×

zbMATH — the first resource for mathematics

Spontaneous formation of travelling localized structures and their asymptotic behaviour in binary fluid convection. (English) Zbl 1275.76095
Summary: We study spontaneous pattern formation and its asymptotic behaviour in binary fluid flow driven by a temperature gradient. When the conductive state is unstable and the size of the domain is large enough, finitely many spatially localized time-periodic travelling pulses (PTPs), each containing a certain number of convection cells, are generated spontaneously in the conductive state and are finally arranged at non-uniform intervals while moving in the same direction. We found that the role of PTP solutions and their strong interactions (collision) are important in characterizing the asymptotic state. Detailed investigations of pulse-pulse interactions showed the differences in asymptotic behaviour between that in a finite but large domain and in an infinite domain.

MSC:
76E06 Convection in hydrodynamic stability
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
76M22 Spectral methods applied to problems in fluid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1143/PTP.96.669 · doi:10.1143/PTP.96.669
[2] DOI: 10.1115/1.1992517 · Zbl 1111.74593 · doi:10.1115/1.1992517
[3] Disc. Cont. Dyn. Sys. S 4 pp 1213– (2011)
[4] DOI: 10.1016/S0167-2789(98)00309-1 · Zbl 0952.37009 · doi:10.1016/S0167-2789(98)00309-1
[5] Theor. Appl. Mech. Japan 59 pp 211– (2010)
[6] DOI: 10.1051/jphys:0198800490110182900 · doi:10.1051/jphys:0198800490110182900
[7] DOI: 10.1103/PhysRevE.69.056224 · doi:10.1103/PhysRevE.69.056224
[8] DOI: 10.1103/PhysRevLett.104.104501 · doi:10.1103/PhysRevLett.104.104501
[9] DOI: 10.1103/PhysRevLett.60.1723 · doi:10.1103/PhysRevLett.60.1723
[10] DOI: 10.1103/PhysRevA.44.6466 · doi:10.1103/PhysRevA.44.6466
[11] DOI: 10.1143/JPSJ.74.538 · doi:10.1143/JPSJ.74.538
[12] J. Fluid Mech. 30 pp 625– (1964)
[13] DOI: 10.1140/epje/i2004-10069-1 · doi:10.1140/epje/i2004-10069-1
[14] DOI: 10.1063/1.2746816 · Zbl 1163.37317 · doi:10.1063/1.2746816
[15] DOI: 10.1016/j.physd.2008.11.010 · Zbl 1167.37043 · doi:10.1016/j.physd.2008.11.010
[16] DOI: 10.1103/PhysRevE.73.056211 · doi:10.1103/PhysRevE.73.056211
[17] DOI: 10.1146/annurev.fl.22.010190.002353 · doi:10.1146/annurev.fl.22.010190.002353
[18] DOI: 10.1137/110843976 · Zbl 1242.35047 · doi:10.1137/110843976
[19] DOI: 10.1103/PhysRevE.84.016204 · doi:10.1103/PhysRevE.84.016204
[20] DOI: 10.1103/PhysRevA.35.2761 · doi:10.1103/PhysRevA.35.2761
[21] DOI: 10.1137/080713306 · Zbl 1200.37015 · doi:10.1137/080713306
[22] Phys. Rev. Lett. 23 pp 2935– (1986)
[23] DOI: 10.1063/1.3633341 · Zbl 06423161 · doi:10.1063/1.3633341
[24] DOI: 10.1016/j.physd.2008.10.005 · Zbl 1156.37321 · doi:10.1016/j.physd.2008.10.005
[25] DOI: 10.1017/S0022112006000759 · Zbl 1122.76029 · doi:10.1017/S0022112006000759
[26] DOI: 10.1103/PhysRevE.51.5662 · doi:10.1103/PhysRevE.51.5662
[27] DOI: 10.1103/PhysRevLett.66.2621 · doi:10.1103/PhysRevLett.66.2621
[28] DOI: 10.1016/0167-2789(92)90175-M · Zbl 0763.35088 · doi:10.1016/0167-2789(92)90175-M
[29] DOI: 10.1016/0167-2789(86)90104-1 · doi:10.1016/0167-2789(86)90104-1
[30] Convection in Liquids (1984) · Zbl 0545.76048
[31] DOI: 10.1063/1.2087127 · Zbl 1144.37393 · doi:10.1063/1.2087127
[32] DOI: 10.1063/1.1592131 · doi:10.1063/1.1592131
[33] DOI: 10.1103/PhysRevE.67.056210 · doi:10.1103/PhysRevE.67.056210
[34] DOI: 10.1103/PhysRevLett.64.1365 · doi:10.1103/PhysRevLett.64.1365
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.