E. Alméras, V. Mathai, D. Lohse, and C. Sun, Experimental investigation of the turbulence induced by a bubble swarm rising within incident turbulence, J. Fluid Mech, vol.825, pp.1091-1112, 2017.

S. S. Alves, S. P. Orvalho, and J. M. Vasconcelos, Effect of bubble contamination on rise velocity and mass transfer, Chem. Engng Sci, vol.60, issue.1, pp.1-9, 2005.

Z. Amoura, C. Besnaci, and F. Risso, Velocity fluctuations generated by the flow through a random array of spheres: a model of bubble-induced agitation, J. Fluid Mech, vol.823, pp.592-616, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01593663

Z. Amoura, V. Roig, F. Risso, and A. Billet, Attenuation of the wake of a sphere in an intense incident turbulence with large length scales, Phys. Fluids, vol.22, p.55105, 2010.

S. P. Antal, R. T. Lahey, and J. E. Flaherty, Analysis of phase distribution in fully developed laminar bubbly two-phase flow, Intl J. Multiphase Flow, vol.17, issue.5, pp.635-652, 1991.

E. Bertakis, S. Großss, J. Grande, O. Fortmeier, A. Reusken et al., Validated simulation of droplet sedimentation with finite-element and level-set methods, Chem. Engng Sci, vol.65, issue.6, pp.2037-2051, 2010.

A. Biesheuvel and L. V. Wijngaarden, Two-phase flow equations for a dilute dispersion of gas bubbles in liquid, J. Fluid Mech, vol.148, pp.301-318, 1984.

G. Bois, Direct numerical simulation of a turbulent bubbly flow in a vertical channel: towards an improved second-order Reynolds stress model, Nucl. Engng Des, vol.321, pp.92-103, 2017.
URL : https://hal.archives-ouvertes.fr/cea-02389168

G. Bois, A. Du-cluzeau, A. Toutant, and J. Martinez, DNS of turbulent bubbly flows in plane channels using the front-tracking algorithm of TrioCFD, Proceedings of the ASME Fluid Engineering Division Summer Meeting & Multiphase Flow Technical Committee, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02419673

G. Bois, G. Fauchet, and A. Toutant, DNS of a turbulent steam/water bubbly flow in a vertical channel, Proceedings of the 9th International Conference on Multiphase Flows (ICMF2016), 2016.

E. Bouche, V. Roig, and F. Risso, Homogeneous swarm of high-Reynolds-number bubbles rising within a thin gap. Part 1: bubble dynamics, J. Fluid Mech, vol.704, pp.211-231, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01325329

E. Bouche, V. Roig, and F. Risso, Homogeneous swarm of high-Reynolds-number bubbles rising within a thin gap. Part 2: liquid dynamics, J. Fluid Mech, vol.758, pp.508-521, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01325329

J. Chahed, V. Roig, and L. Masbernat, Eulerian-Eulerian two-fluid model for turbulent gas liquid bubbly flows, Intl J. Multiphase Flow, vol.29, pp.23-49, 2003.

M. Chandesris and D. Jamet, Boundary conditions at a planar fluid-porous interface for a Poiseuille flow, Intl J. Heat Mass Transfer, vol.49, pp.2137-2150, 2006.

M. Cisse, E. W. Saw, M. Gibert, E. Bodenschatz, and J. Bec, Turbulence attenuation by large neutrally buoyant particles, Phys. Fluids, vol.27, issue.6, pp.1-7, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01198368

C. Colin, J. Fabre, and A. Kamp, Turbulent bubbly flow in pipe under gravity and microgravity conditions, J. Fluid Mech, vol.711, pp.469-515, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00875768

M. Colombo and M. Fairweather, Multiphase turbulence in bubbly flows: RANS simulations, Intl J. Multiphase Flow, vol.77, pp.222-243, 2015.

S. Dabiri and P. Bhuvankar, Scaling law for bubbles rising near vertical walls, Phys. Fluids, vol.28, p.62101, 2016.

D. Dupuy, A. Toutant, and F. Bataille, Turbulence kinetic energy exchanges in flows with highly variable fluid properties, J. Fluid Mech, vol.834, pp.5-54, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01867346

E. A. Ervin and G. Tryggvason, The rise of bubbles in a vertical shear flow, Trans ASME J. Fluids Engng, vol.119, issue.2, pp.443-449, 1997.

X. Feng, C. Yang, Z. Mao, J. Lu, and G. Tryggvason, Bubble induced turbulence model improved by direct numerical simulation of bubbly flow, Chem. Engng J, 2018.

A. Fujiwara, D. Minato, and K. Hishida, Effect of bubble diameter on modification of turbulence in an upward pipe flow, Intl J. Heat Fluid Flow, vol.25, issue.3, pp.481-488, 2004.

S. Hosokawa, T. Suzuki, and A. Tomiyama, Turbulence kinetic energy budget in bubbly flows in a vertical duct, Exp. Fluids, vol.52, issue.3, pp.719-728, 2012.

S. Hosokawa and A. Tomiyama, Bubble-induced pseudo turbulence in laminar pipe flows, Intl J. Heat Fluid Flow, vol.40, pp.97-105, 2013.

M. Ilic, Statistical analysis of liquid phase turbulence based on direct numerical simulations of bubbly flows, 2006.

J. Jeong and F. Hussain, On the identification of a vortex, J. Fluid Mech, vol.285, pp.69-94, 1995.

I. Kataoka, Local instant formulation of two-phase flow, Intl J. Multiphase Flow, vol.12, issue.5, pp.745-758, 1986.

I. Kataoka and A. Serizawa, Basic equations of turbulence in gas-liquid two-phase flow, Intl J. Multiphase Flow, vol.15, issue.5, pp.843-855, 1989.

J. Kim, P. Moin, and R. Moser, Turbulence statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech, vol.177, pp.133-166, 1987.

M. Lance and J. Bataille, Turbulence in the liquid phase of a uniform bubbly air-water flow, J. Fluid Mech, vol.222, pp.95-118, 1358.

M. Lance, J. L. Marie, and J. Bataille, Homogeneous turbulence in bubbly flows, J. Fluids Engng, vol.113, issue.2, pp.295-300, 1991.

B. E. Launder, G. J. Reece, and W. Rodi, Progress in the development of a Reynolds-stress turbulence closure, J. Fluid Mech, vol.68, pp.537-566, 1975.

J. Laviéville, N. Mérigoux, M. Guingo, C. Baudry, and S. Mimouni, A generalized turbulent dispersion model for bubbly flow numerical simulation in NEPTUNE_CFD, NURETH-16, pp.4167-4181, 2015.

. Lopez-de and M. A. Bertodano, Two fluid model for two-phase turbulent jets, Nucl. Engng Des, vol.179, issue.1, pp.65-74, 1998.

J. Lu, S. Biswas, and G. Tryggvason, A DNS study of laminar bubbly flows in a vertical channel, Intl J. Multiphase Flow, vol.32, issue.6, pp.643-660, 2006.

J. Lu and G. Tryggvason, Effect of bubble deformability in turbulent bubbly upflow in a vertical channel, Phys. Fluids, vol.20, p.40701, 2008.

N. Lubchenko, B. Magolan, R. Sugrue, and E. Baglietto, A more fundamental wall lubrication force from turbulent dispersion regularization for multiphase CFD applications, Intl J. Multiphase Flow, vol.98, pp.36-44, 2017.

B. Mathieu, Etudes physique, expérimentale et numérique des mécanismes de base intervenant dans les écoulements diphasiques en micro-fluidique, 2003.

I. M. Mazzitelli, D. Lohse, and F. Toschi, The effect of microbubbles on developed turbulence, Phys. Fluids, vol.15, p.5, 2003.

C. Morel, Mathematical Modeling of Two-Phase Flow, 2015.

E. Olmos, C. Gentric, and N. Midoux, Numerical description of flow regime transitions in bubble column reactors by a multiple gas phase model, Chem. Engng Sci, vol.58, issue.10, pp.2113-2121, 2003.

M. A. Pakhomov and V. I. Terekhov, Modeling of turbulent structure of an upward polydisperse gas-liquid flow, Fluid Dyn, vol.50, issue.2, pp.229-239, 2015.

D. Pfleger and S. Becker, Modelling and simulation of the dynamic flow behaviour in a bubble column, Chem. Engng Sci, vol.56, issue.4, pp.1737-1747, 2001.

E. G. Puckett, A. S. Almgren, J. B. Bell, D. L. Marcus, and W. J. Rider, A high-order projection method for tracking fluid interfaces in variable density incompressible flows, J. Comput. Phys, vol.130, pp.269-282, 1997.

M. W. Reeks, On a kinetic equation for the transport of particles in turbulent flows, Phys. Fluids A, vol.3, issue.3, pp.446-456, 1991.

G. Riboux and D. Legendre, A model of bubble-induced turbulence based on large-scale wake interactions, J. Fluid Mech, vol.719, pp.362-387, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00946094

G. Riboux, F. Risso, and D. Legendre, Experimental characterization of the agitation generated by bubbles rising at high Reynolds number, J. Fluid Mech, vol.643, pp.509-539, 2010.

L. F. Richardson, The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam, Phil. Trans. R. Soc. Lond. A, vol.210, pp.459-470, 1911.

F. Risso, Physical interpretation of probability density functions of bubble-induced agitation, J. Fluid Mech, vol.809, pp.240-263, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01401237

F. Risso, Agitation, mixing, and transfers induced by bubbles, Annu. Rev. Fluid Mech, vol.50, pp.25-48, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01778999

F. Risso and K. Ellingsen, Velocity fluctuations in a homogeneous dilute dispersion of high-Reynolds-number rising bubbles, J. Fluid Mech, vol.453, pp.395-410, 2002.

F. Risso, V. Roig, Z. Amoura, G. Riboux, and A. M. Billet, Wake attenuation in large Reynolds number dispersed two-phase flows, Phil. Trans. R. Soc. Lond. A, vol.366, pp.2177-2190, 2008.

R. Rzehak and E. Krepper, Bubble-induced turbulence: comparison of CFD models, Nucl. Engng Des, vol.258, pp.57-65, 2013.

C. Santarelli and J. Fröhlich, Direct numerical simulations of spherical bubbles in vertical turbulent channel flow. Influence of bubble size and bidispersity, Intl J. Multiphase Flow, vol.81, pp.27-45, 2016.

C. Santarelli, J. Roussel, and J. Fröhlich, Budget analysis of the turbulent kinetic energy for bubbly flow in a vertical channel, Chem. Engng Sci, vol.141, pp.46-62, 2016.

M. E. Shawkat and C. Y. Ching, Liquid turbulence kinetic energy budget of co-current bubbly flow in a large diameter vertical pipe, J. Fluids Engng, vol.133, issue.9, p.91303, 2011.

C. G. Speziale, S. Sarkar, and T. B. Gatski, Modelling the pressure-strain correlation of turbulence: an invariant dynamical systems approach, J. Fluid Mech, vol.227, pp.245-272, 1991.

A. Tomiyama, H. Tamai, I. Zun, and S. Hosokawa, Transverse migration of single bubbles in simple shear flows, Chem. Engng Sci, vol.57, issue.11, pp.1849-1858, 2002.

A. Toutant, M. Chandesris, D. Jamet, and O. Lebaigue, Jump conditions for filtered quantities at an under-resolved discontinuous interface. Part 1: theoretical development, Intl J. Multiphase Flow, vol.35, issue.12, pp.1100-1118, 2009.

A. Toutant, M. Chandesris, D. Jamet, and O. Lebaigue, Jump conditions for filtered quantities at an under-resolved discontinuous interface. Part 2: a priori tests, Intl J. Multiphase Flow, vol.35, issue.12, pp.1119-1129, 2009.

A. Toutant, E. Labourasse, O. Lebaigue, and O. Simonin, DNS of the interaction between a deformable buoyant bubble and a spatially decaying turbulence: a priori tests for LES two-phase flow modelling, Comput. Fluids, vol.37, issue.7, pp.877-886, 2008.

A. Toutant, B. Mathieu, and O. Lebaigue, Volume-conserving mesh smoothing for fronttracking methods, Comput. Fluids, vol.67, pp.16-25, 2012.

A. A. Troshko and Y. A. Hassan, A two-equation turbulence model of turbulent bubbly flows, Intl J. Multiphase Flow, vol.27, issue.11, pp.1965-2000, 2001.

G. Tryggvason, B. Bunner, A. Esmaeeli, and N. Al-rawahi, Computations of multiphase flows, Adv. Appl. Mech, vol.39, issue.C, pp.81-120, 2003.

G. Tryggvason, S. Dabiri, B. Aboulhasanzadeh, and J. Lu, Multiscale considerations in direct numerical simulations of multiphase flows, Phys. Fluids, vol.25, p.31302, 2013.

A. Vaidheeswaran and T. Hibiki, Bubble-induced turbulence modeling for vertical bubbly flows, Intl J. Heat Mass Transfer, vol.115, pp.741-752, 2017.

A. W. Vreman and J. G. Kuerten, Comparison of direct numerical simulation databases of turbulent channel flow at Re = 180, Phys. Fluids, vol.26, issue.1, p.15102, 2014.

D. Wilcox, Turbulence modeling for CFD, 1993.

J. H. Williamson, Low-storage Runge-Kutta schemes, J. Comput. Phys, vol.35, issue.1, pp.48-56, 1980.