R. Adoua, D. Legendre, and J. Magnaudet, Reversal of the lift force on an oblate bubble in a weakly viscous linear shear flow, J. Fluid Mech, vol.628, pp.23-41, 2009.

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

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.

G. K. Batchelor, Sedimentation in a dilute dispersion of spheres, J. Fluid Mech, vol.52, pp.245-272, 1972.

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. M. Martinez, DNS of turbulent bubbly flows in plane channels using the Front-Tracking algorithm of TrioCFD, In Fluids Eng. Div. Summer Meet. Multiph. Flow Tech. Comm. ASME, 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, 9th International Conference on Multiphase Flow. ICMF, 2016.

B. Bunner and G. Tryggvason, Dynamics of homogeneous bubbly flows. Part 1. Rise velocity and microstructure of the bubbles, J. Fluid Mech, vol.466, pp.17-52, 2002.

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, A. D'hueppe, B. Mathieu, D. Jamet, and B. Goyeau, Direct numerical simulation of turbulent heat transfer in a fluid-porous domain, Phys. Fluids, vol.25, p.125110, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00929817

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. Chandesris and D. Jamet, Derivation of jump conditions for the turbulence k-epsilon model at a fluid/porous interface, Intl J. Heat Fluid Flow, vol.30, pp.306-318, 2009.

A. Du-cluzeau, G. Bois, and A. Toutant, Analysis and modeling of Reynolds stresses in turbulent bubbly up-flows from direct numerical simulations, J. Fluid Mech, vol.866, pp.132-168, 2019.

S. Dabiri, J. Lu, and G. Tryggvason, Transition between regimes of a vertical channel bubbly upflow due to bubble deformability, Phys. Fluids, vol.25, p.102110, 2017.

J. M. Delhaye, D. A. Drew, and S. L. Passman, Thermohydraulique des réacteurs, Theory of Multicomponent Fluids, 1999.

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

R. Gatignol, The faxen formulae for a rigid particle in an unsteady non-uniform Stokes flow, J. Méc. Théor. Appl, vol.2, issue.2, pp.143-160, 1983.

J. A. Geurst, Virtual mass in two-phase bubbly flow, Phys. A Stat. Mech. Appl, vol.129, issue.2, pp.233-261, 1985.

J. A. Geurst, Variational principles and two-fluid hydrodynamics of bubbly liquid/gas mixtures, Phys. A Stat. Mech. Appl, vol.135, issue.2-3, pp.455-486, 1986.

M. Ishii and T. Hibiki, Thermo-Fluid Dynamics of Two-Phase Flow, 2006.

M. Ishii and N. Zuber, Drag coefficient and relative velocity in bubbly, droplet or particulate flows, AIChE J, vol.25, issue.5, pp.843-855, 1979.

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.

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.

D. Legendre, J. Borée, and J. Magnaudet, Thermal and dynamic evolution of a spherical bubble moving steadily in a superheated or subcooled liquid, Phys. Fluids, vol.10, pp.1256-1272, 1998.

D. Legendre and J. Magnaudet, The lift force on a spherical bubble in a viscous linear shear flow, J. Fluid Mech, vol.368, pp.81-126, 1998.

D. Lhuillier, C. Morel, and J. M. Delhaye, Bilan d'aire interfaciale dans un mélange diphasique: approche locale versus approche particulaire, Académie des Sci, vol.4620, issue.00, pp.143-149, 2000.

. 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 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.

J. Magnaudet and I. Eames, The motion of high-Reynolds-number bubbles in inhomogeneous flows, Annu. Rev. Fluid Mech, vol.32, pp.659-708, 2002.

J. Magnaudet, J. Fabre, and M. Rivero, Accelerated flows past a rigid sphere or a spherical bubble. Part 1. Steady straining flow, J. Fluid Mech, vol.284, pp.97-135, 1995.

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

D. W. Moore, The velocity of rise of distorted gas bubbles in a liquid of small viscosity, J. Fluid Mech, vol.23, pp.749-766, 1965.

F. J. Moraga, A. E. Larreteguy, D. A. Drew, and R. T. Lahey, A center-averaged two-fluid model for wall-bounded bubbly flows, Comput. Fluids, vol.35, issue.4, pp.429-461, 2006.

C. Pauchon and S. Banerjee, Interphase momentum interaction effects in the averaged multifield model. Part I. Void propagation in bubbly flows, Intl J. Multiphase Flow, vol.12, issue.4, pp.559-573, 1986.

A. Prosperetti and A. V. Jones, Pressure forces in disperse two-phase flow, Intl J. Multiphase Flow, vol.10, issue.4, pp.425-440, 1984.

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

G. Riboux, D. Legendre, and F. Risso, 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

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

O. Simonin, Statistical and continuum modelling of turbulent reactive particulate flows. Part I. Theoretical derivation of dispersed phase Eulerian modelling from probability density function kinetic equation, Lect. Ser. Kareman Inst. Fluid Dyn, vol.6, pp.1-42, 2000.

P. Smereka, On the motion of bubbles in a periodic box, J. Fluid Mech, vol.254, pp.79-112, 1993.

J. H. Stuhmiller, The influence of interfacial pressure forces on the character of two-phase flow model equations, Intl J. Multiphase Flow, vol.3, issue.6, pp.551-560, 1977.

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, Modélisation physique des interactions entre interfaces et turbulence, 2006.

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.

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, . De, and M. L. Bertodano, Interfacial pressure coefficient for ellipsoids and its effect on the two-fluid model eigenvalues, Trans. ASME J. Fluids Engng, vol.138, issue.8, p.81302, 2016.

G. Wallis, Two Phase Flow in Waves, 1990.

L. V. Wijngaarden and C. Kapteyn, Concentration waves in dilute bubble/liquid mixtures, J. Fluid Mech, vol.212, pp.111-137, 1990.

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