André, J. C. & Lesieur, M.
1977
Influence of helicity on high Reynolds number isotropic turbulence. J. Fluid Mech.
81, 187–207.

Antonia, R. A. & Orlandi, P.
2003
The Batchelor constant in decaying isotropic turbulence. Phys. Fluids
15, 2084–2086.

Batchelor, G. K.
1959a
Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech.
5, 113–133.

Batchelor, G. K.
1959b
Small-scale variation of convected quantities like temperature in turbulent fluid. Part 2. The case of large conductivity. J. Fluid Mech.
5, 134–139.

Bogucki, D., Domaradzki, J. A. & Yeung, P. K.
1997
Direct numerical simulations of passive scalars with
$Pr\gt 1$
advected by turbulent flow. J. Fluid Mech.
343, 111–130.
Bos, W. J. T. & Bertoglio, J.-P.
2006
Dynamics of spectrally truncated inviscid turbulence. Phys. Fluids
18, 071701.

Bos, W. J. T. & Bertoglio, J.-P.
2007
Inertial range scaling of scalar flux spectra in uniformly sheared turbulence. Phys. Fluids
19, 025104.

Bos, W. J. T., Rubinstein, R. & Fang, L.
2012
Reduction of mean-square advection in turbulent passive scalar mixing. Phys. Fluids
24, 075104.

Bos, W. J. T., Touil, H. & Bertoglio, J. P.
2005
Reynolds number dependency of the scalar flux spectrum in isotropic turbulence with a uniform scalar gradient. Phys. Fluids
17, 125108.

Chasnov, J., Canuto, V. M. & Rogallo, R. S.
1988
Turbulence spectrum of a passive temperature field: results of a direct numerical simulation. Phys. Fluids
31, 2065–2067.

Comte-Bellot, G. & Corrsin, S.
1966
The use of a contraction to improve the isotropy of grid-generated turbulence. J. Fluid Mech.
25, 657–682.

Corrsin, S.
1951
On the spectrum of isotropic temperature fluctuations in an isotropic turbulence. J. Appl. Phys.
22
(4), 469–473.

Corrsin, S.
1961
The reactant concentration spectrum in turbulent mixing with a first-order reaction. J. Fluid Mech.
11, 407–416.

Corrsin, S.
1964
Further generalization of Onsager’s cascade model for turbulent spectra. Phys. Fluids
7, 1156–1159.

Donzis, D. A., Sreenivasan, K. R. & Yeung, P. K.
2010
The Batchelor spectrum for mixing of passive scalars in isotropic turbulence. Flow Turbul. Combust.
85
(3), 549–566.

Driscoll, R. J. & Kennedy, L. A.
1984
A model for the spectrum of passive scalars in an isotropic turbulence field. Phys. Fluids
28, 72–80.

Gibson, C. H.
1968
Fine structure of scalar fields mixed by turbulence. II. Spectral theory. Phys. Fluids
11, 2316–2327.

Gibson, C. H. & Schwarz, W. H.
1963
The universal equilibrium spectra of turbulent velocity and scalar fields. J. Fluid Mech.
16, 365–377.

Grant, H. L., Hughes, W. M., Vogel, W. M. & Moillet, A.
1968
The spectrum of temperature fluctuations in turbulent flow. J. Fluid Mech.
34, 423–442.

Herr, S., Wang, L. P. & Collins, L. R.
1996
EDQNM model of a passive scalar with a uniform mean gradient. Phys. Fluids
8, 1588–1608.

Herring, J. R., Schertzer, D., Lesieur, M., Newman, G. R., Chollet, J. P. & Larcheveque, M.
1982
A comparative assessment of spectral closures as applied to passive scalar diffusion. J. Fluid Mech.
124, 411–437.

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

Kraichnan, R. H.
1968
Small-scale structure of a scalar field convected by turbulence. Phys. Fluids
11
(5), 945–953.

Krstulovic, G. & Brachet, M. E.
2008
Two-fluid model of the truncated Euler equations. Physica D
237, 2015–2019.

Lesieur, M.
2008
Turbulence in Fluids, 4th edn. Springer.

Lesieur, M., Montmory, C. & Chollet, J.-P.
1987
The decay of kinetic energy and temperature variance in three-dimensional isotropic turbulence. Phys. Fluids
30, 1278–1286.

Meldi, M. & Sagaut, P.
2012
On non-self similar regimes in homogeneous isotropic turbulence decay. J. Fluid Mech.
711, 364–393.

Meldi, M., Sagaut, P. & Lucor, D.
2011
A stochastic view of isotropic turbulence decay. J. Fluid Mech.
668, 351–362.

Miller, P. L. & Dimotakis, P. E.
1996
Measurements of scalar power spectra in high Schmidt number turbulent jets. J. Fluid Mech.
308, 129–146.

Obukhov, A. M.
1949
Temperature field structure in a turbulent flow. Izv. Acad. Nauk SSSR Geogr. Geofiz
13, 58–69.

Obukhov, A. M.
1968 Structure of the temperature field in turbulent flow. *Tech. Rep*. Defense Technical Information Center Document.

Orszag, S. A.
1970
Analytical theories of turbulence. J. Fluid Mech.
41, 363–386.

Pao, Y. H.
1965
Structure of turbulent velocity and scalar fields at large wavenumbers. Phys. Fluids
8, 1063–1075.

Qian, J.
1986
Turbulent passive scalar field of a small Prandtl number. Phys. Fluids
29, 3586–3589.

Qian, J.
1990
The spectrum of a turbulent passive scalar in the viscous-convective range. J. Fluid Mech.
217, 203–212.

Rubinstein, R. & Clark, T. T.
2005
Self-similar turbulence evolution and the dissipation rate transport equation. Phys. Fluids
17, 095104.

Saffman, P. J.
1967
The large-scale structure of homogeneous turbulence. J. Fluid Mech.
27, 581–593.

Sagaut, P. & Cambon, C.
2008
Homogeneous Turbulence Dynamics. Cambridge University Press.

Schlichting, E.
1968
Boundary Layer Theory, 6th edn. McGraw-Hill.

Tchoufag, J., Sagaut, P. & Cambon, C.
2012
Spectral approach to finite Reynolds number effects on Kolmogorov’s
$4/ 5$
law in isotropic turbulence. Phys. Fluids
24, 015107.
Ulitsky, M., Vaithianathan, T. & Collins, L. R.
2002
A spectral study of differential diffusion of passive scalars in isotropic turbulence. J. Fluid Mech.
460, 1–38.

Vignon, J. M. & Cambon, C.
1980
Thermal spectral calculation using Eddy Damped Quasi Normal Markovian theory. Phys. Fluids
23, 1935–1937.

Warhaft, Z.
2000
Passive scalars in turbulent flows. Annu. Rev. Fluid Mech.
32
(1), 203–240.

Warhaft, Z. & Lumley, J. L.
1978
An experimental study of the decay of temperature fluctuations in grid-generated turbulence. J. Fluid Mech.
88, 659–684.

Williams, R. M. & Paulson, C. A.
1977
Microscale temperature and velocity spectra in the atmospheric boundary layer. J. Fluid Mech.
83, 547–567.

Woodruff, S. L. & Rubinstein, R.
2006
Multiple-scale perturbation analysis of slowly evolving turbulence. J. Fluid Mech.
565, 95–103.

Xia, Y., Liu, Y., Vaithianathan, T. & Collins, L. R.
2010
Eddy Damped Quasi Normal Markovian theory for chemically reactive scalars in isotropic turbulence. Phys. Fluids
22, 045103.

Yeung, P. K. & Sreenivasan, K. R.
2013
Spectrum of passive scalars of high molecular diffusivity in turbulent mixing. J. Fluid Mech.
716, R14.