Avila M., Mellibovsky F., Roland N. & Hof B.
2013
Streamwise-localized solutions at the onset of turbulence in pipe flow. Phys. Rev. Lett.
110, 224502.

Avila K., Moxey D., de Lozar A., Avila M., Barkley D. & Hof B.
2011
The onset of turbulence in pipe flow. Science
333, 192–196.

Avila M., Willis A. P. & Hof B.
2010
On the transient nature of localized pipe flow turbulence. J. Fluid Mech.
646, 127–136.

Bird B., Armstrong R. & Hassager O.
1987
Dynamics of Polymeric Liquids. Wiley-Interscience.

Carreau J. P.
1972
Rheological equations from molecular network theories. Trans. Soc. Rheol.
16, 99–127.

Chantry M., Willis A. P. & Kerswell R. R.
2014
Genesis of streamwise-localized solutions from globally periodic traveling waves in pipe flow. Phys. Rev. Lett.
112, 164501.

Dennis D. J. C. & Sogaro F. M.
2014
Distinct organizational states of fully developed turbulent pipe flow. Phys. Rev. Lett.
113, 234501.

Draad A. A., Kuiken G. D. C. & Nieuwstadt F. T. M.
1998
Laminar-turbulent transition in pipe flow for Newtonian and non-Newtonian fluids. J. Fluid Mech.
377, 267–312.

Duguet Y., Pringle C. C. T. & Kerswell R. R.
2008a
Relative periodic orbits in transitional pipe flow. Phys. Fluids
20, 114102.

Duguet Y., Willis A. P. & Kerswell R. R.
2008b
Transition in pipe flow: the saddle structure on the boundary of turbulence. J. Fluid Mech.
613, 255–274.

Eckhardt B., Schneider T. M., Hof B. & Westerweel J.
2007
Turbulence transition in pipe flow. Annu. Rev. Fluid Mech.
39, 447–468.

Escudier M., Poole R., Presti F., Dales C., Nouar C., Desaubry C., Graham L. & Pullum L.
2005
Observations of asymmetrical flow behaviour in transitional pipe flow of yield-stress and other shear-thinning liquids. J. Non-Newtonian Fluid Mech.
127, 143–155.

Escudier M. P., Presti F. & Smith S.
1999
Drag reduction in the turbulent pipe flow of polymers. J. Non-Newtonian Fluid Mech.
81, 197–213.

Escudier M. P., Rosa S. & Poole R. J.
2009
Asymmetry in transitional pipe flow of drag-reducing polymer solutions. J. Non-Newtonian Fluid Mech.
161, 19–29.

Faisst H. & Eckhardt B.
2003
Traveling waves in pipe flow. Phys. Rev. Lett.
91, 224502.

Hof B., van Doorne C. W. H., Westerweel J. & Nieuwstadt F. T. M.
2005
Turbulence regeneration in pipe flow at moderate Reynolds numbers. Phys. Rev. Lett.
95, 214502.

Hof B., van Doorne C. W. H., Westerweel J., Nieuwstadt F. T. M., Faisst H., Eckhardt B., Wedin H., Kerswell R. R. & Waleffe F.
2004
Experimental observation of nonlinear traveling waves in turbulent pipe flow. Science
305, 1594–1598.

Jenny M., Plaut E. & Briard A.
2015
Numerical study of subcritical Rayleigh–Bénard convection rolls in strongly shear-thinning Carreau fluids. J. Non-Newtonian Fluid Mech.
219, 19–34.

Kerswell R. R. & Tutty O. R.
2007
Recurrence of travelling waves in transitional pipe flow. J. Fluid Mech.
584, 69–102.

Li W., Xi L. & Graham M. D.
2006
Nonlinear travelling waves as a framework for understanding turbulent drag reduction. J. Fluid Mech.
565, 353–362.

Liu R. & Liu Q. S.
2012
Nonmodal stability in Hagen–Poiseuille flow of a shear-thinning fluid. Phys. Rev. E
85, 066318.

López Carranza S. N., Jenny M. & Nouar C.
2012
Pipe flow of shear-thinning fluids. C. R. Méc.
340, 602–618.

López Carranza S. N., Jenny M. & Nouar C.
2013
Instability of streaks in pipe flow of shear-thinning fluids. Phys. Rev. E
88, 023005.

Mellibovsky F. & Eckhardt B.
2011
Takens-Bogdanov bifurcation of travelling-wave solutions in pipe flow. J. Fluid Mech.
670, 96–129.

Meseguer A.
2003
Streak breakdown instability in pipe Poiseuille flow. Phys. Fluids
15, 1203–1213.

Pringle C. C. T., Duguet Y. & Kerswell R. R.
2009
Highly symmetric traveling waves in pipe flow. Phil. Trans. R. Soc. Lond. A
367, 457–472.

Pringle C. C. T. & Kerswell R. R.
2007
Asymmetric, helical, and mirror-symmetric traveling waves in pipe flow. Phys. Rev. Lett.
99, 074502.

Roland N., Plaut E. & Nouar C.
2010
Petrov–Galerkin computation of nonlinear waves in pipe flow of shear-thinning fluids: first theoretical evidences for a delayed transition. Comput. Fluids
39, 1733–1743.

Rudman M., Blackburn H. M., Graham L. J. W. & Pullum L.
2004
Turbulent pipe flow of shear-thinning fluids. J. Non-Newtonian Fluid Mech.
118, 33–48.

Toms B. A.
1948
Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. In Proceedings of First International Congress on Rheology, vol. 2, pp. 135–141. North-Holland.

Waleffe F.
1997
On a self-sustaining process in shear flows. Phys. Fluids
9, 883–900.

Waleffe F.
1998
Three-dimensional coherent states in plane shear-flows. Phys. Rev. Lett.
81, 4140–4143.

Wedin H. & Kerswell R. R.
2004
Exact coherent structures in pipe flow: travelling wave solutions. J. Fluid Mech.
508, 333–371.

Willis A. P., Short K. Y. & Cvitanović P.
2016
Symmetry reduction in high dimensions, illustrated in a turbulent pipe. Phys. Rev. E
93, 022204.

Wygnanski I. J. & Champagne F. H.
1973
On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug. J. Fluid Mech.
59, 281–335.

Zikanov O. Y.
1996
On the instability of pipe Poiseuille flow. Phys. Fluids
8, 2923–2932.