},
  title        = {{Complex spectral properties of non-Hermitian operators : An application to open-flow mixing systems}},
  url          = {{http://dx.doi.org/10.1209/0295-5075/83/34001}},
  doi          = {{10.1209/0295-5075/83/34001}},
  volume       = {{83}},
  year         = {{2008}},
}