Abstract
Traveling wave patterns formed at the oscillatory onset of convection in binary mixtures with free slip and permeable horizontal boundary conditions are theoretically derived by means of an order parameter equation for the case of large aspect ratio systems with circular and rectangular geometry. We obtain in addition to ‘Zipper states’ the so called ‘confined states’, which so far has been observed only experimentally. Our present study of traveling wave patterns in circular systems, which are the first theoretical investigations in this respect, exhibit a characteristic change of behaviour. Close to onset the waves travel in radial direction towards the sidewalls. For higher Rayleigh-numbers the waves are confined to the circular boundary traveling in azimuthal direction. The occurrence of this transition should be confirmed experimentally.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Busse, F.H.: Rep. Prog. Phys.41, 1929 (1978)
Platten, J.K., Legros, J.C.: Convection in liquids. Berlin, Heidelberg, New York: Springer 1983
Steinberg, V., Moses, E., Fineberg, J.: Proceedings of the International Conference on ‘The Physics of Chaos and Systems Far From Equilibrium’, Monterey, Jan 10–14, 86. Nucl. Phys. (Proc. Suppl.) B2, 109 (1987)
Kolodner, P., Passner, A., Williams, H.L., Surko, C.M.: Proceedings of the International Conference on ‘The Physics of Chaos and Systems Far From Equilibrium’, Monterey, Jan 10–14, 86. Nucl. Phys. (Proc. Suppl.) B2, 97 (1987)
Heinrichs, R., Ahlers, G., Cannell, D.S.: Phys. Rev. A35, 2761 (1987)
Ahlers, G., Cannell, D.S., Heinrichs, R.: Nucl. Phys. (Proc. Suppl.) B2, 77 (1987)
Kolodner, P., Bensimon, D., Surko, C.M.: Phys. Rev. Lett.60, 1723 (1988)
Fineberg, J., Moses, E., Steinberg, V.: Phys. Rev. Lett.61, 838 (1988)
Cross, M.C.: Phys. Rev. Lett.57, 2935 (1986)
Bestehorn, M., Friedrich, R., Haken, H.: Z. Phys. B — Condensed Matter72, 265 (1988)
Knobloch, E.: Phys. Rev. A34, 1538 (1986)
Deane, A.E., Knobloch, E., Toombre, J.: Phys. Rev. A36, 2862 (1987)
Knobloch, E., Deane, A.E., Toomre, J.: In: Physics of structure and formation: theory and simulation. Güttinger, H., Dangelmayr, G. (eds.). Berlin, Heidelberg, New York: Springer 1987
Surko, C.M., Kolodner, P., Passner, A., Walden, R.W.: Physica23D, 220 (1986)
Brand, H.R., Lomdahl, P.S., Newell, A.C.: Physica D23, 345 (1986); Phys. Lett. A118, 67 (1986)
Coullet, P., Elphik, C., Gil, L., Lega, J.: Phys. Rev. Lett.59, 884 (1987)
Swift, J., Hohenberg, P.C.: Phys. Rev. A15, 319 (1977)
Bestehorn, M., Haken, H.: Z. Phys. B — Condensed Matter57, 329 (1984)
Haken, H.: Synergetics. An introduction. 3rd Edn. Berlin, Heidelberg, New York: Springer 1983
Haken, H.: Advanced synergetics. 2. print. Berlin, Heidelberg, New York: Springer 1987
Greenside, H.S., Coughran, W.M. Jr.: Phys. Rev. A30, 398 (1984)
Siggia, E.D., Zippelius, A.: Phys. Rev. Lett. A47, 835 (1981)
Coullet, P., Elphick, C., Repaux, D.: In: Physics of structure and formation: theory and simulation. Güttinger, H., Dangelmayr, G. (eds.). Berlin, Heidelberg, New York: Springer 1987
Ohta, T., Kawasaki, K.: Physica27D, 21 (1987)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bestehorn, M., Friedrich, R. & Haken, H. Two-dimensional traveling wave patterns in nonequilibrium systems. Z. Physik B - Condensed Matter 75, 265–274 (1989). https://doi.org/10.1007/BF01308010
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01308010