Conditional mode elimination and scale-invariant dissipation in isotropic turbulence

Physica A: Statistical Mechanics and its Applications

Volumn 292, Issue 1-4, 2001, Pages 346-382

  McComb, W D ^a   Johnston, C ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL FLUID DYNAMICS; ENERGY DISSIPATION; EQUATIONS OF MOTION; MARKOV PROCESSES; REYNOLDS NUMBER; SHEAR FLOW;

CONDITIONAL MODE ELIMINATION; ISOTROPIC TURBULENCE; SCALE-INVARIANT DISSIPATION;

TURBULENCE;

EID: 0035280489     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(00)00551-3     Document Type: Article

References (48)

1. R.H. Kraichnan, The structure of Isotropic turbulence at very high Reynolds numbers, J. Fluid Mech. 5 (1959) 497.
2. S.F. Edwards, The statistical dynamics of homogeneous turbulence, J. Fluid Mech. 18 (1964) 18.
3. S.F. Edwards, Turbulence in hydrodynamics and plasma physics, Proceedings of the International Conference on Plasma Physics, Trieste, IAEA, Vienna, 1965, p. 595.
4. J.R. Herring, Self-consistent field approach to turbulence theory, Phys. Fluids 8 (1965) 2219.
5. J.R. Herring, Self-consistent field approach to nonstationary turbulence, Phys. Fluids 9 (1966) 2106.
6. D.C. Leslie, Developments in the Theory of Modern Turbulence, Clarendon Press, Oxford, 1973.
7. W.D. McComb, The Physics of Fluid Turbulence, Oxford University Press, Oxford, 1990.
8. W.D. McComb, Theory of turbulence, Rep. Prog. Phys. 58 (1995) 1117-1206.
9. W.D. McComb, Reformulation of the statistical equations for turbulent shear flow, Phys. Rev. A 26 (2) (1982) 1078-1094.
10. W.D. McComb, V. Shanmugasundaram, Fluid turbulence and the renormalization group: a preliminary calculation of the eddy viscosity, Phys. Rev. A 28 (1983) 2588.
11. W.D. McComb, Application of renormalization group methods to the subgrid modelling problem, in: U. Schumann, R. Friedrich (Eds.), Direct and Large Eddy Simulation of Turbulence, Vieweg, Braunschweig, 1986, pp. 67-81.
12. W.D. McComb, A.G. Watt, Conditional averaging procedure for the elimination of the small-scale modes from incompressible fluid turbulence at high Reynolds numbers, Phys. Rev. Lett. 65 (26) (1990) 3281-3284.
13. W.D. McComb, W. Roberts, A.G. Watt, Conditional-averaging procedure for problems with mode-mode coupling, Phys. Rev. A 45 (6) (1992) 3507-3515.
14. W.D. McComb, A.G. Watt, Two-field theory of incompressible-fluid turbulence, Phys. Rev. A 46 (8) (1992) 4797-4812.
15. W.D. McComb, C. Johnston, Elimination of turblence modes using a conditional average with asymptotic freedom, J. Phys. A 33 (2000) L15-L20.
16. C. Johnston, W.D. McComb, A renormalized expression for the turbulent energy dissipation rate, Phys. Rev. E, to be published.
17. G.K. Batchelor, The Theory of Homogeneous Turbulence, 2nd Edition, Cambridge University Press, Cambridge, 1971.
18. L.F. Richardson, Weather Prediction by Numerical Process, Cambridge University Press, Cambridge, 1963.
19. A.N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, C. R. Acad. Sci. URSS 30 (1941) 301.
20. A.N. Kolmogorov, Dissipation of energy in locally isotropic turbulence, C. R. Acad. Sei. URSS 32 (1941) 16.
21. K.R. Sreenivasan, On the universality of the Kolmogorov constant, Phys. Fluids 7 (1995) 2778.
22. P.K. Yeung, Y. Zhou, Universality of the Kolmogorov constant in numerical simulations of turbulence, Phys. Rev. E 56 (1997) 1746.
23. A.J. Young, Investigation of renormalization group methods for the numerical simulation of isotropic turbulence, Ph.D. Thesis, University of Edinburgh, 1999.
24. Y.-H. Pao, Structure of turbulent velocity and scalar fields at large wavenumbers, Phys. Fluids 8 (1965) 1063.
25. T. Dubois, F. Jauberteau, Y. Zhou, Influences of subgrid scale dynamics on resolvable scale statistics in large-eddy simulations, Physica D 100 (1997) 390.
26. J. Smagorinsky, General circulation experiments with the primitive equations, Mon. Weather Rev. 91 (1963) 99.
27. A. Leonard, Energy cascade in Large-Eddy simulations of turbulent fluid flows, Adv. Geophys. 18 (1974) 237.
28. C. Meneveau, J. Katz, Scale-invariance and turbulence models for large-eddy simulation, Ann. Rev. Fluid Mech. 32 (2000) 1.
29. D.C. Leslie, G.L. Quarini, The application of turbulence theory to the formulation of subgrid modelling procedures, J. Fluid Mech. 91 (1979) 65.
30. P.J. Mason, D.J. Thomson, Stochastic backscatter in large-eddy simulations of boundary layers, J. Fluid Mech. 242 (1992) 51.
31. R.J. Adrian, On the role of conditional averages in turbulence theory, in: J. Zakin, G. Patterson (Eds.), Turbulence in Liquids, Science Press, Princeton, 1999, p. 323.
32. R.J. Adrian, Stochastic estimation of subgrid motions, Appl. Mech. Rev. 43 (1990) S214.
33. G. Berkooz, An observation on probability density equations, Nonlinearity 7 (1994) 313.
34. J.A. Langsford, R.D. Moser, Optimal LES formulation for isotropic turbulence, J. Fluid Mech. 398 (1999) 321.
35. G.L. Eyink, The renormalization group method in statistical hydrodynamics, Phys. Fluids 6 (9) (1994) 3063-3078.
36. D. Forster, D.R. Nelson, M.J. Stephen, Long-time tails and the large-eddy behaviour of a randomly stirred fluid, Phys. Rev. Lett. 36 (15) (1976) 867-869.
37. D. Forster, D.R. Nelson, M.J. Stephen, Large-distance and long-time properties of a randomly stirred fluid, Phys. Rev. A 16 (2) (1997) 732-749.
38. R.H. Kraichnan, Decimated amplitude equations in turbulence dynamics, in: M.Y. Hussaini, D.L. Dwoyer, R.G. Voigt (Eds.), Theoretical Approaches to Turbulence, Springer, Berlin, 1985, pp. 91-135.
39. E.A. Novikov, Statistical balance of vorticity and a new scale for vortical structures in turbulence, Phys. Rev. Lett. 71 (1993) 2718.
40. F. Jauberteau, T. Dubois, R. Temam, Dynamic Multilevel Methods and the Numerical Simulation of Turbulence, Cambridge University Press, Cambridge, 1999.
41. L. Machiels, Predictability of small-scale motion in isotropic fluid turbulence, Phys. Rev. Lett. 79 (18) (1997) 3411-3414.
42. A. Papoulis, Probability, Random Variables and Stochastic Processes, McGraw-Hill, New York, 1991.
43. E.V. Teodorovich, Use of the renormalization-group method to describe intermittency and to derive the corrections to the exponents in the Kolmogorov turbulence theory, Sov. Phys. JETP 73 (3) (1992) 472-478.
44. M. le Bellac, Quantum and Statistica Field Theory, Clarendon Press, Oxford, 1991.
45. A.G. Watt, A Study of Isotropie Turbulence, Ph.D. Thesis, University of Edinburgh, 1991.
46. R.S. Rogallo, J.A. Domeradski, R.W. Metcalfe, J.J. Riley, Analysis of subgrid-scale eddy viscosity with the use of results from direct numerical simulations, Phys. Rev. Lett. 58 (1987) 547.
47. M. Van Dyke, Perturbation Methods in Fluid Mechanics, Parabolic Press, Stanford, CA, 1975.
48. E. Kreyszig, Advanced Engineering Mathematics, Wiley, New York, 1988.