Slip boundary conditions for the velocity field impact on the spectral properties of the advection-diffusion operator describing transport of passive particles in laminar parallel flows. By considering the Hermitian operator (referred to as the weighted Laplacian), describing the interplay between axial convection and cross-sectional diffusion of a scalar field, we show that the spectral watershed between slip and no-slip boundary conditions is a qualitatively different scaling behavior of the mean of the normalized eigenfunctions of the weighted Laplacian. The occurrence of slip conditions also influences the scaling of the density of states as regards both the leading and the subleading term in the Weyl's expansion.

Spectral analysis of the weighted Laplacian in slip and no-slip flows / Giona, Massimiliano; Adrover, Alessandra; Cerbelli, Stefano. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - STAMPA. - 80:6(2009), pp. 066302-1-066302-10. [10.1103/physreve.80.066302]

Spectral analysis of the weighted Laplacian in slip and no-slip flows

GIONA, Massimiliano;ADROVER, Alessandra;CERBELLI, Stefano
2009

Abstract

Slip boundary conditions for the velocity field impact on the spectral properties of the advection-diffusion operator describing transport of passive particles in laminar parallel flows. By considering the Hermitian operator (referred to as the weighted Laplacian), describing the interplay between axial convection and cross-sectional diffusion of a scalar field, we show that the spectral watershed between slip and no-slip boundary conditions is a qualitatively different scaling behavior of the mean of the normalized eigenfunctions of the weighted Laplacian. The occurrence of slip conditions also influences the scaling of the density of states as regards both the leading and the subleading term in the Weyl's expansion.
2009
hermitian matrices; diffusion; two-phase flow; slip flow; laminar flow; eigenvalues and eigenfunctions; convection; laplace equations
01 Pubblicazione su rivista::01a Articolo in rivista
Spectral analysis of the weighted Laplacian in slip and no-slip flows / Giona, Massimiliano; Adrover, Alessandra; Cerbelli, Stefano. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - STAMPA. - 80:6(2009), pp. 066302-1-066302-10. [10.1103/physreve.80.066302]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/228343
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