Alfredsson, P. H., Imayamaa, S., Lingwood, R. J., Orlu, R. & Segalini, A.
2013
Turbulent boundary layers over flat plates and rotating disks – the legacy of von karman: a stockholm perspective. Eur. J. Mech. (B/Fluids)
40, 17–29.

Avsarkisov, V., Oberlack, M. & Hoyas, S.
2014
New scaling laws for turbulent poiseuille flow with wall transpiration. J. Fluid Mech.
746, 99–122.

Barenblatt, G. I.
1993
Scaling laws for fully developed turbulent shear flows. Part 1. Basic hypotheses and analysis. J. Fluid Mech.
248, 513–520.

Barenblatt, G. I.
1996
Scaling, Self-similarity, and Intermediate Asymptotics. Cambridge University Press.

Barenblatt, G. I. & Chorin, A. J.
2004
A mathematical model for the scaling of turbulence. Proc. Natl Acad. Sci. USA
101 (42), 15023–15026.

Batchelor, G. K.
1951
Pressure fluctuations in isotropic turbulence. Math. Proc. Camb. Phil. Soc.
47, 359–374.

Bluman & Kumei
1989
Symmetries and Differential Equations. Springer.

Cantwell, B. J.
2002
Introduction to Symmetry Analysis. Cambridge University Press.

Chen, X. & Hussain, F.
2017
Similarity transformation for equilibrium boundary layers, including effects of blowing and suction. Phys. Rev. Fluids
2, 034605.

Chen, X., Hussain, F. & She, Z. S.
2016a
Predictions of canonical wall-bounded turbulent flows via a modified *k*–𝜔 equation. J. Turbul. doi:10.1080/14685248.2016.1243244.

Chen, X., Hussain, F. & She, Z. S.
2016b
Bulk flow scaling for turbulent channel and pipe flows. Europhys. Lett.
115, 34001.

Chen, X. & She, Z. S.
2016
Analytic prediction for planar turbulent boundary layers. Science China Physics, Mech. Astron.
59 (11), 114711.

Chen, X., Wei, B. B., Hussain, F. & She, Z. S.
2015
Anomalous dissipation and kinetic-energy distribution in pipes at very high Reynolds numbers. Phys. Rev. E
93, 011102(R).

Cipra, B.
1996
A new theory of turbulence causes a stir among experts. Science
272 (5264), 951.

Coles, D.
1956
The law of the wake in the turbulent boundary layer. J. Fluid Mech.
1, 191–226.

Davidson, P. A., Kaneda, Y., Moffatt, K. & Sreenivasan, K. R.
2011
A Voyage through Turbulence. Cambridge University Press.

Del Alamo, J. C. & Jimenez, J.
2006
Linear energy amplification in turbulent channels. J. Fluid Mech.
559, 205–213.

Driest, V.
1956
On turbulent flow near a wall. J. Aeronaut. Sci. (Institute of the Aeronautical Sciences)
23 (11), 1007–1011.

Falkovich, G.
2009
Symmetries of the turbulent state. J. Phys. A
42 (12), 123001.

Frisch, U.
1995
Turbulence. Cambridge University Press.

Frisch, U. & Parisi, G.
1985
Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics (ed. Ghil, M., Benzi, R. & Parisi, G.), p. 71. North-Holland.

George, W. K.
2005
Recent advancements toward the understanding of turbulent boundary layers. In Proceedings of the Fourth AIAA Theoretical Fluid Mechanics Meeting, Toronto, Canada. AIAA Paper 2005-4669.

Gibson, J., Halcrow, J. & Cvitanovic, P.
2009
Equilibrium and travelling-wave solutions of plane Couette flow. J. Fluid Mech.
638, 243–266.

Hoyas, S. & Jimenez, J.
2006
Scaling of the velocity fluctuations in turbulent channels up to *re*
_{𝜏} = 2003. Phys. Fluids
18, 011702.

Hultmark, M., Vallikivi, M., Bailey, S. C. C. & Smits, A. J.
2012
Turbulent pipe flow at extreme Reynolds numbers. Phys. Rev. Lett.
108, 094501.

Hussain, A. K. M. F. & Zaman, K. B. M. Q.
1985
An experimental study of organized motions in the turbulent plane mixing layer. J. Fluid Mech.
159, 85–104.

Kadanoff, L. P.
2009
More is the same; phase transitions and mean field theories. J. Stat. Phys.
137 (5–6), 777–797.

Kelbin, O., Cheviakov, A. F. & Oberlack, M.
2013
New conservation laws of helically symmetric, plane and rotationally symmetric viscous and inviscid flows. J. Fluid Mech.
721, 340–366.

Klewicki, J.
2013
Self-similar mean dynamics in turbulent wall flows. J. Fluid Mech.
718, 596–621.

Klewicki, J., Chin, C., Blackburn, H., Ooi, A. & Marusic, I.
2012
Emergence of the four layer dynamical regime in turbulent pipe flo. Phys. Fluids
24, 045107.

Kolmogorov, A.
1941
The local structure of turbulence in incompressible viscous fluid for very large Reynolds’ numbers. Dokl. Akad. Nauk SSSR
30, 301–305.

Lindgren, B., Osterlund, J. M. & Johansson, A. V.
2004
Evaluation of scaling laws derived from Lie group symmetry methods in zero-pressure-gradient turbulent boundary layers. J. Fluid Mech.
502, 127–152.

L’vov, V. S., Procaccia, I. & Rudenko, O.
2008
Universal model of finite Reynolds number turbulent flow in channels and pipes. Phys. Rev. Lett.
100 (5), 054504.

Marati, N., Davoudi, J., Casciola, C. M. & Eckhardt, B.
2006
Mean profiles for a passive scalar in wall-bounded flows from symmetry analysis. J. Turbul.
7, N61.

Marusic, I., McKeon, B. J., Monkewitz, P. A., Nagib, H. M., Smits, A. J. & Sreenivasan, K. R.
2010
Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids
22 (6), 065103.

Marusic, I., Monty, J. P., Hultmark, M. & Smits, A. J.
2013
On the logarithmic region in wall turbulence. J. Fluid Mech.
716, R3.

McKeon, B. J., Li, J., Jiang, W., Morrison, J. F. & Smits, A. J.
2004
Further observations on the mean velocity distribution in fully developed pipe flow. J. Fluid Mech.
501, 135–147.

Millikan, C. B.
1938
A critical discussion of turbulent flows in channels and circular tubes. In Proceedings 5th International Congress on Applied Mechanics, Cambridge, MA.

Monkewitz, P. A., Chauhan, K. A. & Nagib, H. M.
2007
Self-consistent high-Reynolds-number asymptotics for zero-pressure-gradient turbulent boundary layers. Phys. Fluids
19, 115101.

Monty, J. P.2005 Developments in smooth wall turbulent duct flows. PhD Thesis, University of Melbourne.

Nagib, H. M. & Chauhan, K. A.
2008
Variations of von karman coefficient in canonical flows. Phys. Fluids
20, 101518.

Nickels, T. B.
2004
Inner scaling for wall-bounded flows subject to large pressure gradients. J. Fluid Mech.
521, 217–239.

Oberlack, M.
2001
A unified approach for symmetries in plane parallel turbulent shear flows. J. Fluid Mech.
427, 299–328.

Oberlack, M. & Rosteck, A.
2010
New statistical symmetries of the multi-point equations and its importance for turbulent scaling laws. J. Discrete Continuous Dyn. Syst. S
3, 451–471.

Olver, P. J.
1995
Equivalence, Invariants and Symmetry. Cambridge University Press.

Panton, R. L.
2007
Composite asymptotic expansions and scaling wall turbulence. Phil. Trans. R. Soc. Lond. A
365, 733–754.

Perry, A. E. & Chong, M. S.
1982
On the mechanism of wall turbulence. J. Fluid Mech.
119, 173–217.

Perry, A. E., Henbest, S. M. & Chong, M. S.
1986
A theoretical and experimental study of wall turbulence. J. Fluid Mech.
165, 163–199.

Pope, S. B.
2000
Turbulent Flows. Cambridge University Press.

Prandtl, L.
1925
Bericht uber die entstehung der turbulenz. Z. Angew. Math. Mech
5, 136.

Reynolds, W. C. & Hussain, A. K. M. F.
1972
The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech.
54, 263–288.

Schlatter, P., Li, Q., Brethouwer, G., Johansson, A. V. & Henningson, D. S.
2010
Simulations of spatially evolving turbulent boundary layers up to *Re*𝜃 = 4300. Intl J. Heat Fluid Flow
31 (3), 251–261.

Schoppa, W. & Hussain, F.
2002
Coherent structure generation in near-wall turbulence. J. Fluid Mech.
453, 57–108.

Segalini, A., Orlu, R. & Alfredsson, P. H.
2013
Uncertainty analysis of the von karman constant. Exp. Fluids
54, 1460.

She, Z. S., Chen, X., Wu, Y. & Hussain, F.
2010
New perspective in statistical modeling of wall-bounded turbulence. Acta Mechanica Sin.
26 (6), 847–861.

She, Z. S. & Leveque, E.
1994
Universal scaling laws in fully developed turbulence. Phys. Rev. Lett.
72 (3), 336.

She, Z. S., Wu, Y., Chen, X. & Hussain, F.
2012
A multi-state description of roughness effects in turbulent pipe flow. New J. Phys.
14 (9), 093054.

She, Z. S. & Zhang, Z. X.
2009
Universal hierarchical symmetry for turbulence and general multi-scale fluctuation systems. Acta Mechanica Sin.
25 (3), 279–294.

Smits, A. J. & Marusic, I.
2013
Wall-bounded turbulence. Phys. Today
66 (9), 25.

Smits, A. J., McKeon, B. J. & Marusic, I.
2011
High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech.
43 (1), 353–375.

Townsend, A. A.
1976
The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.

Van Dyke, M.
1964
Perturbation Methods in Fluid Mechanics, vol. 964. Academic.

Von Karman, T.
1930
Mechanische ähnlichkeit und turbulenz, nachr. ges. wiss. göttingen, math.-phys. kl.(1930) 58–76. In Proc. 3. Int. Cong. Appl. Mech., pp. 85–105.

Wei, T., Fife, P., Klewicki, J. & Mcmurtry, P.
2005
Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows. J. Fluid Mech.
522, 303–327.

White, F. M.
2006
Viscous Fluid Flow. McGraw-Hill.

Wilcox, D. C.
2006
Turbulence Modeling for CFD. DCW Industries La Canada.

Wu, B., Bi, W. T., Hussain, F. & She, Z. S.
2017
On the invariant mean velocity profile for compressible turbulent boundary layers. J. Turbul.
18, 186–202.

Wu, X. H. & Moin, P.
2008
A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow. J. Fluid Mech.
608, 81–112.

Wu, Y., Chen, X., She, Z. S. & Hussain, F.
2012
Incorporating boundary constraints to predict mean velocities in turbulent channel flow. Science China Phys., Mech. Astron.
55 (9), 1691.

Wu, Y., Chen, X., She, Z. S. & Hussain, F.
2013
On the karman constant in turbulent channel flow. Phys. Scr.
2013 (T155), 014009.

Zagarola, M. V. & Smits, A. J.
1998
Mean-flow scaling of turbulent pipe flow. J. Fluid Mech.
373, 33–79.

Zhang, Y. S., Bi, W. T., Hussain, F., Li, X. L. & She, Z. S.
2012
Mach-number-invariant mean-velocity profile of compressible turbulent boundary layers. Phys. Rev. Lett.
109, 054502.