Hostname: page-component-848d4c4894-cjp7w Total loading time: 0 Render date: 2024-07-01T22:49:07.628Z Has data issue: false hasContentIssue false
  • English
  • Français

Peripheral mixing of passive scalar at small Reynolds number

Published online by Cambridge University Press:  10 April 2009

G. BOFFETTA ,
F. DE LILLO  and
A. MAZZINO
G. BOFFETTA*
Affiliation:
Dipartimento di Fisica Generale and INFN, Università di Torino, Via P. Giuria 1, 10125 Torino, Italy CNR-ISAC, Sezione di Torino, corso Fiume 4, 10133 Torino, Italy
F. DE LILLO
Affiliation:
Dipartimento di Fisica Generale and INFN, Università di Torino, Via P. Giuria 1, 10125 Torino, Italy
A. MAZZINO
Affiliation:
Dipartimento di Fisica, Università di Genova, INFN and CNISM, Via Dodecaneso 33, 16146 Genova, Italy
*
†E-mail address for correspondence: boffetta@to.infn.it
Get access Rights & Permissions [Opens in a new window]

Abstract

Mixing of a passive scalar in the peripheral region close to a wall is investigated by means of accurate direct numerical simulations of both a three-dimensional Couette channel flow at low Reynolds numbers and a two-dimensional synthetic flow. In both cases, the resulting phenomenology can be understood in terms of the theory recently developed by Lebedev & Turitsyn (Phys. Rev. E, vol. 69, 2004, 036301). Our results prove the robustness of the identified mechanisms responsible for the persistency of scalar concentration close to the wall with important consequences in completely different fields ranging from microfluidic applications to environmental dispersion modelling.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 624 , 10 April 2009 , pp. 151 - 158
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Balkovsky, E. & Fouxon, A. 1999 Universal long-time properties of lagrangian statistics in the batchelor regime and their application to the passive scalar problem. Phys. Rev. E 60 (4), 4164–4174.CrossRefGoogle Scholar
Batchelor, G. K. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. J. Fluid Mech. 5, 113–133.CrossRefGoogle Scholar
Burghelea, T., Segre, E. & Steinberg, V. 2006 Role of elastic stress in statistical and scaling properties of elastic turbulence. Phys. Rev. Lett. 96, 214502.CrossRefGoogle ScholarPubMed
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1988 Spectral Methods in Fluid Dynamics. Springer-Verlag.CrossRefGoogle Scholar
Chertkov, M. & Lebedev, V. 2003 Decay of scalar turbulence revisited. Phys. Rev. Lett. 90, 034501.CrossRefGoogle ScholarPubMed
Chernykh, A. & Lebedev, V. 2008 Passive scalar structures in periferal regions of random flows. JETP Lett. 87, 682.CrossRefGoogle Scholar
De Lillo, F. & Eckhardt, B. 2007 Shear turbulence on a sparse spectral grid. Phys. Rev. E 76 (1), 16301.CrossRefGoogle ScholarPubMed
Falkovich, G., Gawȩdzki, K. & Vergassola, M. 2001 Particles and fields in fluid turbulence. Rev. Mod. Phys. 73 (4), 913–975.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 2001 Efficient mixing at low Reynolds numbers using polymer additives. Nature 410 (6831), 905–908.CrossRefGoogle ScholarPubMed
Haynes, P. H. & Vanneste, J. 2005 What controls the decay of passive scalars in smooth flows? Phys. Fluids 17, 097103.CrossRefGoogle Scholar
Lebedev, V. V. & Turitsyn, K. S. 2004 Passive scalar evolution in peripheral regions. Phys. Rev. E 69 (3), 036301.CrossRefGoogle ScholarPubMed
Malerud, S., Måløy, K. J. & Goldburg, W. I. 1995 Measurements of turbulent velocity fluctuations in a planar Couette cell. Phys. Fluids 7, 1949.CrossRefGoogle Scholar
Pierrehumbert, R. T. 1994 Tracer microstructure in the large-eddy dominated regime. Chaos Solitons Fractals 4 (6), 1091–1110.CrossRefGoogle Scholar
Salman, H. & Haynes, P. H. 2007 A numerical study of passive scalar evolution in peripheral regions. Phys. Fluids 19, 067101.CrossRefGoogle Scholar
Shraiman, B. I. & Siggia, E. D. 2000 Scalar turbulence. Nature 405 (6787), 639–646.CrossRefGoogle ScholarPubMed
Simonnet, C. & Groisman, A. 2005 Chaotic mixing in a steady flow in a microchannel. Phys. Rev. Lett. 94, 134501.CrossRefGoogle Scholar
Son, D. T. 1999 Turbulent decay of a passive scalar in the batchelor limit: exact results from a quantum-mechanical approach. Phys. Rev. E 59 (4), R3811–R3814.CrossRefGoogle Scholar
Squires, T. M. & Quake, S. R. 2005 Microfluidics: fluid physics at the nanoliter scale. Rev. Mod. Phys. 77, 977.CrossRefGoogle Scholar
Williams, B. S., Marteau, D. & Gollub, J. P. 1997 Mixing of a passive scalar in magnetically forced two-dimensional turbulence. Phys. Fluids 9, 2061.CrossRefGoogle Scholar