Duarte, Max, Massot, Marc, Descombes, Stéphane, Tenaud, Christian, Candel, Sebastien, Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion (EM2C), Université Paris Saclay (COmUE)-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec, Center for Turbulence Research [Stanford] (CTR), Stanford University, Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (LIMSI), Université Paris Saclay (COmUE)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université - UFR d'Ingénierie (UFR 919), Sorbonne Université (SU)-Sorbonne Université (SU)-Université Paris-Saclay-Université Paris-Sud - Paris 11 (UP11), and The authors wish to thank Parviz Moin and the Center for Turbulence Research at Stanford University for their hospitality and financial support. Support from the RTRA DIGITEO (Project MUSE, PI M. Massot) and Ecole Centrale Paris fellowship for M. Duarte are gratefully acknowledged. This research was supported by a fundamental project grant from ANR (French National Research Agency - ANR Blancs): Séchelles} (project leader S. Descombes). The support of a Ph.D. grant from Mathematics (INSMI) and Engineering (INSIS) Institutes of CNRS is gratefully acknowledged ad well as the the support by INCA project (National Initiative for Advanced Combustion - CNRS - ONERA - SAFRAN).