T. Gotoh, D. Fukayama, and T. Nakano, Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation, Physics of Fluids, vol.14, issue.3, p.1065, 2002.
DOI : 10.1063/1.1448296

A. Heger, N. Langer, and S. E. Woosley, Presupernova Evolution of Rotating Massive Stars. I. Numerical Method and Evolution of the Internal Stellar Structure, The Astrophysical Journal, vol.528, issue.1, p.368, 2000.
DOI : 10.1086/308158

S. E. Holt, J. R. Koseff, and J. H. Ferziger, A numerical study of the evolution and structure of homogeneous stably stratified sheared turbulence, Journal of Fluid Mechanics, vol.9, issue.-1, p.499, 1992.
DOI : 10.1063/1.1692279

F. G. Jacobitz, S. Sarkar, and C. W. Van-atta, Direct numerical simulations of the turbulence evolution in a uniformly sheared and stably stratified flow, Journal of Fluid Mechanics, vol.342, p.231, 1997.
DOI : 10.1017/S0022112097005478

A. Maeder and G. Meynet, Rotating massive stars: From first stars to gamma ray bursts, Reviews of Modern Physics, vol.84, issue.1, p.25, 2012.
DOI : 10.1103/RevModPhys.84.25

S. Mathis, A. Palacios, and J. Zahn, On shear-induced turbulence in rotating stars, Astronomy and Astrophysics, vol.425, issue.1, p.243, 2004.
DOI : 10.1051/0004-6361:20040279

G. Michaud and J. Zahn, Turbulent Transport in Stellar Interiors, Theoretical and Computational Fluid Dynamics, vol.11, issue.3-4, p.183, 1998.
DOI : 10.1007/s001620050088

A. Palacios, C. Charbonnel, S. Talon, and L. Siess, Rotational mixing in low-mass stars, Astronomy and Astrophysics, vol.453, issue.1, p.261, 2006.
DOI : 10.1051/0004-6361:20053065

A. Palacios, S. Talon, C. Charbonnel, and M. Forestini, Rotational mixing in low-mass stars, Astronomy and Astrophysics, vol.399, issue.2, p.603, 2003.
DOI : 10.1051/0004-6361:20021759

M. H. Pinsonneault, S. D. Kawaler, S. Sofia, and P. Demarque, Evolutionary models of the rotating sun, The Astrophysical Journal, vol.338, p.424, 1989.
DOI : 10.1086/167210

J. Schumacher and B. Eckhardt, On statistically stationary homogeneous shear turbulence, Europhysics Letters (EPL), vol.52, issue.6, p.627, 2000.
DOI : 10.1209/epl/i2000-00484-4

O. Thual, Zero-Prandtl-number convection, Journal of Fluid Mechanics, vol.4, issue.-1, p.229, 1992.
DOI : 10.1017/S0022112081002541

URL : https://hal.archives-ouvertes.fr/jpa-00248343

A. A. Townsend, The effects of radiative transfer on turbulent flow of a stratified fluid, Journal of Fluid Mechanics, vol.236, issue.04, p.361, 1958.
DOI : 10.1088/0370-1301/63/2/305

J. Zahn, Stellar Instability and Evolution, IAU Symposium, pp.185-194, 1974.

M. Aizenman, P. Smeyers, and A. Weigert, Avoided Crossing of Modes of Non-radial Stellar Oscillations, A&A, vol.58, pp.41-46, 1977.

H. M. Antia and S. Basu, Measuring the helium abundance in the solar envelope: The role of the equation of state, The Astrophysical Journal, vol.426, pp.801-811, 1994.
DOI : 10.1086/174117

N. Baker and R. Kippenhahn, Untersuchungen über rotierende Sterne. III. Meridionale Zirkulation bei nichtstarrer Rotation, pp.140-154, 1959.

S. Balachandran, The Lithium Dip in M67: Comparison with the Hyades, Praesepe, and NGC 752 Clusters, The Astrophysical Journal, vol.446, pp.203-227, 1995.
DOI : 10.1086/175779

S. A. Balbus and J. F. Hawley, The stability of differentially rotating, weakly magnetized stellar radiative zones, Monthly Notices of the Royal Astronomical Society, vol.266, issue.4, pp.769-774, 1994.
DOI : 10.1093/mnras/266.4.769

S. Basu, J. Christensen-dalsgaard, W. J. Chaplin, Y. Elsworth, G. R. Isaak et al., Solar internal sound speed as inferred from combined BiSON and LOWL oscillation frequencies, Monthly Notices of the Royal Astronomical Society, vol.292, issue.2, pp.243-251, 1997.
DOI : 10.1093/mnras/292.2.243

P. G. Beck, J. Montalban, T. Kallinger, J. De-ridder, C. Aerts et al., Fast core rotation in red-giant stars as revealed by gravity-dominated mixed modes, Nature, vol.114, issue.7379, pp.55-57, 2012.
DOI : 10.1038/nature10612

URL : https://hal.archives-ouvertes.fr/cea-00881388

L. Bildsten, B. Paxton, K. Moore, and P. J. Macias, ACOUSTIC SIGNATURES OF THE HELIUM CORE FLASH, The Astrophysical Journal, vol.744, issue.1, pp.6-10, 2012.
DOI : 10.1088/2041-8205/744/1/L6

C. T. Bolton and G. L. Rogers, The binary frequency of the OBN and OBC stars, The Astrophysical Journal, vol.222, pp.234-245, 1978.
DOI : 10.1086/156139

J. Braithwaite and H. C. Spruit, A fossil origin for the magnetic field in A stars and white dwarfs, Nature, vol.275, issue.7010, pp.819-821, 2004.
DOI : 10.1086/186413

G. Brethouwer, Direct numerical simulation of turbulent mixing of a passive scalar in pipe flow, European Journal of Mechanics - B/Fluids, vol.18, issue.4, pp.739-756, 1999.
DOI : 10.1016/S0997-7546(99)00102-8

G. Brethouwer, J. C. Hunt, and F. T. Nieuwstadt, Micro-structure and Lagrangian statistics of the scalar field with a mean gradient in isotropic turbulence, J. Fluid. Mech, vol.474, pp.193-225, 2003.

G. Brethouwer and E. Lindborg, Numerical study of vertical dispersion by stratified turbulence, Journal of Fluid Mechanics, vol.76, issue.6, pp.149-163, 2009.
DOI : 10.1017/S0022112083000749

I. Brott, S. E. De-mink, M. Cantiello, N. Langer, A. De-koter et al., Rotating massive main-sequence stars, Astronomy & Astrophysics, vol.530, p.115, 2011.
DOI : 10.1051/0004-6361/201016113

I. Brott, C. J. Evans, I. Hunter, A. De-koter, N. Langer et al., Rotating massive main-sequence stars, Astronomy & Astrophysics, vol.530, p.116, 2011.
DOI : 10.1051/0004-6361/201016114

J. M. Brown, P. Garaud, and S. Stellmach, CHEMICAL TRANSPORT AND SPONTANEOUS LAYER FORMATION IN FINGERING CONVECTION IN ASTROPHYSICS, The Astrophysical Journal, vol.768, issue.1, 2013.
DOI : 10.1088/0004-637X/768/1/34

T. M. Brown, J. Christensen-dalsgaard, W. A. Dziembowski, P. Goode, D. O. Gough et al., Inferring the sun's internal angular velocity from observed p-mode frequency splittings, The Astrophysical Journal, vol.343, pp.526-546, 1989.
DOI : 10.1086/167727

K. A. Brucker, J. C. Isaza, T. Vaithianathan, and L. R. Collins, Efficient algorithm for simulating homogeneous turbulent shear flow without remeshing, Journal of Computational Physics, vol.225, issue.1, pp.20-32, 2007.
DOI : 10.1016/j.jcp.2006.10.018

M. Brüggen and W. Hillebrandt, Mixing through shear instabilities, Monthly Notices of the Royal Astronomical Society, vol.320, issue.1, pp.73-82, 2001.
DOI : 10.1046/j.1365-8711.2001.03951.x

F. H. Busse, Do eddington???sweet circulations exist?, Geophysical & Astrophysical Fluid Dynamics, vol.223, issue.1, pp.215-235, 1981.
DOI : 10.1080/03091928108243683

F. H. Busse, On the problem of stellar rotation, The Astrophysical Journal, vol.259, pp.759-766, 1982.
DOI : 10.1086/160212

K. L. Calder, On the equation of atmospheric diffusion, Quarterly Journal of the Royal Meteorological Society, vol.89, issue.390, pp.514-517, 1965.
DOI : 10.1002/qj.49709139011

V. M. Canuto, Critical Richardson numbers and gravity waves, Astronomy and Astrophysics, vol.384, issue.3, pp.1119-1123, 2002.
DOI : 10.1051/0004-6361:20011773

B. Chaboyer and J. Zahn, Effect of horizontal turbulent diffusion on transport by meridional circulation, A&A, vol.253, pp.173-177, 1992.

K. L. Chan and S. Sofia, Validity Tests of the Mixing-Length Theory of Deep Convection, Science, vol.235, issue.4787, pp.465-467, 1987.
DOI : 10.1126/science.235.4787.465

S. Chandrasekhar, Stochastic Problems in Physics and Astronomy, Reviews of Modern Physics, vol.15, issue.1, pp.1-89, 1943.
DOI : 10.1103/RevModPhys.15.1

W. J. Chaplin, J. Christensen-dalsgaard, Y. Elsworth, R. Howe, G. R. Isaak et al., Rotation of the solar core from BiSON and LOWL frequency observations, Monthly Notices of the Royal Astronomical Society, vol.308, issue.2, pp.405-414, 1999.
DOI : 10.1046/j.1365-8711.1999.02691.x

P. Charbonneau, S. Tomczyk, J. Schou, and M. J. Thompson, The Rotation of the Solar Core Inferred by Genetic Forward Modeling, The Astrophysical Journal, vol.496, issue.2, pp.1015-1030, 1998.
DOI : 10.1086/305400

C. Charbonnel and S. Talon, Influence of Gravity Waves on the Internal Rotation and Li Abundance of Solar-Type Stars, Science, vol.309, issue.5744, pp.2189-2191, 2005.
DOI : 10.1126/science.1116849

C. Chiosi and A. Maeder, The Evolution of Massive Stars with Mass Loss, Annual Review of Astronomy and Astrophysics, vol.24, issue.1, pp.329-375, 1986.
DOI : 10.1146/annurev.aa.24.090186.001553

J. Christensen-dalsgaard, Helioseismology, Reviews of Modern Physics, vol.74, issue.4, pp.1073-1129, 2002.
DOI : 10.1103/RevModPhys.74.1073

J. Christensen-dalsgaard, T. L. Duvall, J. , D. O. Gough, J. W. Harvey et al., Speed of sound in the solar interior, Nature, vol.34, issue.6018, pp.378-382, 1985.
DOI : 10.1038/315378a0

J. Christensen-dalsgaard and J. Schou, « Differential rotation in the solar interior, Seismology of the Sun and Sun-Like Stars, pp.149-153, 1988.

J. Christensen-dalsgaard, J. Schou, and M. J. Thompson, A comparison of methods for inverting helioseismic data, Monthly Notices of the Royal Astronomical Society, vol.242, issue.3, pp.353-369, 1990.
DOI : 10.1093/mnras/242.3.353

D. Chung and G. Matheou, Direct numerical simulation of stationary homogeneous stratified sheared turbulence, Journal of Fluid Mechanics, vol.23, pp.434-467
DOI : 10.1063/1.1762200

S. Corrsin, Limitations of Gradient Transport Models in Random Walks and in Turbulence, Adv. Geophys, vol.18, p.25, 1974.
DOI : 10.1016/S0065-2687(08)60451-3

T. G. Cowling, The Non-radial Oscillations of Polytropic Stars, Monthly Notices of the Royal Astronomical Society, vol.101, issue.8, pp.367-375, 1941.
DOI : 10.1093/mnras/101.8.367

T. G. Cowling and R. A. Newing, The Oscillations of a Rotating Star., The Astrophysical Journal, vol.109, pp.149-158, 1949.
DOI : 10.1086/145114

F. D. Antona and I. Mazzitelli, Lithium depletion in stars -Pre-main sequence burning and extra-mixing, A&A, vol.138, pp.431-442, 1984.

W. Däppen, D. O. Gough, A. G. Kosovichev, and M. J. Thompson, A new inversion for the hydrostatic stratification of the sun, Challenges to Theories of the Structure of Moderate-Mass Stars, pp.111-120, 1991.
DOI : 10.1007/3-540-54420-8_57

C. Reese, J. Regulo, T. Schou, L. Stahn, J. Casagrande et al., Seismic Evidence for a Rapidly Rotating Core in a Lower-giant-branch Star Observed with Kepler, ApJ, vol.756, pp.19-34, 2012.

P. A. Denissenkov, N. S. Ivanova, and A. Weiss, Main-sequence stars of 10 and 30 M_sun : approaching the steady-state rotation, A&A, vol.341, pp.181-189, 1999.

R. G. Deupree, Stellar evolution with arbitrary rotation laws. I - Mathematical techniques and test cases, The Astrophysical Journal, vol.357, pp.175-187, 1990.
DOI : 10.1086/168903

J. D. Do-nascimento, J. , M. Castro, J. Meléndez, M. Bazot et al., Age and mass of solar twins constrained by lithium abundance, Astronomy and Astrophysics, vol.501, issue.2, pp.687-694, 2009.
DOI : 10.1051/0004-6361/200911935

P. A. Durbin, A random flight model of inhomogeneous turbulent dispersion, Physics of Fluids, vol.23, issue.11, pp.2151-2153, 1980.
DOI : 10.1063/1.862908

T. L. Duvall, J. , W. A. Dziembowski, P. R. Goode, D. O. Gough et al., Internal rotation of the Sun, Nature, vol.5, issue.5972, pp.22-25, 1984.
DOI : 10.1038/310022a0

W. A. Dziembowski and P. R. Goode, Effects of differential rotation on stellar oscillations - A second-order theory, The Astrophysical Journal, vol.394, pp.670-687, 1992.
DOI : 10.1086/171621

W. A. Dziembowski, P. R. Goode, and K. G. Libbrecht, The radial gradient in the sun's rotation, The Astrophysical Journal, vol.337, pp.53-57, 1989.
DOI : 10.1086/185377

A. S. Eddington, Circulating currents in rotating stars. The Observatory 48, pp.73-75, 1925.

P. Eggenberger, G. Meynet, A. Maeder, R. Hirschi, C. Charbonnel et al., The Geneva stellar evolution code, Astrophysics and Space Science, vol.322, issue.1-4, pp.43-54, 2008.
DOI : 10.1007/s10509-007-9511-y

P. Eggenberger, J. Montalbán, and A. Miglio, Angular momentum transport in stellar interiors constrained by rotational splittings of mixed modes in red giants, Astronomy & Astrophysics, vol.544, p.4, 2012.
DOI : 10.1051/0004-6361/201219729

S. Ekström, C. Georgy, P. Eggenberger, G. Meynet, N. Mowlavi et al., Grids of stellar models with rotation. I. Models from 0, A&A, vol.8, issue.537, p.146, 2012.

A. S. Endal and S. Sofia, The evolution of rotating stars. I - Method and exploratory calculations for a 7-solar-mass star, The Astrophysical Journal, vol.210, pp.184-198, 1976.
DOI : 10.1086/154817

A. S. Endal and S. Sofia, The evolution of rotating stars. II - Calculations with time-dependent redistribution of angular momentum for 7- and 10-solar-mass stars, The Astrophysical Journal, vol.220, pp.279-290, 1978.
DOI : 10.1086/155904

F. , E. Lara, and M. Rieutord, Gravity darkening in rotating stars, A&A, vol.533, 2011.

F. , E. Lara, and M. Rieutord, Self-consistent 2D models of fast-rotating early-type stars, A&A, vol.552, pp.35-2013

V. Eswaran and S. B. Pope, Direct numerical simulations of the turbulent mixing of a passive scalar, Physics of Fluids, vol.31, issue.3, pp.506-520, 1988.
DOI : 10.1063/1.866832

C. J. Evans, D. J. Lennon, S. J. Smartt, and C. Trundle, The VLT-FLAMES survey of massive stars : observations centered on the Magellanic Cloud clusters NGC 330, NGC 2004, and the N11 region, pp.623-638, 2006.

E. Feireisl and A. Novotný, Small P??clet Number Approximation as a Singular Limit of the Full Navier-Stokes-Fourier System with Radiation, New Directions in Mathematical Fluid Mechanics, Advances in Mathematical Fluid Mechanics, pp.123-152, 2010.
DOI : 10.1007/978-3-0346-0152-8_8

V. C. Ferraro, The Non-uniform Rotation of the Sun and its Magnetic Field, Monthly Notices of the Royal Astronomical Society, vol.97, issue.6, pp.458-472, 1937.
DOI : 10.1093/mnras/97.6.458

J. Fliegner, N. Langer, and K. A. Venn, Boron in main sequence B stars : a critical test for rotational mixing, A&A, vol.308, pp.13-16, 1996.

B. E. Freeman, Tensor Diffusivity of a Trace Constituent in a Stratified Boundary Layer, Journal of the Atmospheric Sciences, vol.34, issue.1, pp.124-136, 1977.
DOI : 10.1175/1520-0469(1977)034<0124:TDOATC>2.0.CO;2

K. Fricke, Instabilität stationärer Rotation in Sternen, pp.317-344, 1968.

T. Gerz, U. Schumann, and S. E. Elghobashi, Direct numerical simulation of stratified homogeneous turbulent shear flows, Journal of Fluid Mechanics, vol.176, issue.-1, pp.563-594, 1989.
DOI : 10.1146/annurev.fl.16.010184.000531

D. R. Gies and D. L. Lambert, Carbon, nitrogen, and oxygen abundances in early B-type stars, The Astrophysical Journal, vol.387, pp.673-700, 1992.
DOI : 10.1086/171116

P. Goldreich and G. Schubert, Differential Rotation in Stars, The Astrophysical Journal, vol.150, pp.571-587, 1967.
DOI : 10.1086/149360

D. O. Gough, Mixing-length theory for pulsating stars, The Astrophysical Journal, vol.214, pp.196-213, 1977.
DOI : 10.1086/155244

D. O. Gough, A new measure of the solar rotation, Monthly Notices of the Royal Astronomical Society, vol.196, issue.3, pp.731-745, 1981.
DOI : 10.1093/mnras/196.3.731

F. Harvey, J. W. Hill, M. J. Leibacher, O. Monteiro, T. Richard et al., The Seismic Structure of the Sun, Science, vol.272, pp.1296-1300, 1996.

P. Gualtieri, C. M. Casciola, R. Benzi, G. Amati, and R. Piva, Scaling laws and intermittency in homogeneous shear flow, Physics of Fluids, vol.14, issue.2, pp.583-596, 2002.
DOI : 10.1063/1.1427919

C. J. Hansen, J. P. Cox, and H. M. Van-horn, The effects of differential rotation on the splitting of nonradial modes of stellar oscillation, The Astrophysical Journal, vol.217, pp.151-159, 1977.
DOI : 10.1086/155564

A. Heger and N. Langer, Presupernova Evolution of Rotating Massive Stars. II. Evolution of the Surface Properties, The Astrophysical Journal, vol.544, issue.2, pp.1016-1035, 2000.
DOI : 10.1086/317239

A. Heger, N. Langer, and S. E. Woosley, Presupernova Evolution of Rotating Massive Stars. I. Numerical Method and Evolution of the Internal Stellar Structure, The Astrophysical Journal, vol.528, issue.1, pp.368-396, 2000.
DOI : 10.1086/308158

A. Herrero, L. J. Corral, M. R. Villamariz, and E. L. Martín, Fundamental parameters of galactic luminous OB stars. III. Spectroscopic analysis of O stars in Cygnus OB2, A&A, vol.348, pp.542-552, 1999.

A. Herrero, R. P. Kudritzki, J. M. Vilchez, D. Kunze, K. Butler et al., Intrinsic parameters of galactic luminous OB stars, A&A, vol.261, pp.209-234, 1992.

S. Hirabayashi and T. Sato, A novel numerical forcing for homogeneous stratified turbulence in full energy equilibrium, Computers & Fluids, vol.39, issue.10, pp.1789-1795, 2010.
DOI : 10.1016/j.compfluid.2010.06.001

R. Hirschi and A. Maeder, The GSF instability and turbulence do not account for the relatively low rotation rate of pulsars, Astronomy and Astrophysics, vol.519, 2010.
DOI : 10.1051/0004-6361/201014222

R. Hirschi, G. Meynet, and A. Maeder, Stellar evolution with rotation, Astronomy and Astrophysics, vol.425, issue.2, pp.649-670, 2004.
DOI : 10.1051/0004-6361:20041095

S. E. Holt, J. R. Koseff, and J. H. Ferziger, A numerical study of the evolution and structure of homogeneous stably stratified sheared turbulence, Journal of Fluid Mechanics, vol.9, issue.-1, pp.499-539, 1992.
DOI : 10.1063/1.1692279

J. C. Hunt, D. D. Stretch, and R. E. Britter, « Length scales in stably stratified turbulent flows and their use in turbulence models, Stably stratified flows and dense gas dispersion, pp.285-321, 1988.

I. Hunter, I. Brott, N. Langer, D. J. Lennon, P. L. Dufton et al., The VLT-FLAMES survey of massive stars: constraints on stellar evolution from the chemical compositions of rapidly rotating Galactic and Magellanic Cloud B-type stars, Astronomy and Astrophysics, vol.496, issue.3, pp.841-853, 2009.
DOI : 10.1051/0004-6361/200809925

I. Hunter, I. Brott, D. J. Lennon, N. Langer, P. L. Dufton et al., The VLT FLAMES Survey of Massive Stars: Rotation and Nitrogen Enrichment as the Key to Understanding Massive Star Evolution, The Astrophysical Journal, vol.676, issue.1, pp.29-32, 2008.
DOI : 10.1086/587436

T. Ishihara, K. Yoshida, and Y. Kaneda, Anisotropic Velocity Correlation Spectrum at Small Scales in a Homogeneous Turbulent Shear Flow, Physical Review Letters, vol.88, issue.15, p.154501, 2002.
DOI : 10.1103/PhysRevLett.88.154501

F. G. Jacobitz, S. Sarkar, and C. W. Van-atta, Direct numerical simulations of the turbulence evolution in a uniformly sheared and stably stratified flow, Journal of Fluid Mechanics, vol.342, pp.231-261, 1997.
DOI : 10.1017/S0022112097005478

H. Kaltenbach, T. Gerz, and U. Schumann, Large-eddy simulation of homogeneous turbulence and diffusion in stably stratified shear flow, Journal of Fluid Mechanics, vol.195, issue.-1, pp.1-40, 1994.
DOI : 10.1016/0377-0265(88)90021-8

S. D. Kawaler, T. Sekii, and D. Gough, Prospects for Measuring Differential Rotation in White Dwarfs through Asteroseismology, The Astrophysical Journal, vol.516, issue.1, pp.349-365, 1999.
DOI : 10.1086/307087

R. Kippenhahn and H. Thomas, « A Simple Method for the Solution of the Stellar Structure Equations Including Rotation and Tidal Forces, IAU Colloq. 4 : Stellar Rotation, pp.20-29, 1970.

H. H. Klahr and P. Bodenheimer, Turbulence in Accretion Disks: Vorticity Generation and Angular Momentum Transport via the Global Baroclinic Instability, The Astrophysical Journal, vol.582, issue.2, pp.869-892, 2003.
DOI : 10.1086/344743

E. Knobloch and H. C. Spruit, Stability of differential rotation in stars, A&A, vol.113, pp.261-268, 1982.

D. Lecoanet, E. G. Zweibel, R. H. Townsend, and Y. Huang, VIOLATION OF RICHARDSON'S CRITERION VIA INTRODUCTION OF A MAGNETIC FIELD, The Astrophysical Journal, vol.712, issue.2, pp.1116-1128, 2010.
DOI : 10.1088/0004-637X/712/2/1116

P. Ledoux and T. Walraven, Variable Stars, pp.353-604, 1958.
DOI : 10.1007/978-3-642-45908-5_6

S. K. Lele, Compact finite difference schemes with spectral-like resolution, Journal of Computational Physics, vol.103, issue.1, pp.16-42, 1992.
DOI : 10.1016/0021-9991(92)90324-R

P. Lesaffre, S. M. Chitre, A. T. Potter, and C. A. Tout, A two-dimensional mixing length theory of convective transport, Monthly Notices of the Royal Astronomical Society, vol.431, issue.3, pp.2200-2208, 2013.
DOI : 10.1093/mnras/stt317

G. Lesur and J. C. Papaloizou, The subcritical baroclinic instability in local accretion disc models, Astronomy and Astrophysics, vol.513, 2010.
DOI : 10.1051/0004-6361/200913594

URL : https://hal.archives-ouvertes.fr/hal-00631989

L. H. Li, P. Ventura, S. Basu, S. Sofia, and P. Demarque, Two???dimensional Stellar Evolution Code Including Arbitrary Magnetic Fields. I. Mathematical Techniques and Test Cases, The Astrophysical Journal Supplement Series, vol.164, issue.1, pp.215-254, 2006.
DOI : 10.1086/502800

F. Lignières, The small-Péclet-number approximation in stellar radiative zones, A&A, vol.348, pp.933-939, 1999.

F. Lignières, F. Califano, and A. Mangeney, Shear layer instability in a highly diffusive stably stratified atmosphere, A&A, vol.349, pp.1027-1036, 1999.

E. Lindborg and E. Fedina, Vertical turbulent diffusion in stably stratified flows, Geophysical Research Letters, vol.317, issue.1, p.1605, 2009.
DOI : 10.1029/2008GL036437

C. C. Lovekin, R. G. Deupree, and C. I. Short, Surface Temperature and Synthetic Spectral Energy Distributions for Rotationally Deformed Stars, The Astrophysical Journal, vol.643, issue.1, pp.460-470, 2006.
DOI : 10.1086/501492

H. Ludwig, B. Freytag, and M. Steffen, A calibration of the mixing-length for solartype stars based on hydrodynamical simulations. I. Methodical aspects and results for solar metallicity, A&A, vol.346, pp.111-124, 1999.

L. S. Lyubimkov, Evolutionary increase in the nitrogen abundance in the atmospheres of early B stars, Astrophysics, vol.247, issue.3, pp.255-266, 1984.
DOI : 10.1007/BF01005414

L. S. Lyubimkov, Correlation between the helium abundances in the atmospheres of early B stars and their ages and masses, Astrophysics, vol.59, issue.3, pp.704-713, 1988.
DOI : 10.1007/BF01004212

L. S. Lyubimkov, D. L. Lambert, T. M. Rachkovskaya, S. I. Rostopchin, A. E. Tarasov et al., Surface abundances of light elements for a large sample of early B-type stars -- I. Spectral observations of 123 stars; measurements of hydrogen and helium lines; infrared photometry, Monthly Notices of the Royal Astronomical Society, vol.316, issue.1, pp.19-32, 2000.
DOI : 10.1046/j.1365-8711.2000.03413.x

L. S. Lyubimkov, S. I. Rostopchin, and D. L. Lambert, Surface abundances of light elements for a large sample of early B-type stars - III. An analysis of helium lines in spectra of 102 stars, Monthly Notices of the Royal Astronomical Society, vol.351, issue.2, pp.745-767, 2004.
DOI : 10.1111/j.1365-2966.2004.07825.x

A. Maeder, On the Richardson criterion for shear instabilities in rotating stars, A&A, vol.299, pp.84-88, 1995.

A. Maeder, Stellar evolution with rotation. II. A new approach for shear mixing, A&A, vol.321, pp.134-144, 1997.
DOI : 10.1051/0004-6361:20020938

A. Maeder, Stellar rotation: Evidence for a large horizontal turbulence and its effects on evolution, Astronomy and Astrophysics, vol.399, issue.1, pp.263-269, 2003.
DOI : 10.1051/0004-6361:20021731

A. Maeder and G. Meynet, Diffusive mixing by shears in rotating stars, A&A, vol.313, pp.140-144, 1996.

A. Maeder and G. Meynet, Stellar evolution with rotation. VII., Astronomy and Astrophysics, vol.373, issue.2, pp.555-571, 2001.
DOI : 10.1051/0004-6361:20010596

A. Maeder and G. Meynet, Stellar evolution with rotation and magnetic fields, Astronomy and Astrophysics, vol.422, issue.1, pp.225-237, 2004.
DOI : 10.1051/0004-6361:20034583

A. Maeder and G. Meynet, Stellar evolution with rotation and magnetic fields, Astronomy and Astrophysics, vol.440, issue.3, pp.1041-1049, 2005.
DOI : 10.1051/0004-6361:20053261

A. Maeder, G. Meynet, N. Lagarde, and C. Charbonnel, The thermohaline, Richardson, Rayleigh-Taylor, Solberg???H??iland, and GSF criteria in rotating stars, Astronomy & Astrophysics, vol.553, p.1, 2013.
DOI : 10.1051/0004-6361/201220936

A. Maeder and J. Zahn, Stellar evolution with rotation. III. Meridional circulation with µ-gradients and non-stationarity, A&A, vol.334, pp.1000-1006, 1998.

J. P. Marques, M. J. Goupil, Y. Lebreton, S. Talon, A. Palacios et al., Seismic diagnostics for transport of angular momentum in stars, Astronomy & Astrophysics, vol.549, p.74, 2013.
DOI : 10.1051/0004-6361/201220211

URL : https://hal.archives-ouvertes.fr/hal-00856138

F. Martins, E. Depagne, D. Russeil, and L. Mahy, Evidence for quasi-chemically homogeneous evolution of massive stars up to solar metallicity. ArXiv e-prints 1304, 2013.

F. Martins, D. J. Hillier, J. C. Bouret, E. Depagne, C. Foellmi et al., Properties of WNh stars in the Small Magellanic Cloud: evidence for homogeneous evolution, Astronomy and Astrophysics, vol.495, issue.1, pp.257-270, 2009.
DOI : 10.1051/0004-6361:200811014

URL : https://hal.archives-ouvertes.fr/hal-00384700

S. Mathis, A. Palacios, and J. Zahn, On shear-induced turbulence in rotating stars, Astronomy and Astrophysics, vol.425, issue.1, pp.243-247, 2004.
DOI : 10.1051/0004-6361:20040279

S. Mathis and J. Zahn, Transport and mixing in the radiation zones of rotating stars, Astronomy and Astrophysics, vol.425, issue.1, pp.229-242, 2004.
DOI : 10.1051/0004-6361:20040278

J. T. Mendel, K. A. Venn, C. R. Proffitt, A. M. Brooks, and D. L. Lambert, Testing Rotational Mixing Predictions with New Boron Abundances in Main???Sequence B???Type Stars, The Astrophysical Journal, vol.640, issue.2, pp.1039-1050, 2006.
DOI : 10.1086/500252

K. Menou and J. L. Mer, Magnetorotational Transport in the Early Sun, The Astrophysical Journal, vol.650, issue.2, pp.1208-1216, 2006.
DOI : 10.1086/507022

G. Meynet and A. Maeder, Stellar evolution with rotation. I. The computational method and the inhibiting effect of the µ-gradient, A&A, vol.321, pp.465-476, 1997.

G. Meynet and A. Maeder, Stellar evolution with rotation. V. Changes in all the outputs of massive star models, A&A, vol.361, pp.101-120, 2000.

G. Michaud and J. Zahn, Turbulent Transport in Stellar Interiors, Theoretical and Computational Fluid Dynamics, vol.11, issue.3-4, pp.183-193, 1998.
DOI : 10.1007/s001620050088

A. Miglio, J. Montalbán, F. Baudin, P. Eggenberger, A. Noels et al., Probing populations of red giants in the galactic disk with CoRoT, Astronomy and Astrophysics, vol.503, issue.3, pp.21-24, 2009.
DOI : 10.1051/0004-6361/200912822

J. D. Monnier, M. Zhao, E. Pedretti, N. Thureau, M. Ireland et al., Imaging the Surface of Altair, Science, vol.317, issue.5836, pp.342-345, 2007.
DOI : 10.1126/science.1143205

URL : https://hal.archives-ouvertes.fr/hal-00398386

J. Montalbán and E. Schatzman, Mixing by internal waves. III. Li and Be abundance dependence on spectral type, age and rotation, A&A, vol.354, pp.943-959, 2000.

B. Mosser, M. J. Goupil, K. Belkacem, J. P. Marques, P. G. Beck et al., Spin down of the core rotation in red giants, Astronomy & Astrophysics, vol.548, 2012.
DOI : 10.1051/0004-6361/201220106

P. E. Nissen, Evidence of helium abundance differences between young groups of stars, A&A, vol.50, pp.343-352, 1976.

J. Norris, Neutral-Helium Line Strengths. V. The Weak-Helium Stars of Population I, The Astrophysical Journal Supplement Series, vol.23, pp.213-233, 1971.
DOI : 10.1086/190237

S. A. Orszag, Numerical Methods for the Simulation of Turbulence, Physics of Fluids, vol.12, issue.12, pp.250-257, 1969.
DOI : 10.1063/1.1692445

S. A. Orszag and G. S. Patterson, Numerical Simulation of Three-Dimensional Homogeneous Isotropic Turbulence, Physical Review Letters, vol.28, issue.2, pp.76-79, 1972.
DOI : 10.1103/PhysRevLett.28.76

Y. Osaki, Meridional Circulation in a Rotating Star, PASJ, vol.24, pp.509-516, 1972.

T. R. Osborn, Estimates of the Local Rate of Vertical Diffusion from Dissipation Measurements, Journal of Physical Oceanography, vol.10, issue.1, pp.83-89, 1980.
DOI : 10.1175/1520-0485(1980)010<0083:EOTLRO>2.0.CO;2

T. R. Osborn and L. E. Bilodeau, Temperature Microstructure in the Equatorial Atlantic, Journal of Physical Oceanography, vol.10, issue.1, pp.66-82, 1980.
DOI : 10.1175/1520-0485(1980)010<0066:TMITEA>2.0.CO;2

T. R. Osborn and C. S. Cox, Oceanic fine structure, Geophysical Fluid Dynamics, vol.14, issue.1, pp.321-345, 1972.
DOI : 10.1017/S0022112068001035

G. Pace, M. Castro, J. Meléndez, S. Théado, J. Do-nascimento et al., Lithium in M??67: From the main sequence to the red giant branch, Astronomy & Astrophysics, vol.541, p.150, 2012.
DOI : 10.1051/0004-6361/201117704

A. Palacios, C. Charbonnel, S. Talon, and L. Siess, Rotational mixing in low-mass stars, Astronomy and Astrophysics, vol.453, issue.1, pp.261-278, 2006.
DOI : 10.1051/0004-6361:20053065

A. Palacios, S. Talon, C. Charbonnel, and M. Forestini, Rotational mixing in low-mass stars, Astronomy and Astrophysics, vol.399, issue.2, pp.603-616, 2003.
DOI : 10.1051/0004-6361:20021759

E. N. Parker, The Formation of Sunspots from the Solar Toroidal Field., The Astrophysical Journal, vol.121, pp.491-507, 1955.
DOI : 10.1086/146010

H. J. Pearson, J. S. Puttock, and J. C. Hunt, A statistical model of fluid-element motions and vertical diffusion in a homogeneous stratified turbulent flow, Journal of Fluid Mechanics, vol.16, issue.-1, pp.219-249, 1983.
DOI : 10.1175/1520-0450(1981)020 2.0.CO;2

C. L. Pekeris, Nonradial Oscillations of Stars., The Astrophysical Journal, vol.88, pp.189-199, 1938.
DOI : 10.1086/143971

M. Pinsonneault, MIXING IN STARS, Annual Review of Astronomy and Astrophysics, vol.35, issue.1, pp.557-605, 1997.
DOI : 10.1146/annurev.astro.35.1.557

M. H. Pinsonneault, S. D. Kawaler, S. Sofia, and P. Demarque, Evolutionary models of the rotating sun, The Astrophysical Journal, vol.338, pp.424-452, 1989.
DOI : 10.1086/167210

E. Pitts and R. J. Tayler, The adiabatic stability of stars containing magnetic fields - VI. The influence of rotation, Monthly Notices of the Royal Astronomical Society, vol.216, issue.2, pp.139-154, 1985.
DOI : 10.1093/mnras/216.2.139

A. T. Potter, C. A. Tout, and I. Brott, Towards a unified model of stellar rotation - II. Model-dependent characteristics of stellar populations, Monthly Notices of the Royal Astronomical Society, vol.423, issue.2, pp.1221-1233, 2012.
DOI : 10.1111/j.1365-2966.2012.20952.x

L. Prandtl, Über die ausgebildete turbulenz (investigations on turbulent flow), Z. Angew . Math. Mech, vol.5, pp.136-139, 1925.

V. Prat and F. Lignières, Turbulent transport in radiative zones of stars, Astronomy & Astrophysics, vol.551, p.3, 2013.
DOI : 10.1051/0004-6361/201220577

A. Pumir, Turbulence in homogeneous shear flows, Physics of Fluids, vol.8, issue.11, pp.3112-3127, 1996.
DOI : 10.1063/1.869100

G. Randers, Large-Scale Motion in Stars., The Astrophysical Journal, vol.94, pp.109-123, 1941.
DOI : 10.1086/144316

J. J. Riley, G. S. Patterson, and J. , Diffusion experiments with numerically integrated isotropic turbulence, Physics of Fluids, vol.17, issue.2, pp.292-297, 1974.
DOI : 10.1063/1.1694714

R. S. Rogallo, Numerical experiments in homogeneous turbulence, 1981.

M. M. Rogers, N. N. Mansour, and W. C. Reynolds, An algebraic model for the turbulent flux of a passive scalar, Journal of Fluid Mechanics, vol.18, pp.77-101, 1989.
DOI : 10.1017/S0022112081002930

M. M. Rogers and P. Moin, The structure of the vorticity field in homogeneous turbulent flows, Journal of Fluid Mechanics, vol.162, issue.-1, pp.33-66, 1987.
DOI : 10.1017/S0022112077002286

I. W. Roxburgh, On stellar rotation, I. The rotation of upper main-sequence stars. MN- RAS 128, pp.157-171, 1964.

R. Rubinstein and J. M. Barton, Renormalization group analysis of anisotropic diffusion in turbulent shear flows, Physics of Fluids A: Fluid Dynamics, vol.3, issue.3, pp.415-421, 1991.
DOI : 10.1063/1.858097

S. Sarkar, The stabilizing effect of compressibility in turbulent shear flow, Journal of Fluid Mechanics, vol.2, issue.-1, pp.163-186, 1995.
DOI : 10.1146/annurev.fl.23.010191.000543

B. L. Sawford and P. K. Yeung, Lagrangian statistics in uniform shear flow: Direct numerical simulation and Lagrangian stochastic models, Physics of Fluids, vol.13, issue.9, pp.2627-2634, 2001.
DOI : 10.1063/1.1388539

J. Schou, J. Christensen-dalsgaard, and M. J. Thompson, On comparing helioseismic two-dimensional inversion methods, The Astrophysical Journal, vol.433, pp.389-416, 1994.
DOI : 10.1086/174653

]. J. Schumacher, Derivative moments in stationary homogeneous shear turbulence, Journal of Fluid Mechanics, vol.441
DOI : 10.1017/S0022112001005031

J. Schumacher, Relation between shear parameter and Reynolds number in statistically stationary turbulent shear flows, Physics of Fluids, vol.16, issue.8, pp.3094-3102, 2004.
DOI : 10.1063/1.1764431

J. Schumacher and B. Eckhardt, On statistically stationary homogeneous shear turbulence, Europhysics Letters (EPL), vol.52, issue.6, pp.627-632, 2000.
DOI : 10.1209/epl/i2000-00484-4

J. Schumacher, K. R. Sreenivasan, and P. K. Yeung, Very fine structures in scalar mixing, Journal of Fluid Mechanics, vol.531, pp.113-122, 2005.
DOI : 10.1017/S0022112005004040

U. Schumann, Algorithms for direct numerical simulation of shear-periodic turbulence, Numerical Methods in Fluid Dynamics, pp.492-496, 1985.
DOI : 10.1007/3-540-13917-6_187

U. Schumann and T. Gerz, Turbulent Mixing in Stably Stratified Shear Flows, Journal of Applied Meteorology, vol.34, issue.1, pp.33-48, 1995.
DOI : 10.1175/1520-0450-34.1.33

E. A. Spiegel, A Generalization of the Mixing-Length Theory of Turbulent Convection., The Astrophysical Journal, vol.138, pp.216-225, 1963.
DOI : 10.1086/147628

E. A. Spiegel and J. Zahn, Instabilities of Differential Rotation. Comments Astrophys . Space Phys, pp.178-183, 1970.

E. A. Spiegel and J. Zahn, The solar tachocline, A&A, vol.265, pp.106-114, 1992.

H. C. Spruit, Differential rotation and magnetic fields in stellar interiors, A&A, vol.349, pp.189-202, 1999.

H. C. Spruit, Dynamo action by differential rotation in a stably stratified stellar interior, Astronomy and Astrophysics, vol.381, issue.3, pp.923-932, 2002.
DOI : 10.1051/0004-6361:20011465

S. Starrfield, J. W. Truran, W. M. Sparks, and G. S. Kutter, CNO Abundances and Hydrodynamic Models of the Nova Outburst, The Astrophysical Journal, vol.176, pp.169-176
DOI : 10.1086/151619

P. A. Sweet, The Importance of Rotation in Stellar Evolution, Monthly Notices of the Royal Astronomical Society, vol.110, issue.6, pp.548-558, 1950.
DOI : 10.1093/mnras/110.6.548

S. Talon and C. Charbonnel, Hydrodynamical stellar models including rotation, internal gravity waves, and atomic diffusion, Astronomy and Astrophysics, vol.440, issue.3, pp.981-994, 2005.
DOI : 10.1051/0004-6361:20053020

S. Talon and J. Zahn, Anisotropic diffusion and shear instabilities, A&A, vol.317, pp.749-751, 1997.

J. Tassoul and M. Tassoul, Meridional circulation in rotating stars. I - A boundary layer analysis of mean steady motions in early-type stars, The Astrophysical Journal Supplement Series, vol.49, pp.317-350, 1982.
DOI : 10.1086/190801

R. J. Tayler, The Adiabatic Stability of Stars Containing Magnetic Fields-I: TOROIDAL FIELDS, Monthly Notices of the Royal Astronomical Society, vol.161, issue.4, pp.365-380, 1973.
DOI : 10.1093/mnras/161.4.365

G. I. Taylor, Diffusion by Continuous Movements, Proc. London Math. Soc, pp.196-212, 1921.
DOI : 10.1112/plms/s2-20.1.196

H. Tennekes and J. L. Lumley, First Course in Turbulence, 1972.

S. Tomczyk, J. Schou, and M. J. Thompson, Measurement of the Rotation Rate in the Deep Solar Interior, The Astrophysical Journal, vol.448, issue.1, pp.57-60, 1995.
DOI : 10.1086/309598

A. A. Townsend, The effects of radiative transfer on turbulent flow of a stratified fluid, Journal of Fluid Mechanics, vol.236, issue.04, pp.361-375, 1958.
DOI : 10.1088/0370-1301/63/2/305

D. J. Tritton and P. A. Davies, Instabilities in geophysical fluid dynamics, pp.229-270, 1985.

V. M. Tsarenko and A. M. Yaglom, Semiempirical theories of turbulent diffusion in a neutrally stratified atmospheric surface layer, Physics of Fluids A: Fluid Dynamics, vol.3, issue.9, pp.2199-2206, 1991.
DOI : 10.1063/1.857901

S. Vauclair and S. Théado, On the Coupling between Helium Settling and Rotation???induced Mixing in Stellar Radiative Zones. I. Analytical Approach, The Astrophysical Journal, vol.587, issue.2, pp.777-783, 2003.
DOI : 10.1086/368259

K. A. Venn, A???Type Supergiant Abundances in the Small Magellanic Cloud: Probes of Evolution, The Astrophysical Journal, vol.518, issue.1, pp.405-421, 1999.
DOI : 10.1086/307278

K. A. Venn, A. M. Brooks, D. L. Lambert, M. Lemke, N. Langer et al., Boron Abundances in B???Type Stars: A Test of Rotational Depletion during Main???Sequence Evolution, The Astrophysical Journal, vol.565, issue.1, pp.571-586, 2002.
DOI : 10.1086/324435

E. Vitense, Die Wasserstoffkonvektionszone der Sonne, pp.135-164, 1953.

H. Vogt, Zum Strahlungsgleichgewicht der Sterne, Astronomische Nachrichten, vol.60, issue.14, pp.229-232, 1925.
DOI : 10.1002/asna.19242231403

S. V. Vorontsov and H. Shibahashi, Asymptotic inversion of the solar oscillation frequencies -Sound speed in the solar interior, PASJ, vol.43, pp.739-753, 1991.

N. R. Walborn, Some Spectroscopic Characteristics of the OB Stars: a Nitrogen Anomaly, The Astrophysical Journal, vol.161, pp.149-152, 1970.
DOI : 10.1086/180589

N. R. Walborn, The OBn and OBc stars., The Astrophysical Journal, vol.205, pp.419-425, 1976.
DOI : 10.1086/154292

F. Waleffe, On a self-sustaining process in shear flows, Physics of Fluids, vol.9, issue.4, pp.883-900, 1997.
DOI : 10.1063/1.869185

G. Wallerstein, G. H. Herbig, and P. S. Conti, Observations of the Lithium Content of Main-Sequence Stars in the Hyades., The Astrophysical Journal, vol.141, pp.610-616, 1965.
DOI : 10.1086/148148

J. Wasiutynski, Studies in Hydrodynamics and Structure of Stars and Planets, Astrophys . Nor, vol.4, pp.1-497, 1946.

T. R. White, T. R. Bedding, D. Stello, J. Christensen-dalsgaard, D. Huber et al., CALCULATING ASTEROSEISMIC DIAGRAMS FOR SOLAR-LIKE OSCILLATIONS, The Astrophysical Journal, vol.743, issue.2, p.161, 2011.
DOI : 10.1088/0004-637X/743/2/161

T. S. Wood, P. Garaud, and S. Stellmach, A NEW MODEL FOR MIXING BY DOUBLE-DIFFUSIVE CONVECTION (SEMI-CONVECTION). II. THE TRANSPORT OF HEAT AND COMPOSITION THROUGH LAYERS, The Astrophysical Journal, vol.768, issue.2, 2013.
DOI : 10.1088/0004-637X/768/2/157

D. R. Xiong and L. Deng, Lithium depletion in late-type dwarfs, Monthly Notices of the Royal Astronomical Society, vol.395, issue.4, pp.2013-2028, 2009.
DOI : 10.1111/j.1365-2966.2009.14581.x

V. Yakhot, A simple model for self-sustained oscillations in homogeneous shear flow, Physics of Fluids, vol.15, issue.2, pp.17-20, 2003.
DOI : 10.1063/1.1536973

P. K. Yeung and S. B. Pope, Lagrangian statistics from direct numerical simulations of isotropic turbulence, Journal of Fluid Mechanics, vol.30, issue.-1, pp.531-586, 1989.
DOI : 10.1017/S0022112071001460

J. Zahn, Circulation and turbulence in rotating stars, A&A, vol.265, pp.115-132, 1992.

F. Zaussinger and H. C. Spruit, Semiconvection: numerical simulations, Astronomy & Astrophysics, vol.554, issue.119, 2013.
DOI : 10.1051/0004-6361/201220573

URL : http://arxiv.org/abs/1303.4522