Prog. Theor. Phys. Vol. 106 No. 6 (2001) pp. 1115-1128
Nonlinear Convective States in a Fluid Mixture with Through-Flow
1Department of Applied Physics,
Faculty of Engineering, Fukui University,
Fukui 910-8507, Japan
2Department of Human and Artificial Intelligent Systems,
Faculty of Engineering,
Fukui University, Fukui 910-8507, Japan
3Institute for Fluid Dynamics, Xi'an University of Technology, Xi'an 710048,
(Received June 25, 2001)
We report a numerical study on traveling-wave convection in a binary fluid mixture with a laterally
imposed weak through-flow. Nonlinear convective states were determined by solving two-dimensional
basic hydrodynamic field equations subject to nonperiodic lateral boundary conditions. This system has
previously been found to exhibit repeated and coexisting dynamical states for a channel with small
aspect ratio. We study the patterns observed in channels with large aspect ratio and the influence of
the aspect ratio on convection evolution. In long channels, traveling waves in one convective cycle have
sufficient space to relax in the downstream region, while in short channels, the system appears to exert
some stabilizing influence on traveling waves. This causes the critical Rayleigh number (at which the
convective pattern makes a transition from one type to another) to depend on the aspect ratio. It is also
found that the cycle periods of repeated evolution are not determined simply by the linear growth rates
of convective perturbations, but are influenced greatly by the length of the convection channel.
DOI : 10.1143/PTP.106.1115
M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65 (1993), 851[APS].
- E. Bodenschatz, W. Pesch and G. Ahlers, Annu. Rev. Fluid Mech. 32 (2000), 709.
P. Kolodner, A. Passner, C. M. Surko and R. W. Walden, Phys. Rev. Lett. 56 (1986), 2621[APS].
H. L. Williams and C. Moe, J. Chem. Phys. 88 (1988), 6512[CrossRef].
E. Moses, J. Fineberg and V. Steinberg, Phys. Rev. A 35 (1987), 2757[APS].
P. Kolodner, H. L. Williams and C. Moe, J. Chem. Phys. 88 (1988), 6512[CrossRef].
H. Yahata, Prog. Theor. Phys. Suppl. No. 99 (1989), 493[PTP].
W. van Saarloos and P. C. Hohenberg, Physica D 56 (1992), 303[CrossRef].
D. Bensimon, P. Kolodner, C. M. Surko, H. L. Williams and V. Croquette, J. Fluid Mech. 217 (1990), 441[CrossRef].
P. Kolodner, Phys. Rev. E 48 (1993), R4187[APS];
ibid. 50 (1994), 2731[APS].
H. Riecke and W. J. Pappel, Phys. Rev. Lett. 75 (1995), 4035[APS].
La Porta and C. M. Surko, Phys. Rev. Lett. 77 (1996), 2678[APS].
St. Hollinger, M. Lücke and H. W. Muller, Phys. Rev. E 57 (1998), 4250[APS].
K. Lerman, D. S. Cannell and G. Ahlers, Phys. Rev. E 59 (1999), 2975[APS].
O. Batiste, M. Net, I. Mercader and E. Knobloch, Phys. Rev. Lett. 86 (2001), 2309[APS].
For a comprehensive review and additional references see Refs. 1) and 16).
K. J. Lee and H. L. Swinney, Phys. Rev. E 51 (1995), 1899[APS].
R. Kapral, Physica D 86 (1995), 149[CrossRef].
A. Belmonte, J. M. Flesselles and Q. Ouyang, Europhys. Lett. 35 (1996), 665[CrossRef].
P. B. Umbanhowar, Nature 389 (1997), 541[CrossRef].
- Y. Kamotani and S. Ostrach, J. Heat Transfer 98 (1976), 62.
K. Fukui and M. Nakajima, Int. J. Heat Mass Transfer 26 (1983), 109.
G. Evans and R. Greif, Int. J. Heat Mass Transfer 32 (1989), 895.
C. H. Yu, M. Y. Chang and T. F. Lin, Int. J. Heat Mass Transfer 40 (1997), 333.
Y. Kato and K. Fujimura, Phys. Rev. E 62 (2000), 601[APS].
K. M. S. Bajaj, J. Liu, B. Naberhuis and G. Ahlers, Phys. Rev. Lett. 81 (1998), 806[APS].
Y. Hu, W. Pesch, G. Ahlers and R. E. Ecke, Phys. Rev. E 58 (1998), 5821[APS].
K. E. Daniels, B. B. Plapp and E. Bodenschatz, Phys. Rev. Lett. 84 (2000), 5320[APS].
- J. K. Platten and J. C. Legros, Convection in liquids (Springer, Berlin, 1984).
- M. T. Ouazzani, J. K. Platten and A. Mojtabi, Int. J. Heat Mass Transfer 33 (1990), 1417.
H. R. Brand, G. Ahlers and R. J. Deissler, Phys. Rev. A 43 (1991), 4262[APS].
D. T. J. Hurle and E. Jakeman, J. Fluid Mech. 47 (1972), 667[CrossRef].
J. K. Platten and G. Chavepeyer, J. Fliud. Mech. 60 (1973), 305.
R. W. Walden, P. Kolodner, A. Passner and C. M. Surko, Phys. Rev. Lett. 55 (1985), 496[APS].
Ch. Jung, M. Lücke and P. Büchel, Phys. Rev. E 54 (1996), 1510[APS].
P. Büchel and M. Lücke, Phys. Rev. E 61 (2000), 3793[APS].
- G.-D. Li, Prog. Theor. Phys. 106 (2001), 293[PTP].
W. Barten, M. Lücke, M. Kamps and R. Schmitz, Phys. Rev. E 51 (1995), 5636[APS];
ibid. 51 (1995), 5662[APS].
- H. Yahata, Prog. Theor. Phys. 85 (1991), 93[PTP].
L. Ning, Y. Harada and H. Yahata, Prog. Theor. Phys. 97 (1997), 831[PTP].
H. W. Muller, M. Lücke and M. Kamps, Phys. Rev. A 45 (1992), 3714[APS].
- J. M. Luijkx, J. K. Platten and J. C. Legros, Int. J. Heat Mass Transfer 24 (1981), 1287.
- S. Suhas and V. Patankar, Numerical Heat Transfer and Fluid Flow (McGraw-Hill, 1980).
W. Barten, M. Lücke, M. Hort and M. Kamps, Phys. Rev. Lett. 63 (1989), 376[APS].
St. Hollinger, P. Büchel and M. Lücke, Phys. Rev. Lett. 78 (1997), 235[APS].
O. Batiste, I. Mercader, M. Net and E. Knobloch, Phys. Rev. E 59 (1999), 6730[APS].
A. Couairon and J. M. Chomaz, Phys. Rev. Lett. 79 (1997), 2666[APS].