Scaling behaviour in a hyper-viscous Navier-Stokes equation with random initial conditions

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 231, Issue 3-4, 1997, Pages 235-239

  Periwal, Vipul ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

VISCOUS FLOW;

FIXED POINTS; INCOMPRESSIBLE FLUID; INFINITE NUMBERS; INITIAL CONDITIONS; RANDOM INITIAL CONDITIONS; SCALING BEHAVIOURS; STABLE FIXED POINTS; VISCOUS FORCES;

NAVIER STOKES EQUATIONS;

EID: 0040567470     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0375-9601(97)00279-X     Document Type: Article

References (50)

1. G. Gallavotti, chao-dyn/9505013, and references therein.
2. D.J. Tritton, Physical fluid dynamics (Van Nostrand Reinhold, Cambridge, 1977).
3. A.N. Kolmogorov, C.R. Acad. Sci. USSR 30 (1941) 301; L.F. Richardson, Weather prediction by numerical process (Cambridge Univ. Press, Cambridge, 1922).
4. A.N. Kolmogorov, C.R. Acad. Sci. USSR 30 (1941) 301; L.F. Richardson, Weather prediction by numerical process (Cambridge Univ. Press, Cambridge, 1922).
5. E. Leveque and Z.-S. Shen, Phys. Rev. Lett. 72 (1994) 336.
6. N. Schörghofer, L.P. Kadanoff and D. Lohse, chao-dyn/9502014, Physica D, in press; G.I. Barenblatt and N. Goldenfeld, cond-mat/9507132.
7. N. Schörghofer, L.P. Kadanoff and D. Lohse, chao-dyn/9502014, Physica D, in press; G.I. Barenblatt and N. Goldenfeld, cond-mat/9507132.
8. M. Nelkin, Phys. Rev. A 9 (1974) 388; P.G. de Gennes, in: Fluctuation, instability and phase transitions, Series B, Proc. NATO Adv. Study Inst., Geilo, Norway, ed. T. Riste (Noordhoff, Leiden, 1975) p. 1; H.A. Rose and P.L. Sulem, J. de Phys. 39 (1978) 441.
9. M. Nelkin, Phys. Rev. A 9 (1974) 388; P.G. de Gennes, in: Fluctuation, instability and phase transitions, Series B, Proc. NATO Adv. Study Inst., Geilo, Norway, ed. T. Riste (Noordhoff, Leiden, 1975) p. 1; H.A. Rose and P.L. Sulem, J. de Phys. 39 (1978) 441.
10. M. Nelkin, Phys. Rev. A 9 (1974) 388; P.G. de Gennes, in: Fluctuation, instability and phase transitions, Series B, Proc. NATO Adv. Study Inst., Geilo, Norway, ed. T. Riste (Noordhoff, Leiden, 1975) p. 1; H.A. Rose and P.L. Sulem, J. de Phys. 39 (1978) 441.
11. G. Eyink, Phys. Rev. E 48 (1993) 1823.
12. G. Eyink and N. Goldenfeld, Phys. Rev. E 50 (1994) 4679; M. Nelkin, Adv. Phys. 43 (1994) 143.
13. G. Eyink and N. Goldenfeld, Phys. Rev. E 50 (1994) 4679; M. Nelkin, Adv. Phys. 43 (1994) 143.
14. R.H. Kraichnan, J. Fluid Mech. 5 (1959) 497; H.W. Wyld, Ann. Phys. 14 (1961) 143; R.H. Kraichnan, Phys. Fluids 8 (1965) 575; 9 (1966) 1728.
15. R.H. Kraichnan, J. Fluid Mech. 5 (1959) 497; H.W. Wyld, Ann. Phys. 14 (1961) 143; R.H. Kraichnan, Phys. Fluids 8 (1965) 575; 9 (1966) 1728.
16. R.H. Kraichnan, J. Fluid Mech. 5 (1959) 497; H.W. Wyld, Ann. Phys. 14 (1961) 143; R.H. Kraichnan, Phys. Fluids 8 (1965) 575; 9 (1966) 1728.
17. R.H. Kraichnan, J. Fluid Mech. 5 (1959) 497; H.W. Wyld, Ann. Phys. 14 (1961) 143; R.H. Kraichnan, Phys. Fluids 8 (1965) 575; 9 (1966) 1728.
18. D. Forster, D.R. Nelson and M.J. Stephen, Phys. Rev. A 16 (1977) 732; S. Grossmann and E. Schnedler, Z. Phys. B 26 (1977) 307; P.C. Martin and C. de Dominicis, Prog. Theor. Phys. Suppl. 64 (1978) 108; C. de Dominicis and P.C. Martin, Phys. Rev. A 19 (1979) 419; V. Yakhot and S.A. Orszag, J. Sci. Comp. 1 (1986) 3; S.F. Edwards, J. Fluid Mech. 18 (1964) 239
19. D. Forster, D.R. Nelson and M.J. Stephen, Phys. Rev. A 16 (1977) 732; S. Grossmann and E. Schnedler, Z. Phys. B 26 (1977) 307; P.C. Martin and C. de Dominicis, Prog. Theor. Phys. Suppl. 64 (1978) 108; C. de Dominicis and P.C. Martin, Phys. Rev. A 19 (1979) 419; V. Yakhot and S.A. Orszag, J. Sci. Comp. 1 (1986) 3; S.F. Edwards, J. Fluid Mech. 18 (1964) 239
20. D. Forster, D.R. Nelson and M.J. Stephen, Phys. Rev. A 16 (1977) 732; S. Grossmann and E. Schnedler, Z. Phys. B 26 (1977) 307; P.C. Martin and C. de Dominicis, Prog. Theor. Phys. Suppl. 64 (1978) 108; C. de Dominicis and P.C. Martin, Phys. Rev. A 19 (1979) 419; V. Yakhot and S.A. Orszag, J. Sci. Comp. 1 (1986) 3; S.F. Edwards, J. Fluid Mech. 18 (1964) 239
21. D. Forster, D.R. Nelson and M.J. Stephen, Phys. Rev. A 16 (1977) 732; S. Grossmann and E. Schnedler, Z. Phys. B 26 (1977) 307; P.C. Martin and C. de Dominicis, Prog. Theor. Phys. Suppl. 64 (1978) 108; C. de Dominicis and P.C. Martin, Phys. Rev. A 19 (1979) 419; V. Yakhot and S.A. Orszag, J. Sci. Comp. 1 (1986) 3; S.F. Edwards, J. Fluid Mech. 18 (1964) 239
22. D. Forster, D.R. Nelson and M.J. Stephen, Phys. Rev. A 16 (1977) 732; S. Grossmann and E. Schnedler, Z. Phys. B 26 (1977) 307; P.C. Martin and C. de Dominicis, Prog. Theor. Phys. Suppl. 64 (1978) 108; C. de Dominicis and P.C. Martin, Phys. Rev. A 19 (1979) 419; V. Yakhot and S.A. Orszag, J. Sci. Comp. 1 (1986) 3; S.F. Edwards, J. Fluid Mech. 18 (1964) 239
23. D. Forster, D.R. Nelson and M.J. Stephen, Phys. Rev. A 16 (1977) 732; S. Grossmann and E. Schnedler, Z. Phys. B 26 (1977) 307; P.C. Martin and C. de Dominicis, Prog. Theor. Phys. Suppl. 64 (1978) 108; C. de Dominicis and P.C. Martin, Phys. Rev. A 19 (1979) 419; V. Yakhot and S.A. Orszag, J. Sci. Comp. 1 (1986) 3; S.F. Edwards, J. Fluid Mech. 18 (1964) 239
24. V.S. L'vov and I. Procaccia, chao-dyn/9502010.
25. A.S. Monin and A.M. Yaglom, in: Statistical fluid mechanics: mechanics of turbulence, ed. J.L. Lumley (MIT Press, Cambridge, MA, 1975); W.D. McComb, The physics of fluid turbulence (Clarendon, Oxford, 1990).
26. A.S. Monin and A.M. Yaglom, in: Statistical fluid mechanics: mechanics of turbulence, ed. J.L. Lumley (MIT Press, Cambridge, MA, 1975); W.D. McComb, The physics of fluid turbulence (Clarendon, Oxford, 1990).
27. D. Ronis, Phys. Rev. A 36 (1987) 3322; 38 (1988) 874; J.-Y. Yuan and D. Ronis, Phys. Rev. A 45 (1992) 5578.
28. D. Ronis, Phys. Rev. A 36 (1987) 3322; 38 (1988) 874; J.-Y. Yuan and D. Ronis, Phys. Rev. A 45 (1992) 5578.
29. D. Ronis, Phys. Rev. A 36 (1987) 3322; 38 (1988) 874; J.-Y. Yuan and D. Ronis, Phys. Rev. A 45 (1992) 5578.
30. V. Gurarie, Nucl. Phys. B 441 (1995) 569; hep-th/9501021; V.S. L'vov and I. Procaccia, chao-dyn/9507005, 9507006, 9507007, 9507008; V.S. L'vov, E. Podivilov and I. Procaccia, chao-dyn/9601001; A.M. Polyakov, Turbulence without pressure, Princeton report PUPT-1546 (1995); G.L. Eyink, chao-dyn/9602018, 9602019.
31. V. Gurarie, Nucl. Phys. B 441 (1995) 569; hep-th/9501021; V.S. L'vov and I. Procaccia, chao-dyn/9507005, 9507006, 9507007, 9507008; V.S. L'vov, E. Podivilov and I. Procaccia, chao-dyn/9601001; A.M. Polyakov, Turbulence without pressure, Princeton report PUPT-1546 (1995); G.L. Eyink, chao-dyn/9602018, 9602019.
32. V. Gurarie, Nucl. Phys. B 441 (1995) 569; hep-th/9501021; V.S. L'vov and I. Procaccia, chao-dyn/9507005, 9507006, 9507007, 9507008; V.S. L'vov, E. Podivilov and I. Procaccia, chao-dyn/9601001; A.M. Polyakov, Turbulence without pressure, Princeton report PUPT-1546 (1995); G.L. Eyink, chao-dyn/9602018, 9602019.
33. V. Gurarie, Nucl. Phys. B 441 (1995) 569; hep-th/9501021; V.S. L'vov and I. Procaccia, chao-dyn/9507005, 9507006, 9507007, 9507008; V.S. L'vov, E. Podivilov and I. Procaccia, chao-dyn/9601001; A.M. Polyakov, Turbulence without pressure, Princeton report PUPT-1546 (1995); G.L. Eyink, chao-dyn/9602018, 9602019.
34. V. Gurarie, Nucl. Phys. B 441 (1995) 569; hep-th/9501021; V.S. L'vov and I. Procaccia, chao-dyn/9507005, 9507006, 9507007, 9507008; V.S. L'vov, E. Podivilov and I. Procaccia, chao-dyn/9601001; A.M. Polyakov, Turbulence without pressure, Princeton report PUPT-1546 (1995); G.L. Eyink, chao-dyn/9602018, 9602019.
35. W. Liao, J. Phys. A 22 (1989) L737; J. Stat. Phys. 65 (1991) 1.
36. W. Liao, J. Phys. A 22 (1989) L737; J. Stat. Phys. 65 (1991) 1.
37. J.L. Cardy, J. Phys. A 25 (1992) 2765.
38. P.C. Martin, E.D. Siggia and H.A. Rose, Phys. Rev. A 8 (1973) 423; R. Bausch, H.K. Janssen and H. Wagner, Z. Phys. B 24 (1976) 113.
39. P.C. Martin, E.D. Siggia and H.A. Rose, Phys. Rev. A 8 (1973) 423; R. Bausch, H.K. Janssen and H. Wagner, Z. Phys. B 24 (1976) 113.
40. E. Brézin, J.C. Le Guillou and J. Zinn-Justin, in: Phase transitions and critical phenomena, eds. C. Domb and M.S. Green (Academic Press, London, 1976); N. Goldenfeld, Lectures on phase transitions and the renormalization group (Addison-Wesley, Reading, MA, 1992).
41. E. Brézin, J.C. Le Guillou and J. Zinn-Justin, in: Phase transitions and critical phenomena, eds. C. Domb and M.S. Green (Academic Press, London, 1976); N. Goldenfeld, Lectures on phase transitions and the renormalization group (Addison-Wesley, Reading, MA, 1992).
42. J. Zinn-Justin, Quantum field theory and critical phenomena, 2nd Ed. (Oxford Univ. Press, Oxford, 1993).
43. A.M. Obukhov, Atmos. Oceanic Phys. 7 (1971) 41; E.D. Siggia, Phys. Rev. A 17 (1977) 1166.
44. A.M. Obukhov, Atmos. Oceanic Phys. 7 (1971) 41; E.D. Siggia, Phys. Rev. A 17 (1977) 1166.
45. R.H. Kraichnan, Phys. Rev. Lett. 31 (1973) 744.
46. A.L. Grant, A.W. Stuart, and A. Moilliet, J. Fluid Mech. 12 (1962) 241; A.M. Obukhov, J. Fluid Mech. 13 (1962) 77; A.N. Kolmogorov, J. Fluid Mech. 13 (1962) 82.
47. A.L. Grant, A.W. Stuart, and A. Moilliet, J. Fluid Mech. 12 (1962) 241; A.M. Obukhov, J. Fluid Mech. 13 (1962) 77; A.N. Kolmogorov, J. Fluid Mech. 13 (1962) 82.
48. A.L. Grant, A.W. Stuart, and A. Moilliet, J. Fluid Mech. 12 (1962) 241; A.M. Obukhov, J. Fluid Mech. 13 (1962) 77; A.N. Kolmogorov, J. Fluid Mech. 13 (1962) 82.
49. R.H. Kraichnan, Phys. Fluids 28 (1985) 10; C. Meneveau and M. Nelkin, Phys. Rev. A 39 (1989) 3732, and references therein.
50. R.H. Kraichnan, Phys. Fluids 28 (1985) 10; C. Meneveau and M. Nelkin, Phys. Rev. A 39 (1989) 3732, and references therein.