On the inverse parabolicity of PDF equations in turbulent flows

Quarterly Journal of Mechanics and Applied Mathematics

Volumn 57, Issue 1, 2004, Pages 79-93

  Klimenko, A Y ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION; FLUID MECHANICS; INVERSE PROBLEMS; MARKOV PROCESSES; TURBULENT FLOW; VELOCITY;

CONDITIONAL MOMENT CLOSURE; INVERSE PARABOLICITY; MARKOV DIFFUSION PROCESS; REVERSED-TIME DIFFUSION;

PROBABILITY DENSITY FUNCTION;

EID: 2342570293     PISSN: 00335614     EISSN: None     Source Type: Journal    
DOI: 10.1093/qjmam/57.1.79     Document Type: Article

References (24)

1. S. B. Pope, Pdf methods for turbulent reactive flows, Prog. Energy Combust. Sci. 11 (1985) 119-192.
2. V. R. Kuznetsov and V. A. Sabelnikov, Turbulence and Combustion (Hemisphere, New York 1989).
3. C. Dopazo, Recent developments in pdf methods, Turbulent Reacting Flows (ed. P. A. Libby and F. A. Williams: Academic Press, London 1994) 375-474.
4. A. Y. Klimenko and R. W. Bilger, Conditional moment closure for turbulent combustion, Prog. Energy Combust. Sci. 25 (1999) 595-687.
5. S. B. Pope, Turbulent Flows (Cambridge University Press, Cambridge 2000).
6. P. C. Chatwin, Some remarks on modelling the pdf of the concentration of a dispersing scalar in turbulence, Euro. J. Appl. Math. 13 (2002) 95-108.
7. A. Einstein, On the theory of Brownian motion, Ann. Phys. Leipzig 19 (1906) 371-381.
8. H. Risken, The Fokker-Planck Equation (Springer, Berlin 1989).
9. G. I. Taylor, Diffusion by continuous movements, Proc. London Math. Soc. (2) 20 (1921) 1920-1922.
10. B. D. O. Anderson, Reverse-time diffusion equation models, Stochastic Processes and their Application 12 (1982) 313-326.
11. A. N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, C.R. Acad. Sci. U.S.S.R. 4 (1941) 301-305.
12. L. F. Richardson, Atmospheric diffusion shown on a distance-neighbour graph, Proc. R. Soc. (1926) 709-737.
13. T. D. Dreeben and S. B. Pope, Probability density function and Reynolds-stress modeling of near-wall turbulent flows, Phys. Fluids 9 (1997) 154-163.
14. R. W. Bilger, Turbulent flows with nonpremixed reactants, In Turbulent Reacting Flows (ed. P. A. Libby and F. A. Williams: Springer, Berlin 1980).
15. A. Y. Klimenko, Conditional methods in application for Lagrangian modelling, Phys. Fluids 10 (1998) 922-927.
16. 1 by DMS of a continuous scalar, ibid. 11 (2000) 3205-3220.
17. E. Krasnoff and R. L. Peskin, The Langevin model for turbulent diffusion, Geophys. Fluid Dyn. 2 (1971) 123.
18. P. K. Yeung and S. B. Pope, Lagrangian statistics from direct numerical simulations of isotropic turbulence, J. Fluid Mech. 207 (1989) 531-586.
19. B. L. Sawford, Reynolds number effects in Lagrangian statistical models of turbulent dispersion, Phys. Fluids A 3 (1991) 1577.
20. A. Y. Klimenko, Note on conditional moment closure in turbulent shear flows, ibid. 7 (1995) 446.
21. N. Peters, Turbulent Combustion (Cambridge University Press, Cambridge 2000).
22. A. Y. Klimenko, On the relation between the conditional moment closure and unsteady flamelets, Combust. Theory Modelling 5 (2001) 275-294.
23. A. Y. Klimenko, Conditional moment closure and fluctuations of scalar dissipation. Fluid Dynamics 28 (1993) 630-637.
24. A. P. Wandel, N. S. A. Smith and A. Y. Klimenko, Verification of Markov hypothesis for conserved scalar process: validation of conditional moment closure for turbulent combustion, Anziam J. (E) 44 (2003) C802-C819.