We study the steady-state characterization of an advecting-diffusing three-dimensional flow defined in the annular region between coaxial cylinders of finite length that can rotate independently. A phase transition occurs when the cylinder velocities vary, which controls the spectral properties of the dominant eigenvalue and eigenfunction of the advection-diffusion equation for high Péclet numbers. The localization abscissa of the dominant eigenfunction can be used as the order parameter of the transition, and is a continuous function of the wall velocity. Conversely, the exponent characterizing the scaling of the real part of the dominant eigenvalue displays a discontinuous behavior at the critical point. Theoretical arguments support the localization properties observed numerically and provide a simple explanation of this phenomenon. © 2008 The American Physical Society.
Localization and spectral phase transition in an open advecting-diffusing three-dimensional Stokes flow / Giona, Massimiliano; Cerbelli, Stefano. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - 78:4(2008), pp. 046303-1-046303-9. [10.1103/physreve.78.046303]
Localization and spectral phase transition in an open advecting-diffusing three-dimensional Stokes flow
GIONA, Massimiliano;CERBELLI, Stefano
2008
Abstract
We study the steady-state characterization of an advecting-diffusing three-dimensional flow defined in the annular region between coaxial cylinders of finite length that can rotate independently. A phase transition occurs when the cylinder velocities vary, which controls the spectral properties of the dominant eigenvalue and eigenfunction of the advection-diffusion equation for high Péclet numbers. The localization abscissa of the dominant eigenfunction can be used as the order parameter of the transition, and is a continuous function of the wall velocity. Conversely, the exponent characterizing the scaling of the real part of the dominant eigenvalue displays a discontinuous behavior at the critical point. Theoretical arguments support the localization properties observed numerically and provide a simple explanation of this phenomenon. © 2008 The American Physical Society.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.