Shorttime behavior of advectingdiffusing scalar fields in Stokes flows
(2013) In Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 87(6). Abstract
 This article addresses the shortterm decay of advectingdiffusing scalar fields in Stokes flows. The analysis is developed in two main subparts. In the first part, we present an analytic approach for a class of simple flow systems expressed mathematically by the onedimensional advectiondiffusion equation w(y)∂ξ=É∂y2+iV(y)É′, where ξ is either time or axial coordinate and iV(y) an imaginary potential. This class of systems encompasses both open and closedflow models and corresponds to the dynamics of a single Fourier mode in parallel flows. We derive an analytic expression for the shorttime (shortlength) decay of , and show that this decay is characterized by a universal behavior that depends solely on the singularity of the ratio... (More)
 This article addresses the shortterm decay of advectingdiffusing scalar fields in Stokes flows. The analysis is developed in two main subparts. In the first part, we present an analytic approach for a class of simple flow systems expressed mathematically by the onedimensional advectiondiffusion equation w(y)∂ξ=É∂y2+iV(y)É′, where ξ is either time or axial coordinate and iV(y) an imaginary potential. This class of systems encompasses both open and closedflow models and corresponds to the dynamics of a single Fourier mode in parallel flows. We derive an analytic expression for the shorttime (shortlength) decay of , and show that this decay is characterized by a universal behavior that depends solely on the singularity of the ratio of the transversetoaxial velocity components Veff(y)=V(y)/w(y), corresponding to the effective potential in the imaginary potential formulation. If Veff(y) is smooth, then L2(ξ)=exp(É′ξbξ3) , where b>0 is a constant. Conversely, if the effective potential is singular, then L2(ξ)=1aξν with a>0. The exponent ν attains the value 53 at the very early stages of the process, while for intermediate stages its value is 35. By summing over all of the Fourier modes, a stretched exponential decay is obtained in the presence of nonimpulsive initial conditions, while impulsive conditions give rise to an earlystage powerlaw behavior. In the second part, we consider generic, chaotic, and nonchaotic autonomous Stokes flows, providing a kinematic interpretation of the results found in the first part. The kinematic approach grounded on the warpedtime transformation complements the analytical theory developed in the first part. © 2013 American Physical Society. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/a48ddabdcc444df7a2cc509cb825f4bb
 author
 Giona, Massimiliano; Anderson, P.D. and Garofalo, Fabio ^{LU}
 publishing date
 20130617
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
 volume
 87
 issue
 6
 publisher
 American Physical Society
 external identifiers

 scopus:84879669284
 ISSN
 15393755
 DOI
 10.1103/PhysRevE.87.063011
 language
 English
 LU publication?
 no
 id
 a48ddabdcc444df7a2cc509cb825f4bb
 date added to LUP
 20160627 10:30:39
 date last changed
 20190220 09:55:07
@article{a48ddabdcc444df7a2cc509cb825f4bb, abstract = {This article addresses the shortterm decay of advectingdiffusing scalar fields in Stokes flows. The analysis is developed in two main subparts. In the first part, we present an analytic approach for a class of simple flow systems expressed mathematically by the onedimensional advectiondiffusion equation w(y)∂ξ=É∂y2+iV(y)É′, where ξ is either time or axial coordinate and iV(y) an imaginary potential. This class of systems encompasses both open and closedflow models and corresponds to the dynamics of a single Fourier mode in parallel flows. We derive an analytic expression for the shorttime (shortlength) decay of , and show that this decay is characterized by a universal behavior that depends solely on the singularity of the ratio of the transversetoaxial velocity components Veff(y)=V(y)/w(y), corresponding to the effective potential in the imaginary potential formulation. If Veff(y) is smooth, then L2(ξ)=exp(É′ξbξ3) , where b>0 is a constant. Conversely, if the effective potential is singular, then L2(ξ)=1aξν with a>0. The exponent ν attains the value 53 at the very early stages of the process, while for intermediate stages its value is 35. By summing over all of the Fourier modes, a stretched exponential decay is obtained in the presence of nonimpulsive initial conditions, while impulsive conditions give rise to an earlystage powerlaw behavior. In the second part, we consider generic, chaotic, and nonchaotic autonomous Stokes flows, providing a kinematic interpretation of the results found in the first part. The kinematic approach grounded on the warpedtime transformation complements the analytical theory developed in the first part. © 2013 American Physical Society.}, articleno = {063011}, author = {Giona, Massimiliano and Anderson, P.D. and Garofalo, Fabio}, issn = {15393755}, language = {eng}, month = {06}, number = {6}, publisher = {American Physical Society}, series = {Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)}, title = {Shorttime behavior of advectingdiffusing scalar fields in Stokes flows}, url = {http://dx.doi.org/10.1103/PhysRevE.87.063011}, volume = {87}, year = {2013}, }