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Boundary layer of elastic turbulence

  • S. Belan (a1), A. Chernykh (a2) (a3) and V. Lebedev (a4) (a5)


We investigate theoretically the near-wall region in elastic turbulence of a dilute polymer solution in the limit of large Weissenberg number. As has been established experimentally, elastic turbulence possesses a boundary layer where the fluid velocity field can be approximated by a steady shear flow with relatively small fluctuations on the top of it. Assuming that at the bottom of the boundary layer the dissolved polymers can be considered as passive objects, we examine analytically and numerically the statistics of the polymer conformation, which is highly non-uniform in the wall-normal direction. Next, imposing the condition that the passive regime terminates at the border of the boundary layer, we obtain an estimate for the ratio of the mean flow to the magnitude of the flow fluctuations. This ratio is determined by the polymer concentration, the radius of gyration of polymers and their length in the fully extended state. The results of our asymptotic analysis reproduce the qualitative features of elastic turbulence at finite Weissenberg numbers.


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Afonso, M. M. & Vincenzi, D. 2005 Nonlinear elastic polymers in random flow. J. Fluid Mech. 540, 99108.
Ahmad, A. & Vincenzi, D. 2016 Polymer stretching in the inertial range of turbulence. Phys. Rev. E 93 (5), 052605.
Balkovsky, E., Fouxon, A. & Lebedev, A. 2000 Turbulent dynamics of polymer solutions. Phys. Rev. Lett. 84, 47654768.
Balkovsky, E., Fouxon, A. & Lebedev, V. 2001 Turbulence of polymer solutions. Phys. Rev. E 64, 056301.
Berti, S., Bistagnino, A., Boffetta, G., Celani, A. & Musacchio, S. 2008 Two-dimensional elastic turbulence. Phys. Rev. E 77, 055306(R).
Berti, S. & Boffetta, G. 2010 Elastic waves and transition to elastic turbulence in a two-dimensional viscoelastic Kolmogorov flow. Phys. Rev. E 82, 036314.
Bird, R. B., Armstrong, R. C. & Hassager, O. 1977 Dynamics of Polymeric Liquids, vol. 1: Fluid Mechanics. Wiley.
Bird, R. B., Hassager, O., Armstrong, R. C. & Curtiss, C. F. 1987 Dynamics of Polymeric Liquids, vol. 2: Kinetic Theory. Wiley.
Bodiguel, H., Beaumont, J., Machado, A., Martinie, L., Kellay, H. & Colin, A. 2015 Flow enhancement due to elastic turbulence in channel flows of shear thinning fluids. Phys. Rev. Lett. 114, 028302.
Burghelea, T., Segre, E. & Steinberg, V. 2006 Role of elastic stress in statistical and scaling properties of elastic turbulence. Phys. Rev. Lett. 96, 214502.
Burghelea, T., Segre, E. & Steinberg, V. 2007 Elastic turbulence in von Karman swirling flow between two disks. Phys. Fluids 19, 053104.
Celani, A., Musacchio, S. & Vincenzi, D. 2005 Polymer transport in random flow. J. Stat. Phys. 118 (3–4), 531554.
Celani, A., Puliafito, A. & Turitsyn, K. 2005 Polymers in linear shear flow: a numerical study. Europhys. Lett. 70 (4), 464.
Chertkov, M. 2000 Polymer stretching by turbulence. Phys. Rev. Lett. 84, 47614764.
Chernykh, A. & Lebedev, V. 2011 Passive scalar transport in peripheral regions of random flows. J. Expl Theor. Phys. 113 (2), 352362.
Chertkov, M., Kolokolov, I., Lebedev, V. & Turitsyn, K. 2005 Polymer statistics in a random flow with mean shear. J. Fluid. Mech. 531, 251260.
Fouxon, A. & Lebedev, V. 2003 Spectra of turbulence in dilute polymer solutions. Phys. Fluids 15, 20602072.
Gerashchenko, S., Chevallard, C. & Steinberg, V. 2005 Single-polymer dynamics: coil-stretch transition in a random flow. Europhys. Lett. 71, 221227.
Groisman, A. & Steinberg, V. 2000 Elastic turbulence in a polymer solution flow. Nature 405, 5355.
Groisman, A. & Steinberg, V. 2001 Efficient mixing at low Reynolds numbers using polymer additives. Nature 410, 905908.
Groisman, A. & Steinberg, V. 2004 Elastic turbulence in curvilinear flows of polymer solutions. New J. Phys. 6, 29.
Jun, Y. & Steinberg, V. 2011 Elastic turbulence in a curvilinear channel flow. Phys. Rev. E 84, 056325.
Jun, Y. & Steinberg, V. 2017 Polymer concentration and properties of elastic turbulence in a von Karman swirling flow. Phys. Rev. Fluids 2 (10), 103301.
Landau, L. D. & Lifshitz, E. M. 1987 Course of Theoretical Physics, vol. 6: Fluid Mechanics. Pergamon Press.
Lebedev, V. V. & Turitsyn, K. S. 2004 Passive scalar evolution in peripheral regions. Phys. Rev. E 69, 036301.
Pan, L., Morozov, A., Wagner, C. & Arratia, P. E. 2013 Nonlinear elastic instability in channel flows at low Reynolds numbers. Phys. Rev. Lett. 110, 174502.
Turitsyn, K. S. 2007 Polymer dynamics in chaotic flows with strong shear component. J. Expl Theor. Phys. 105 (3), 655664.
Vincenzi, D., Perlekar, P., Biferale, L. & Toschi, F. 2015 Impact of the Peterlin approximation on polymer dynamics in turbulent flows. Phys. Rev. E 92 (5), 053004.
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Boundary layer of elastic turbulence

  • S. Belan (a1), A. Chernykh (a2) (a3) and V. Lebedev (a4) (a5)


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