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Influence of a strongly shear-thinning rheology on nonlinear waves with a 3-fold rotational symmetry in pipe flow: asymptotic regime

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The influence of a shear-thinning rheology on nonlinear waves with a 3-fold rotational symmetry in pipe flow is studied. We focus on the family of waves discovered by Faisst & Eckhardt in 2003, Wedin & Kerswell in 2004. The Carreau model, which is quite regular, is chosen to describe the rheology of the fluid. The pseudo-spectral code of Roland et al. 2010 is used to compute the nonlinear waves, by continuation, starting from the Newtonian case. The retardation effect found in 2010 is studied in a more systematic manner: the influence of the axial wavenumber is analyzed. An asymptotic regime is discovered in the limit of quite strong shear-thinning effects, where the fluid behaves like a power-law fluid. If one admits that the nonlinear waves are ‘precursors’ of turbulence, this gives a lower bound for the onset of turbulence in the pipe flow of some Carreau and power-law fluids.

Author(s):

Emmanuel Plaut    
Lemta, UMR CNRS - Univ. Lorraine
France

Nicolas Roland    
MPI for Dynamics and Self-Organization, Goettingen
Germany

Cherif Nouar    
Lemta, UMR CNRS - Univ. Lorraine
France