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Nonlinear dynamics of the viscoelastic Kolmogorov flow

Published online by Cambridge University Press:  15 October 2007

A. BISTAGNINO ,
G. BOFFETTA ,
A. CELANI ,
A. MAZZINO ,
A. PULIAFITO  and
M. VERGASSOLA
A. BISTAGNINO
Affiliation:
Dipartimento di Fisica Generale and INFN, Università di Torino, via P. Giuria 1, 10125 Torino, Italy
G. BOFFETTA
Affiliation:
Dipartimento di Fisica Generale and INFN, Università di Torino, via P. Giuria 1, 10125 Torino, Italy
A. CELANI
Affiliation:
CNRS, INLN, 1361 Route des Lucioles, 06560 Valbonne, France
A. MAZZINO
Affiliation:
Dipartimento di Fisica, Università di Genova, and CNISM, INFN, Sezione di Genova, via Dodecaneso 33, 16146 Genova, Italy
A. PULIAFITO
Affiliation:
CNRS, INLN, 1361 Route des Lucioles, 06560 Valbonne, France Dipartimento di Fisica, Università di Genova, and CNISM, INFN, Sezione di Genova, via Dodecaneso 33, 16146 Genova, Italy
M. VERGASSOLA
Affiliation:
CNRS URA 2171, Inst. Pasteur, 25 rue du Dr Roux, 75724 Paris Cedex 15, France
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Abstract

The weakly nonlinear dynamics of large-scale perturbations in a viscoelastic flow is investigated both analytically, via asymptotic methods, and numerically. For sufficiently small elasticities, dynamics is ruled by a Cahn–Hilliard equation with a quartic potential. Physically, this amounts to saying that, for small elasticities, polymers do not alter the purely hydrodynamical mechanisms responsible for the nonlinear dynamics in the Newtonian case (i.e. without polymers). The approach to the steady state is quantitatively similar to the Newtonian case as well, the dynamics being ruled by the same kink–antikink interactions as in the Newtonian limit. The above scenario does not extend to large elasticities. We found a critical value above which polymers drastically affect the dynamics of large-scale perturbations. In this latter case, a new dynamics not observed in the Newtonian case emerges. The most evident fingerprint of the new dynamics is the slowing down of the annihilation processes which lead to the steady states via weaker kink–antikink interactions. In conclusion, polymers strongly affect the large-scale dynamics. This takes place via a reduction of drag forces we were able to quantify from the asymptotic analysis. This suggests a possible relation of this phenomenon with the dramatic drag-reduction effect taking place in the far turbulent regime.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 590 , 10 November 2007 , pp. 61 - 80
Copyright
Copyright © Cambridge University Press 2007

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