Exploring the beta distribution in variable-density turbulent mixing

References

• Rayleigh , Lord . 1882 . Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density . Proc. London Math. Soc. , 1–14 : 170 – 177 .
   Google Scholar
• Taylor , G. I. 1950 . The instability of liquid surfaces when accelerated in a direction perpendicular to their planes . Proc. R. Soc. Lon. Ser.-A , 201 : 192 – 196 .
   Web of Science ®Google Scholar
• Sharp , D. H. 1984 . An overview of the Rayleigh–Taylor instability . Physica D , 12 : 3 – 18 .
   Web of Science ®Google Scholar
• Fox , R. O. 2003 . Computational models for turbulent reacting flows , Cambridge, UK : Cambridge University Press .
   Google Scholar
• Pope , S. B. 1985 . PDF methods for turbulent reactive flows . Prog. Energ. Combust. , 11 : 119 – 192 .
   Web of Science ®Google Scholar
• Girimaji , S. S. 1991 . Assumed β-pdf model for turbulent mixing: Validation and extension to multiple scalar mixing . Combust. Sci. Technol. , 78 : 177 – 196 .
   Web of Science ®Google Scholar
• Eswaran , V. and Pope , S. B. 1988 . Direct numerical simulations of the turbulent mixing of a passive scalar . Phys. Fluids , 31 : 506 – 520 .
   Web of Science ®Google Scholar
• Livescu , D. and Ristorcelli , J. R. 2008 . Variable-density mixing in buoyancy-driven turbulence . J. Fluid Mech. , 605 : 145 – 180 .
   Web of Science ®Google Scholar
• Livescu , D. , Ristorcelli , J. R. , Gore , R. A. , Dean , S. H. , Cabot , W. H. and Cook , A. W. 2009 . High-Reynolds number Rayleigh–Taylor turbulence . J. Turbul. , 10 ( 13 ) : 43 – 73 .
   Google Scholar
• Ristorcelli , J. R. and Clark , T. T. 2004 . Rayleigh–Taylor turbulence: Self-similar analysis and direct numerical simulations . J. Fluid Mech. , 507 : 213 – 253 .
   Web of Science ®Google Scholar
• Livescu , D. and Ristorcelli , J. R. 2009 . “ The mixing asymmetry in variable density turbulence ” . In Advances in Turbulence XII , Edited by: Eckhardt , B. 132 New York : Springer .
   Google Scholar
• Bakosi , J. and Ristorcelli , J. R. Extending the Langevin model to variable-density pressure-gradient-driven turbulence submitted to J. Turbul., in press
   Google Scholar
• Bakosi , J. and Ristorcelli , J. R. Probability density function method for variable-density pressure-gradient-driven turbulence and mixing submitted to J. Turbul., in press
   Google Scholar
• Livescu , D. and Ristorcelli , J. R. 2007 . Buoyancy-driven variable-density turbulence . J. Fluid Mech. , 591 : 43 – 71 .
   Web of Science ®Google Scholar
• Bilger , R. W. 1989 . Turbulent diffusion flames . Annu. Rev. Fluid Mech. , 21 : 101 – 135 .
   Web of Science ®Google Scholar
• Klimenko , A. Y. and Bilger , R. W. 1999 . Conditional moment closure for turbulent combustion . Prog. Energ. Combust. , 25 : 595 – 687 .
   Web of Science ®Google Scholar
• Bilger , R. W. , Libby , P. A. and Williams , F. A. 1980 . Turbulent Reacting Flows , Berlin : Springer Verlag .
   Google Scholar
• Villermaux , J. and Devillon , J. C. Représentation de la coalescence et de la redispersion des domaines de ségrégation dans un fluide par un modéle d'interaction phénoménologique . Proceedings of the 2nd International Symposium on Chemical Reaction Engineering . pp. 1 – 13 . New York : Elsevier .
   Google Scholar
• Dopazo , C. and O'Brien , E. E. 1974 . An approach to the autoignition of a turbulent mixture . Acta Astronaut. , 1 : 1239 – 1266 .
   Web of Science ®Google Scholar
• Gardiner , C. W. 2004 . Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, , 3rd ed. Berlin, Heidelberg, New York
   Google Scholar
• Haworth , D. C. and Pope , S. B. 1986 . A generalized Langevin model for turbulent flows . Phys. Fluids , 29 : 387 – 405 .
   Web of Science ®Google Scholar
• Pope , S. B. and Chen , Y. L. 1990 . The velocity-dissipation probability density function model for turbulent flows . Phys. Fluids , 2 : 1437 – 1449 .
   Web of Science ®Google Scholar
• van Slooten, Jayesh , P. R. and Pope , S. B. 1998 . Advances in PDF modeling for inhomogeneous turbulent flows . Phys. Fluids , 10 : 246 – 265 .
   Web of Science ®Google Scholar
• Fox , R. O. 1992 . The Fokker–Planck closure for turbulent molecular mixing: Passive scalars . Phys. Fluids , 4 : 1230 – 1244 .
   Web of Science ®Google Scholar
• Fox , R. O. 1999 . The Lagrangian spectral relaxation model for differential diffusion in homogeneous turbulence . Phys. Fluids , 11 : 1550 – 1571 .
   Web of Science ®Google Scholar
• Cai , G. Q. and Lin , Y. K. 1996 . Generation of non-Gaussian stationary stochastic processes . Phys. Rev. E , 54 : 299 – 303 .
   PubMed Web of Science ®Google Scholar
• Besnard , D. , Harlow , F. H. , Rauenzahn , R. M. and Zemach , C. Turbulence transport equations for variable-density turbulence and their relationship to two-field models , Washington, DC : Los Alamos National Laboratory, NM; US DOE . Publisher: United States; 1992-06-01. Availability: E10160146; OSTI; NTIS; GPO Dep. Repository ID: info:lanl-repo/ecd/10160146
   Google Scholar
• Lele , S. K. 1994 . Compressibility effects on turbulence . Annu. Rev. Fluid Mech. , 26 : 211 – 254 .
   Web of Science ®Google Scholar