Prandtl number dependence of the viscous boundary layer and the Reynolds numbers in Rayleigh-Bénard convection

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 65, Issue 6, 2002, Pages

  Lam, Siu ^a   Shang, Xiao Dong ^a   Zhou, Sheng Qi ^a   Xia, Ke Qing ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

ASPECT RATIO; BOUNDARY LAYER FLOW; ENERGY DISSIPATION; LASER DOPPLER VELOCIMETERS; PRANDTL NUMBER; REFRACTIVE INDEX; REYNOLDS NUMBER; SIGNAL TO NOISE RATIO;

KINETIC ENERGY DISSIPATION; RAYLEIGH-BÉNARD CONVECTION; VERTICAL VELOCITY; VISCOUS BOUNDARY LAYER;

HEAT CONVECTION;

EID: 41349099819     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.65.066306     Document Type: Article

References (36)

1. S. Grossmann and D. Lohse, J. Fluid Mech. 407, 27 (2000).
2. J.J. Niemela, L. Skrbek, K.R. Sreenivasan, and R.J. Donnelly, Nature (London) 404, 837 (2000).
3. K.-Q. Xia, S. Lam, and S.-Q. Zhou, Phys. Rev. Lett. 88, 064501 (2002).
4. Y.-B. Xin, K.-Q. Xia, and P. Tong, Phys. Rev. Lett. 77, 1266 (1996).
5. Y.-B. Xin and K.-Q. Xia, Phys. Rev. E 56, 3010 (1997).
6. A. Belmonte, A. Tilgner, and A. Libchaber, Phys. Rev. Lett. 70, 4067 (1993).
7. A. Naert, T. Segawa, and M. Sano, Phys. Rev. E 56, R1302 (1997).
8. See, for example, B.I. Shraiman and E.D. Siggia, Physica D 97, 286 (1996).
9. These are (Formula presented) pure solvents purchased from Acros Organics, Ltd.
10. F. Busse, J. Fluid Mech. 30, 625 (1967).
11. C.L. Yaws, Chemical Properties Handbook (McGraw-Hill, New York, 1999).
12. S.-L. Lui and K.-Q. Xia, Phys. Rev. E 57, 5494 (1998).
13. K.-Q. Xia, Y.-B. Xin, and P. Tong, J. Opt. Soc. Am. A 12, 1571 (1995).
14. X.-L. Qiu and K.-Q. Xia, Phys. Rev. E 58, 486 (1998).
15. We achieve the density match between the glass spheres and the liquid by first spinning the suspension in a centrifuge and then drawing out the middle part of the suspension with a syringe needle after the liquid has settled for a long time.
16. Because the large refractive index of the fluid (compared to water) causes bending of the laser beams, we are not able to position them very close to the surface of the plate where there is a large refractive index gradient. Thus we do not know whether the velocity profile in Fig. 11 will become linear inside the thermal layer (Formula presented) for the present one, which is also the lowest point measured).
17. J. Zhang, S. Childress, and A. Libchaber, Phys. Fluids 9, 1034 (1997).
18. J. Zhang, S. Childress, and A. Libchaber, Phys. Fluids 10, 1534 (1998).
19. K.-Q. Xia and S.-Q. Zhou, Physica A 288, 308 (2000).
20. J.A. Glazier, T. Segawa, A. Naert, and M. Sano, Nature (London) 398, 307 (1999).
21. S. Grossmann and D. Lohse, Phys. Rev. Lett. 86, 3316 (2001).
22. G. Ahlers and X. Xu, Phys. Rev. Lett. 86, 3320 (2001).
23. F. Heslot, B. Castaing, and A. Libchaber, Phys. Rev. A 36, 5870 (1987).
24. The flow at this Pr is very slow, so even with very long averages the data still show large scatter.
25. R. Verzicco and R. Camussi, J. Fluid Mech. 383, 55 (1999).
26. A. Tilgner, Phys. Rev. E 53, 4847 (1996).
27. X.-L. Qiu, S.H. Yao, and P. Tong, Phys. Rev. E 61, R6075 (2000).
28. X.-D. Shang and K.-Q. Xia, Phys. Rev. E 64, 065301(R) (2001).
29. S. Ashkenazi and V. Steinberg, Phys. Rev. Lett. 83, 3641 (1999).
30. S. Ashkenazi and V. Steinberg, Phys. Rev. Lett. 83, 4760 (1999).
31. The highest shear Reynolds number based on the boundary layer thickness, (Formula presented), reached in the experiment is about 200, whereas the critical value for instability is about 420 [see, for example, L.D. Landau and E.M. Lifshitz, Fluid Mechanics (Pergamon Press, Oxford, 1987)].
32. B.I. Shraiman and E.D. Siggia, Phys. Rev. A 42, 3650 (1990).
33. B. Castaing, G. Gunaratne, F. Heslot, L.P. Kadanoff, A. Libchaber, S. Thomae, X.-Z. Wu, S. Zaleski, and G. Zanetti, J. Fluid Mech. 204, 1 (1989).
34. R.H. Kraichnan, Phys. Fluids 5, 1374 (1962).
35. X.-L. Qiu and P. Tong, Phys. Rev. E 64, 036304 (2001).
36. X. Chavanne, F. Chillà, B. Chabaud, B. Castaing, and B. Hébral, Phys. Fluids 13, 1300 (2001).