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Delaying transition to turbulence in channel flow: revisiting the stability of shear-thinning fluids. (English) Zbl 1128.76026
Summary: A viscosity stratification is considered as a possible mean to postpone the onset of transition to turbulence in channel flow. As a prototype problem, we focus on the linear stability of shear-thinning fluids modelled by Carreau rheological law. To assess whether there is a stabilization and by how much, it is important both to account for a viscosity disturbance in the perturbation equations, and to employ an appropriate viscosity scale in the definition of Reynolds number. Failure to do so can yield qualitatively and quantitatively incorrect conclusions. Results are obtained for both exponentially and algebraically growing disturbances, demonstrating that a viscous stratification is a viable approach to maintain laminarity.

MSC:
76F06 Transition to turbulence
76A05 Non-Newtonian fluids
76E05 Parallel shear flows in hydrodynamic stability
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