Localization and spectral phase transition in an open advecting-diffusing three-dimensional Stokes flow.
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.
Giona
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Dipartimento di Ingegneria Chimica, Università di Roma La Sapienza, via Eudossiana 18, 00184 Roma, Italy. max@giona.ing.uniroma1.it
Cerbelli
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