, Grant2019-2613) are also gratefully acknowledged. The authors also acknowledge funding by the UK's Engineering and Physical Science, CINES/IDRIS

C. Aalburg, B. Van-leer, G. M. Faeth, and K. A. Sallam, Properties of nonturbulent round liquid jets in uniform gaseous cross ows, Atomization and Sprays, vol.15, p.271294, 2005.

C. Ng, R. Sankarakrishnan, and K. A. Sallam, Bag breakup of nonturbulent liquid jets in crossow, International Journal of Multiphase Flow, vol.34, p.241259, 2008.

C. T. Brown and V. G. Mcdonell, Proceedings of the ILASS Americas, 19th Annual Conference on Liquid Atomization and Spray Systems, 2006.

R. K. Madabhushi, M. A. Leong, C. T. Brown, and V. G. Mcdonell, Proceedings of the ILASS Americas, 19th Annual Conference on Liquid Atomization and Spray Systems, 2006.

P. K. Wu, K. A. Kirkendall, R. O. Fuler, and A. S. Nejad, Breakup processes of liquid jets in subsonic crossows, Journal of Propulsion and Power, vol.13, p.6473, 1997.

J. N. Stenzler, J. G. Lee, D. A. Santavicca, and W. Lee, Penetration of liquid jets in a cross-ow, Atomization and Sprays, vol.16, p.887906, 2006.

S. B. Leask, V. G. Mcdonell, and S. Samuelsen, Critical evaluation of momentum ux ratio relative to a liquid jet in crossow, Atomization and Sprays, vol.28, p.599620, 2018.

M. Broumand and M. Birouk, Liquid jet in a subsonic gaseous crossow: Recent progress and remaining challenges, Progress in Energy and Combustion Science, vol.57, p.129, 2016.

M. Herrmann, Detailed numerical simulations of the primary atomization of a turbulent liquid jet in crossow, Journal of Engineering for Gas Turbines and Power, vol.132, p.061506106150610, 2010.

M. Herrmann, The inuence of density ratio on the primary atomization of a turbulent liquid jet in crossow, Proceedings of the Combustion Institute, vol.33, p.20792088, 2011.

M. Herrmann, M. Arienti, and M. C. Soteriou, The impact of density ratio on the liquid core dynamics of a turbulent liquid jet injected into a crossow, Journal of Engineering for Gas Turbines and Power, vol.133, p.61501, 2011.

S. Ghods and M. Herrmann, Proceedings of the ILASS Americas, p.25

, Annual Conference on Liquid Atomization and Spray Systems, 2013.

M. Owkes, M. G. Pai, and O. Desjardins, Proceedings of the AIAA SciTech Forum, 2014.

Y. Gopala, Breakup characteristics of a liquid jet in subsonic crossow, 2012.

X. Li and M. C. Soteriou, High delity simulation and analysis of liquid jet atomization in a gaseous crossow at intermediate weber numbers, Physics of Fluids, vol.28, p.082101108210135, 2016.

X. Li and M. C. Soteriou, Detailed numerical simulation of liquid jet atomization in crossow of increasing density, International Journal of Multiphase Flow, vol.104, p.214232, 2018.

A. Mukundan, T. Ménard, A. Berlemont, J. C. Brändle-de-motta, and M. Herrmann, Proceedings of the ILASS Americas, 30th Annual Conference on Liquid Atomization and Spray Systems, 2019.

A. Mukundan, T. Ménard, M. Herrmann, J. C. Brändle-de-motta, and A. Berlemont, Proceedings of the AIAA SciTech Forum, 2020.

T. Ménard, S. Tanguy, and A. Berlemont, Coupling level set/VOF/ghost uid methods: Validation and application to 3D simulation of the primary break-up of a liquid jet, International Journal of Multiphase Flow, vol.33, p.510524, 2007.

S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, p.1249, 1988.

G. D. Weymouth, D. K. , and .. Yue, Conservative Volume-of-Fluid method for free-surface simulations on Cartesian-grids, Journal of Computational Physics, vol.229, p.28532865, 2010.

G. Vaudor, T. Ménard, W. Aniszewski, M. Doring, and A. Berlemont, A consistent mass and momentum ux computation method for two phase ows. Application to atomization process, Computers & Fluids, vol.152, p.204216, 2017.

A. Mukundan, T. Ménard, J. C. Brändle-de-motta, and A. Berlemont, A 3D Moment of Fluid method for simulating complex turbulent multiphase ows, Computers & Fluids, vol.198, 2020.

S. Navarro-martinez, Large eddy simulation of spray atomization with a probability density function method, International Journal of Multiphase Flow, vol.63, p.1122, 2014.

L. Valiño, A eld monte carlo formulation for calculating the probability density function of a single scalar in a turbulent ow, Flow, turbulence and combustion, vol.60, p.157172, 1998.

R. Lebas, T. Ménard, P. A. Beau, A. Berlemont, and F. X. Demoulin, Numerical simulation of primary break-up and atomization: Dns and modelling study, International Journal of Multiphase Flow, vol.35, p.247260, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00649748

B. Duret, J. Réveillon, T. Ménard, and F. X. Demoulin, Improving primary atomization modeling through DNS of two-phase ows, International Journal of Multiphase Flow, vol.55, p.130137, 2013.

H. Jasak, A. Jemcov, and Z. Tukovic, International workshop on coupled methods in numerical dynamics, vol.1000, p.120

F. Nicoud and F. Ducros, Subgrid-scale stress modelling based on the square of the velocity gradient tensor, Flow, turbulence and Combustion, vol.62, p.183200, 1999.

H. G. Weller, A new approach to VOF-based interface capturing methods for incompressible and compressible ow, 2008.

P. E. Kloeden and E. Platen, Numerical solution of stochastic dierential equations, vol.23, 2013.

C. W. Gardiner, Handbook of stochastic methods, vol.3, 1985.

A. Andreini, C. Bianchini, S. Puggelli, and F. Demoulin, Development of a turbulent liquid ux model for EulerianEulerian multiphase ow simulations, International Journal of Multiphase Flow, vol.81, p.88103, 2016.

S. Puggelli, L. Mazzei, and A. Andreini, Proceedings of the 1st Global Power and Propulsion Forum GPPF, p.19, 2017.

M. Behzad, A. Mashayek, and N. Ashgriz, Proceedings of the ILASS Americas, 22nd Annual Conference on Liquid Atomization and Spray Systems, pp.2010-112