Publication: Fluctuations in fluids in thermal nonequilibrium states below the convective Rayleigh-Benard instability
Loading...
Official URL
Full text at PDC
Publication Date
2001-11-01
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
Starting from the linearized fluctuating Boussinesq equations we derive an expression for the structure factor of fluids in stationary convection-free thermal nonequilibrium. states, taking into account both gravity and finite-size effects. It is demonstrated how the combined effects of gravity and finite size cause the structure factor to go through a maximum value as a function of the wave number q. The appearance of this maximum is associated with a crossover from a q^-4 dependence for larger q to a q^2 dependence for very small q. The relevance of this theoretical result for the interpretation of light scattering and shadowgraph experiments is elucidated. The relationship with studies on various aspects of the problem by other investigators is discussed. The paper thus provides a unified treatment for dealing with fluctuations in fluid layers subjected to a stationary temperature gradient regardless of the sign of the Rayleigh number R, provided that R is smaller than the critical value R_c associated with the appearance of Rayleigh-Benard convection.
Description
© 2001 Elsevier Science B.V
The authors acknowledge some valuable discussions with G. Ahlers, D.S. Cannell, T.R. Kirkpatrick, R. Pérez Cordón and M.G. Velarde. The research at the University of Marylandis supportedby the Chemical Sciences, Geosciences andBiosciences Division of the OIce of Basic Energy Sciences of the US Department of Energy under Grant No. DE-FG-02-95ER14509. J.V.S. acknowledges the hospitality of the Departamento deFísica Aplicada I, Universidad Complutense de Madrid, where the manuscript was completed.
UCM subjects
Unesco subjects
Keywords
Citation
1.- V. Zaitsev, M. Shliomis Sov. Phys. JETP, 32 (1971), p. 866
2.- R. Graham Phys. Rev. A, 10 (1974), p. 1762
3.- R. Graham, H. Pleiner Phys. Fluids, 18 (1975), p. 130
4.- J.B. Swift, P.C. Hohenberg Phys. Rev. A, 15 (1977), p. 319
5.- M.C. Cross, P.C. Hohenberg Rev. Mod. Phys., 65 (1993), p. 851
6.- T.R. Kirkpatrick, E.G.D. Cohen, J.R. Dorfman Phys. Rev. A, 26 (1982), p. 995
7.- D. Ronis, I. Procaccia Phys. Rev. A, 26 (1982), p. 1812
8.- R. Schmitz, E.G.D. Cohen J. Stat. Phys., 39 (1985), p. 285
9.- B.M. Law, J.V. Sengers J. Stat. Phys., 57 (1989), p. 531
10.- B.M. Law, R.W. Gammon, J.V. Sengers Phys. Rev. Lett., 60 (1988), p. 1554
11.- B.M. Law, P.N. Segrè, R.W. Gammon, J.V. Sengers Phys. Rev. A, 41 (1990), p. 816
12.- P.N. Segrè, R.W. Gammon, J.V. Sengers, B.M. Law Phys. Rev. A, 45 (1992), p. 714
13.- J.V. Sengers, J.M. Ortiz de Zárate, in: W. Köhler, S. Wiegand (Eds.), Thermal Nonequilibrium Phenomena in Fluid Mixtures, Springer, Berlin, 2001, in press.
14.- A.L. Garcı́a, M. Malek Mansour, G.C. Lie, E. Clementi J. Stat. Phys., 47 (1987), p. 209
15.- J.M. Rubı́, A. Dı́az-Guilera, L. Torner Physica A, 141 (1987), p. 220
16.- C.Z.-W Liu, I. Oppenheim J. Stat. Phys., 86 (1997), p. 179
17.- A.L. Garcı́a, G. Sonnino, M. Malek Mansour J. Stat. Phys., 90 (1998), p. 1489
18.- M. Malek Mansour, M. Mareschal, G. Sonnino, E. Kestemont M. Mareschal, B. Holian (Eds.), Microscopic Simulations of Complex Hydrodynamic Phenomena, Plenum, London (1992), p. 87
19.- A. Suárez, J.P. Boon, P. Grosfils Phys. Rev. E, 54 (1996), p. 1208
20.- P.N. Segrè, R. Schmitz, J.V. Sengers Physica A, 195 (1993), p. 31
21.- P.N. Segrè, J.V. Sengers Physica A, 198 (1993), p. 46
22.- A. Vailati, M. Giglio Phys. Rev. Lett., 77 (1996), p. 1484
23.- A. Vailati, M. Giglio Prog. Colloid. Polym. Sci., 104 (1997), p. 76
24.- J.M. Ortiz de Zárate, R. Pérez Cordón, J.V. Sengers Physica A, 291 (2001), p. 113
25.- J.M. Ortiz de Zárate, L. Muñoz Redondo, Euro. Phys. J. B 21 (2001) 135.
26.- T.R. Kirkpatrick, E.G.D. Cohen J. Stat. Phys., 33 (1983), p. 639
27.- R. Schmitz, E.G.D. Cohen J. Stat. Phys., 40 (1985), p. 431
28.- M. Wu, G. Ahlers, D.S. Cannell Phys. Rev. Lett., 75 (1995), p. 1743
29.- G. Ahlers, M.C. Cross, P.C. Hohenberg, S. Safran J. Fluid Mech., 110 (1981), p. 297
30.- C.W. Meyer, G. Ahlers, D.S. Cannell Phys. Rev. Lett., 59 (1987), p. 1577
31.- H. van Beijeren, E.G.D. Cohen J. Stat. Phys., 53 (1988), p. 77
32.- G. Ahlers, C.W. Meyer, D.S. Cannell J. Stat. Phys., 54 (1989), p. 1121
33.- C.W. Meyer, G. Ahlers, D.S. Cannell Phys. Rev. A, 44 (1991), p. 2514
34.- I. Rehberg, S. Rasenat, M. de la Torre Juárez, W. Schöpf, F. Hörner, G. Ahlers, H.R. Brand Phys. Rev. Lett., 67 (1991), p. 596
35.- S. Chandrasekhar Hydrodynamic and Hydromagnetic Stability, Oxford University Press, Oxford (1961)
36.- P.C. Hohenberg, J.B. Swift Phys. Rev. A, 46 (1992), p. 4773
37.- J. Garcı́a Ojalvo, A. Hernández Machado, J.M. Sancho Phys. Rev. Lett., 71 (1993), p. 1542
38.- D.D. Gray, A. Giorgini Int. J. Heat Mass Transfer, 19 (1976), p. 545
39.- D.J. Tritton Physical Fluid Dynamics (2nd Edition), Oxford University Press, Oxford (1988)
40.- C. Normand, Y. Pomeau, M.G. Velarde Rev. Mod. Phys., 49 (1977), p. 581
41.- F.H. Busse J. Fluid Mech., 30 (1967), p. 625
42.- G. Ahlers J. Fluid Mech., 98 (Part I) (1980), p. 137
43.- E. Bodenschatz, J.R. de Bruyn, G. Ahlers, D.S. Cannell Phys. Rev. Lett., 67 (1991), p. 3078
44.- L.D. Landau, E.M. Lifshitz Fluid Mechanics, Addison-Wesley, Reading, MA (1959)
45.- D. Ronis, I. Procaccia J. Machta, Phys. Rev. A, 22 (1980), p. 714
46.- B.J. Berne, R. Pecora Dynamic Light Scattering, Wiley, New York (1976)
47.- J.V. Sengers, J.M. Ortiz de Zárate, Revista Mexicana de Fı́sica (2001), in press.
48.- P. Manneville Dissipative Structures and Weak Turbulence, Academic Press, San Diego (1990)
49.- I.S. Gradstein, I.M. Ryzhik Table of Integrals, Series, and Products (5th Edition), Academic Press, San Diego (1994)
50.- J.R. de Bruyn, E. Bodenschatz, S.W. Morris, S.P. Trainoff, Y. Hu, D.S. Cannell, G. Ahlers Rev. Sci. Instrum., 67 (1996), p. 2043
51.- E. Bodenschatz, W. Pesch, G. Ahlers Annu. Rev. Fluid Mech., 32 (2000), p. 709
52.- A. Vailati, M. Giglio Nature, 390 (1997), p. 262
53.- D. Brogioli, A. Vailati, M. Giglio Phys. Rev. E, 61 (2000), p. R1
54.- D. Brogioli, A. Vailati, M. Giglio J. Phys.: Condens. Matter, 12 (2000), p. A39
55.- J. Garcı́a Ojalvo, J.M. Sancho Noise in Spatially Extended Systems, Springer, New York (1999)
56.- K. Staliunas, Spatial and temporal spectra of noise driven stripe pattern, available at http://xxx.lanl.gov/abs/cond-mat/0103018, 2001.
57.- W.B. Li, P.N. Segrè, R.W. Gammon, J.V. Sengers Physica A, 204 (1994), p. 399
58.- M.A. Scherer, G. Ahlers, F. Hörner, I. Rehberg Phys. Rev. Lett., 85 (2000), p. 3754
59.- L. Torner, J.M. Rubı́ Phys. Rev. A, 44 (1991), p. 1077
60.- I. Pagonabarraga, J.M. Rubı́, L. Torner Physica A, 173 (1991), p. 111
61.- H.-P. Breuer, F. Petruccione Phys. Lett. A, 185 (1994), p. 385
62.- M. Malek Mansour, J.W. Turner, A.L. Garcı́a J. Stat. Phys., 48 (1987), p. 1157
63.- I. Bena, M. Malek Mansour, F. Baras Phys. Rev. E, 59 (1999), p. 5503