Araya, G. & Castillo, L.
2012
DNS of turbulent thermal boundary layers up to *Re*
_{𝜃} = 2300. Intl J. Heat Mass Transfer
55, 4003–4019.

Bernard, P. S.
2013
Vortex dynamics in transitional and turbulent boundary layers. AIAA J.
51, 1828–1842.

Bernard, P. S. & Handler, R. A.
1990
Reynolds stress and the physics of turbulent momentum transport. J. Fluid Mech.
220, 99–124.

Bernard, P. S., Thomas, J. M. & Handler, R. A.
1993
Vortex dynamics and the production of Reynolds stress. J. Fluid Mech.
253, 385–419.

Bernard, P. S. & Wallace, J. M.
2002
Turbulent Flow: Analysis, Measurement and Prediction. Wiley.

Boudjemadi, R., Maupu, V., Laurence, D. & Qur, P. L.
1997
Budgets of turbulent stresses and fluxes in a vertical slot natural convection flow at Rayleigh *Ra* = 10^{5} and 5. 4 10^{5}
. Intl J. Heat Fluid Flow
18, 70–79.

Corrsin, S.
1974
Limitations of gradient transport models in random walks and turbulence. Adv. Geophys.
18A, 25–60.

Dimitropoulos, C. D., Sureshkumar, R., Beris, A. N. & Handler, R. A.
2001
Budgets of Reynolds stress, kinetic energy and streamwise enstrophy in viscoelastic turbulent channel flow. Phys. Fluids
13, 1016–1027.

Egolf, P. W.
1994
Difference-quotient turbulence model: a generalization of Prandtl’s mixing-length theory. Phys. Rev. E
49, 1260–1268.

Egolf, P. W.
2009
Lévy statistics and beta model: a new solution of ‘wall’ turbulence with a critical phenomenon. Intl J. Refrig.
32, 1815–1836.

Egolf, P. W. & Weiss, D. A.
1998
Difference-quotient turbulence model: the axisymmetric isothermal jet. Phys. Rev. E
58, 459–469.

Gatski, T. B. & Speziale, C. G.
1993
On explicit algebraic stress models for complex turbulent flows. J. Fluid Mech.
254, 59–78.

Graham, J., Kanov, K., Yang, X. I. A., Lee, M., Malaya, N., Lalescu, C. C., Burns, R., Eyink, G., Szalay, A., Moser, R. D. & Meneveau, C.
2016
A web services accessible database of turbulent channel flow and its use for testing a new integral wall model for LES. J. Turbul.
17, 181–215.

Hamba, F.
2005
Nonlocal analysis of the Reynolds stress in turbulent shear flow. Phys. Fluids
17, 115102.

Hamba, F.
2013
Exact transport equation for local eddy viscosity in turbulent shear flow. Phys. Fluids
25, 085102.

Handler, R. A., Bernard, P. S., Rovelstad, A. & Swearingen, J.
1992
On the role of accelerating particles in the generation of Reynolds stress. Phys. Fluids A
4, 1317–1319.

Jones, W. P. & Launder, B. E.
1972
The prediction of laminarization with a two-equation model of turbulence. Intl J. Heat Mass Transfer
15, 301–314.

Kays, W. M. & Crawford, M. E.
1993
Convective Heat and Mass Transfer, 3rd edn. McGraw-Hill.

Lesieur, M. & Métais, O.
1996
New trends in large-eddy simulations of turbulence. Annu. Rev. Fluid Mech.
28, 45–82.

Li, Y., Perlman, E., Wan, M., Yang, Y., Meneveau, C., Burns, R., Chen, S., Szalay, A. & Eyink, G.
2008
A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence. J. Turbul.
9, 1–29.

Mansour, N. N., Kim, J. & Moin, P.
1988
Reynolds-stress and dissipation-rate budgets in a turbulent channel flow. J. Fluid Mech.
194, 15–44.

Massey, F. J.
1951
The Kolmogorov–Smirnov test for goodness of fit. J. Am. Stat. Assoc.
46, 68–78.

Menter, F. R.
1994
Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J.
8, 1598–1605.

Perlman, E., Burns, R., Li, Y. & Meneveau, C.
2007
Data exploration of turbulence simulations using a database cluster. In Proceedings of the 2007 ACM/IEEE Conference on Supercomputing, pp. 1–11. ACM.

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

Prandtl, L.
1925
Bericht über Untersuchungen zur ausgebildeten Turbulenz. Z. Angew. Math. Mech.
5, 136–139.

Prandtl, L.
1942
Bemerkungen zur Theorie der freien Turbulenz. Z. Angew. Math. Mech.
22, 241–243.

Sagaut, P.
2006
Large Eddy Simulation for Incompressible Flows, 3rd edn. Springer.

Schmitt, F. G.
2007
About Boussinesq’s turbulent viscosity hypothesis: historical remarks and a direct evaluation of its validity. C. R. Mécanique
335, 617–627.

Spalart, P. R. & Allmaras, S. R.
1994
A one-equation turbulence model for aerodynamic flows. Rech. Aerosp.
1, 5–21.

Speziale, C. G.
1987
On nonlinear *k*–*l* and *k*–𝜖 models of turbulence. J. Fluid Mech.
178, 459–475.

Taylor, G. I.
1932
The transport of vorticity and heat through fluids in turbulent motion. Proc. R. Soc. Lond. A
135, 685–705.

Toschi, F. & Bodenschatz, E.
2009
Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech.
41, 375–404.

Wilcox, D. C.
2008
Formulation of the *k*–𝜔 turbulence model revisited. AIAA J.
46, 2823–2838.

Wu, X. & Moin, P.
2009
Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. J. Fluid. Mech.
630, 5–41.

Yoshizawa, A.
1984
Statistical analysis of the deviation of the Reynolds stress from its eddy-viscosity representation. Phys. Fluids
27, 1377–1387.