Two-layer thermal convection in miscible viscous fluids

Journal of Fluid Mechanics

Volumn 379, Issue , 1999, Pages 223-253

  Davaille, Anne ^a,b  

^a YALE UNIVERSITY   (United States)

^b IPG   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CELLULOSE; DENSITY (SPECIFIC GRAVITY); HEAT CONVECTION; HEAT TRANSFER; INTERFACES (MATERIALS); MASS TRANSFER; PRANDTL NUMBER; SALTS; THERMAL STRATIFICATION; VISCOSITY;

MISCIBLE VISCOUS FLUIDS; RAYLEIGH NUMBER; TWO LAYER THERMAL CONVECTION;

VISCOUS FLOW;

EID: 0032654826     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112098003322     Document Type: Article

References (54)

1. ASAEDA, T. & WATANABE, K. 1989 The mechanism of heat transport in thermal convection at high Rayleigh numbers. Phys. Fluids A 1, 861-867.
2. BEARDSLEY, R. C. & FESTA. J. F. 1972 A numerical model of convection driven by a surface stress and non-uniform heating. J. Phys. Oceanogr. 2, 444-455.
3. BIRD, R. B., STEWART, W. E. & LIGHTFOOT, E. N. 1966 Transport Phenomena. Wiley.
4. BLAIR, L. M. & QUINN, J. A. 1969 The onset of cellular convection in a fluid layer with time-dependent density gradients. J. Fluid Mech. 36, 385-400.
5. Boss, A. P. & SACKS, I. S. 1986 High spatial resolution models of time-dependent, layered convection. Geophys. J. R. Astron. Soc. 87, 241-264.
6. BUSSE, F. H. 1981 On the aspect ratios of two-layer mantle convection. Phys. Earth Planet. Inter. 24, 320-324.
7. CASTAING, B., GUNARATNE, G., HESLOT, F., KADANOF, L., LIBCHABER, A., THOMAS, S. & WU, X.-Z. 1989 Scaling of hard turbulence in Rayleigh-Bénard convection. J. Fluid Mech. 204, 1-30.
8. CHRISTENSEN, U. 1980 Numerical experiments on convection in a chemically layered mantle. J. Geophys. Res. 49, 82-84.
9. CHRISTENSEN, U. & YUEN, D. A. 1984 The interaction of a subducting slab with a chemical or phase boundary. J. Geophys. Res. 89, 4389-4402.
10. CHU, T. Y. & GOLDSTEIN, R. J. 1965 Turbulent convection in a horizontal layer of water. J. Fluid Mech. 60, 141-159.
11. CSEREPES, L. & RABINOWICZ, M. 1985 Gravity and convection in a two-layered mantle. Earth Planet. Sci. Lett. 76, 193-207.
12. CSEREPES, L., RABINOWICZ, M. & ROSEMBERG-BOROT, C. 1988 Three-dimensional infinite Prandtl number convection in one and two layers with implications for the Earth's gravity field. J. Geophys. Res. 93, 12009-12025.
13. DAVAILLE, A. 1998 Thermal convection in two superimposed miscible fluids with different viscosities. Part I: linear stability analysis.
14. DAVAILLE, A. & JAUPART, C. 1993 Transient high-Rayleigh-number convection with large viscosity variations. J. Fluid Mech. 253, 141-166.
15. DAVAILLE, A. & JAUPART, C. 1994 Onset of thermal convection in fluids with temperature-dependent viscosity: application to the oceanic mantle. J. Geophys. Res. 99, 19853-19866.
16. DEARDORFF, J. W., WILLIS, G. E. & LILLY, D. K. 1969 Laboratory investigation of non-steady penetrative convection. J. Fluid Mech. 35, 7-31.
17. ELLSWORTH, K. & SCHUBERT, G. 1988 Numerical models of thermally and mechanically coupled two-layered convection in highly viscous fluids. Geophys. J. 93, 347-363.
18. FERNANDO, H. J. S. 1989 Buoyancy transfer across a diffusive interface. J. Fluid Mech. 209, 1-34.
19. FERNANDO, H. J. S. 1991 Turbulent mixing in stratified fluids. Ann. Rev. Fluid Mech. 23, 455-493.
20. GOLDSTEIN, R. J., CHIANG, H. D. & SEE, D. L. 1990 High Rayleigh-number convection in a horizontal enclosure. J. Fluid Mech. 213, 111-126.
21. GUILLOU, L. & JAUPART, C. 1995 On the effect of continents on mantle convection. J. Geophys. Res. 100, 24217-24238.
22. HOWARD, L. N. 1964 Convection at high Rayleigh number. In Proc. 117th Intl Congr. Applied Mechanics (ed. H. Görtler), pp. 1109-1115. Springer, Berlin.
23. HUPPERT, H. E., SPARKS, R. S. & TURNER, J. S. 1984 Some effects of viscosity on the dynamics of replenished magma chambers. J. Geophys. Res. 89, 6857-6877.
24. JARVIS, G. T. & PELTIER, W. R. 1982 Mantle convection as a boundary layer phenomenon. Geophys. J. R. Astron. Soc. 68, 389-427.
25. JEONG, J.-T. & MOFFATT, H. K. 1992 Free-surface cusps associated with flow at low Reynolds number. J. Fluid Mech. 241, 1-22.
26. JOSEPH, D. D., NELSON, J., RENARDY, M. & RENARDY, Y. 1991 Two-dimensional cusped interfaces. J. Fluid Mech. 223, 383-409.
27. JOSEPH, D. D. & RENARDY, M. 1993 Fundamentals of Two-Fluids Dynamics. Springer, New York, pp. 443.
28. KAVIANY, M. 1980 The onset of thermal convection in a fluid layer subjected to transient heating from below. J. Heat Transfer 106, 817-823.
29. KENYON, P. M. & TURCOTTE, D. L. 1983 Convection in a two-layer mantle with a strongly temperature-dependent viscosity. J. Geophys. Res. 88, 6403-6414.
30. KRISHNAMURTI, R. 1970 On the transition to turbulent convection. J. Fluid Mech. 42, 295-320.
31. LINDEN, P. F. & SHIRTCLIFFE, T. G. L. 1978 The diffusive interface in double-diffusive convection. J. Fluid Mech. 87, 417-423.
32. LISTER, J. R. 1989 Selective withdrawal from a viscous two-layer sytem. J. Fluid Mech. 198, 231-254.
33. NATAF, H.-C, MORENO, S. & CARDIN, P. 1988 What is responsible for thermal coupling in layered convection? J. Phys. France 49, 1707-1714.
34. NEWELL, T. A. 1984 Characteristics of a double diffusive interface at high density stability ratios. J. Fluid Mech. 149, 385-401.
35. OLSON, P. 1984 An experimental approach to thermal convection in a two-layered mantle. J. Geophys. Res. 89, 11293-11301.
36. OLSON, P., SILVER, P. G. & CARLSON, R. W. 1990 The large scale structure of convection in the Earth's mantle. Nature 344, 209-215.
37. OLSON, P., SCHUBERT, G. & ANDERSON, C. 1993 Structure of axisymmetric mantles plumes. J. Geophys. Res. 98, 6829-6844.
38. PELLEW, A. & SOUTHWELL, R. V. 1940 On maintained convective motion in a fluid heated from below. Proc. R. Soc. Lond. A 176, 312-343.
39. PROCTOR, M. R. E. & JONES, C. A. 1988 The interaction of two spatially resonant patterns in thermal convection. Part 1. Exact 1:2 resonance. J. Fluid Mech. 188, 301-355.
40. OTTINO, J. M. 1989 The Kinematics of Mixing: Stretching, Chaos, and Transport. Cambridge University Press, 364 pp.
41. RASENAT, S., BUSSE, F. H. & REHBERG, I. 1989 A theoretical and experimental study of double-layer convection. J. Fluid Mech. 199, 519-540.
42. RENARDY, Y. & JOSEPH, D. D. 1985 Oscillatory instability in a Bénard problem of two fluids. Phys. Fluids 28, 788-793.
43. RENARDY, Y. & JOSEPH, D. D. 1985 Perturbation analysis of steady and oscillatory onset in a Bénard problem with two similar liquids. Phys. Fluids 28, 2699-2708.
44. RENARDY, M. & RENARDY, Y. 1985 Perturbation analysis of steady and oscillatory onset in a Bénard problem with two similar liquids. Phys. Fluids 28, 2699-2708.
45. RICHTER, F. M. & JOHNSON, C. E. 1974 Stability of a chemically layered mantle. J. Geophys. Res. 79, 1635-1639.
46. RICHTER, F. M. & MCKENZIE, D. P. 1981 On some consequences and possible causes of layered convection. J. Geophys. Res. 86, 6133-6124.
47. ROSSBY, H. T. 1965 On thermal convection driven by non-uniform heating from below: an experimental study. Deep-Sea Res. 12, 9-16.
48. RUDDICK, B. R. & SHIRTCLIFFE, T. G. L. 1979 Data for double-diffusers: physical properties of aqueous salt-sugar solutions. Deep-Sea Res. 26, 775-787.
49. SCHMITT, R. W. 1994 Double diffusive oceanography. Ann. Rev. Fluid Mech. 26, 255-285.
50. SINGER, H. A. 1986 Heat transport by steady state plumes with strongly temperature-dependent viscosity. PhD thesis. The Johns Hopkins University, Baltimore, MD, 196 pp.
51. SOLOMON, T. H. & GOLLUB, J. P. 1988 Passive transport in Steady Rayleigh-Bénard Convection. Phys. Fluids 31, 1372-1379.
52. SOTIN, C. & PARMENTIER, E. M. 1989 On the stability of a fluid layer containing a univariant phase transition: application to planetary interiors. Phys. Earth Planet. Inter. 55, 10-25.
53. TAIT, S. & JAUPART, C. 1989 Compositional convection in viscous melts. Nature 338, 571-574.
54. TURNER, J. S. 1979 Buoyancy Effects in Fluids. Cambridge University Press. 368 pp.