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Article Navigation >  Applied Mathematics and Mechanics  > 2017  >  38(11): 1230-1239
NING Li-zhong, QU Ya-wei, NING Bi-bo, YUAN Zhe, TIAN Wei-li, LIU Shuang. A New-Type Counterpropagating Wave Pattern of Vertical Mirror Symmetry in Binary Fluid Convection[J]. Applied Mathematics and Mechanics, 2017, 38(11): 1230-1239. doi: 10.21656/1000-0887.370367
Citation: NING Li-zhong, QU Ya-wei, NING Bi-bo, YUAN Zhe, TIAN Wei-li, LIU Shuang. A New-Type Counterpropagating Wave Pattern of Vertical Mirror Symmetry in Binary Fluid Convection[J]. Applied Mathematics and Mechanics, 2017, 38(11): 1230-1239. doi: 10.21656/1000-0887.370367
shu

A New-Type Counterpropagating Wave Pattern of Vertical Mirror Symmetry in Binary Fluid Convection

doi: 10.21656/1000-0887.370367

  • 1Institute of Water Resources and HydroElectric Engineering, Xi’an University of Technology, Xi’an 710048, P.R.China;2School of Architecture and Civil Engineering, Jiaxing University, Jiaxing, Zhejiang 314001, P.R.China;3China Water Resources Pearl River Planning Surveying & Designing Co. Ltd., Guangzhou 510610, P.R.China;4Department of Architecture, Shanghai University, Shanghai 200444, P.R.China

Funds:  The National Natural Science Foundation of China(10872164)
  • Received Date: 2016-11-28
  • Rev Recd Date: 2017-05-14
  • Publish Date: 2017-11-15
    Abstract
  • The 2D hydrodynamic equations for binary fluid convection were numerically simulated with the SIMPLE method. For separation ratio ψ=－0.6 of the binary fluid mixture and aspect ratio Γ=20 of the rectangular cell, a newtype counterpropagating wave pattern of vertical mirror symmetry was found for the first time and its dynamics was preliminarily studied. At the center of the counterpropagating wave pattern of vertical mirror symmetry was a standing wave, of which the wavelength extended with time. As the wavelength increased to a certain critical value, a roll split into 2 rolls, and a new roll with a 180° phase difference formed between them 2. The roll located at the center line only has phase mutation and wavelength contraction or extension, without moving toward the left or right. The convective rolls propagating toward the left or right exist on both sides of the center line. The 2 phase mutations of the standing wave form a period, and the standing wave period increases with reduced Rayleigh number Rar. This type of convective structure exists in the range of Rar∈(3.6,4.3].The convection system produces the traveling wave pattern with defect for Rar≤3.6. The system shifts to the traveling wave pattern for Rar>4.3.The work shows that the counterpropagating wave pattern of vertical mirror symmetry is a stable flow pattern between the traveling wave pattern with defect and the traveling wave pattern.
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    • References(35)
  • [1]
    Cross M C, Hohenberg P C. Pattern formation outside of equilibrium[J]. Reviews of Modern Physics,1993,65(3): 851-1112.
    [2]
    Getling A V. Rayleigh-Bénard Convection [M]. London: World Scientific, 1998.
    [3]
    Chandrasekhar S. Hydrodynamic and Hydromagnetic Stability [M]. Oxford: Clarendon Press, 1961.
    [4]
    Rabinovich M I, Ezersky A B, Weidman P D. The Dynamics of Patterns [M]. Singapore: World Scientific, 2000.
    [5]
    Walden R W, Kolodner P, Passner A, et al. Traveling waves and chaos in convection in binary fluid mixtures[J]. Physical Review Letters,1985,55(5): 496-499.
    [6]
    Niemela J J, Ahlers G, Cannell D S. Localized traveling-wave states in binary-fluid convection[J]. Physical Review Letters,1990,64(12): 1365-1368.
    [7]
    Harada Y, Masuno Y, Sugihara K. Convective motion in space and time: defect mediated localized traveling waves[J]. Vistas in Astronomy,1993,37: 107-110.
    [8]
    Ma Y-P, Burke J, Knobloch E. Defect-mediated snaking: a new growth mechanism for localized structures[J]. Physica D: Nonlinear Phenomena,2010,239(19): 1867-1883.
    [9]
    Watanabe T, Iima M, Nishiura Y. Spontaneous formation of travelling localized structures and their asymptotic behaviours in binary fluid convection[J]. Journal of Fluid Mechanics,2012,712: 219-243.
    [10]
    Muller H W, Tveitereid M, Trainoff S. Rayleigh-Bénard problem with imposed weak through-flow: two coupled Ginzburg-Landau equations[J]. Physical Review E,1993,48(1): 263-272.
    [11]
    王卓运, 宁利中, 王娜, 等. 基于振幅方程组的行波对流的数值模拟[J]. 西安理工大学学报, 2014,30(2): 163-169.(WANG Zhuo-yun, NING Li-zhong, WANG Na, et al. Numerical simulation of traveling wave convection based on amplitude equations[J]. Journal of Xi’an University of Technology,2014,30(2): 163-169.(in Chinese))
    [12]
    Yahata H. Travelling convection rolls in a binary fluid mixture[J]. Progress of Theoretical Physics,1991,85(5): 933-937.
    [13]
    Barten W, Lucke M, Kamps M. Localized traveling-wave convection in binary-fluid mixtures[J]. Physical Review Letters,1991,66(20): 2621-2624.
    [14]
    Barten W, Lücke M, Kamps M, et al. Convection in binary fluid mixtures I: extended traveling-wave and stationary states[J]. Physical Review E,1995,51(6): 5636-5661.
    [15]
    Barten W, Lücke M, Kamps M, et al. Convection in binary fluid mixtures II: localized traveling waves[J]. Physical Review E,1995,51(6): 5662-5682.
    [16]
    NING Li-zhong, Harada Y, Yahata H. Localized traveling waves in binary fluid convection[J]. Progress of Theoretical Physics,1996,96(4): 669-682.
    [17]
    NING Li-zhong, Harada Y, Yahata H. Modulated traveling waves in binary fluid convection in an intermediate-aspect-ratio rectangular cell[J]. Progress of Theoretical Physics,1997,97(6): 831-848.
    [18]
    NING Li-zhong, Harada Y, Yahata H. Formation process of the traveling-wave state with a defect in binary fluid convection[J]. Progress of Theoretical Physics,1997,98(3): 551-566.
    [19]
    NING Li-zhong, Harada Y, Yahata H, et al. Fully-developed traveling wave convection in binary fluid mixtures with lateral flows[J]. Progress of Theoretical Physics,2001,106(3): 503-512.
    [20]
    宁利中, 齐昕, 周洋, 等. 混合流体Rayleigh-Benard 行波对流中的缺陷结构[J]. 物理学报, 2009,58(4): 2528-2534.(NING Li-zhong, QI Xin, ZHOU Yang, et al. Defect structures of Rayleigh-Benard travelling wave convection in binary fluid mixtures[J]. Acta Physica Sinica,2009,58(4): 2528-2534.(in Chinese))
    [21]
    宁利中, 余荔, 袁喆, 等. 沿混合流体对流分叉曲线上部分支行波斑图的演化[J]. 中国科学(G辑: 物理学 力学 天文学), 2009,39(5): 746-751.(NING Li-zhong, YU Li, YUAN Zhe, et al. Evolution of traveling wave patterns along upper branch of bifurcation diagram in binary fluid convection[J]. Science in China(Series G: Physics, Mechanics & Astronomy),2009,39(5): 746-751.(in Chinese))
    [22]
    宁利中, 王娜, 袁喆, 等. 分离比对混合流体Rayleigh-Bénard对流解的影响[J]. 物理学报, 2014,63(10): 104401. doi: 10.7498/aps.63.104401.(NING Li-zhong, WANG Na, YUAN Zhe, et al. Influence of separation ratio on Rayleigh-Bénard convection solutions in a binary fluid mixture[J].Acta Physica Sinica,2014,63(10): 104401. doi: 10.7498/aps.63.104401.(in Chinese))
    [23]
    宁利中, 王永起, 袁喆, 等. 两种不同结构的混合流体局部行波对流斑图[J]. 科学通报, 2016,61(8): 872-880.(NING Li-zhong, WANG Yong-qi, YUAN Zhe, et al. Two types of patterns of localized traveling wave convection in binary fluid mixtures with different structures[J]. Chinese Science Bulletin,2016,61(8): 872-880.(in Chinese))
    [24]
    宁利中, 胡彪, 宁碧波, 等. Poiseuille-Rayleigh-Bénard流动中对流斑图的分区和成长[J]. 物理学报, 2016,65(21): 214401. doi: 10.7498/aps.65.214401.(NING Li-zhong, HU Biao, NING Bi-bo, et al. Partition and growth of convection patterns in Poiseuille-Rayleigh-Bénard flow[J]. Acta Physica Sinica,2016,65(21): 214401. doi: 10.7498/aps.65.214401.(in Chinese))
    [25]
    NING Li-zhong, QI Xin, YUAN Zhe, et al. A counter propagating wave state with a periodically horizontal motion of defects[J]. Journal of Hydrodynamics,2008,20(5): 567-573.
    [26]
    胡军, 尹协远. 双流体Poiseuille-Rayleigh-Bénard流动中脉冲扰动的时空演化[J]. 中国科学技术大学学报, 2007,37(10): 1267-1272.(HU Jun, YIN Xie-yuan. Spatio-temporal evolution of pulse like perturbation for Poiseuille-Rayleigh-Bénard flows in binary fluids[J]. Journal of University of Science and Technology of China,2007,37(10): 1267-1272.(in Chinese))
    [27]
    HU Jun, YIN Xie-yuan. Two-dimensional simulation of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect[J]. Progress in Nature Science,2007,17(12): 1389-1396.
    [28]
    ZHAO Bing-xin, TIAN Zhen-fu. Numerical investigation of binary fluid convection with a weak negative separation ratio in finite containers[J]. Physics of Fluids,2015,27: 074102.
    [29]
    Taraut A V, Smorodin B L, Lucke M. Collisions of localized convection structures in binary fluid mixtures[J]. New Journal of Physics,2012,14(9): 093055.
    [30]
    Mercader I, Batiste O, Alonso A, et al. Travelling convectons in binary fluid convection[J]. Journal of Fluid Mechanics,2013,722: 240-266.
    [31]
    Mercader I, Batiste O, Alonso A, et al. Convectons in periodic and bounded domains[J]. Fluid Dynamics Research,2010,42: 025505. doi: 10.1088/0169-5983/42/2/025505.
    [32]
    Mercader I, Batiste O, Alonso A, et al. Convectons, anticonvectons and multiconvectons in binary fluid convection[J]. Journal of Fluid Mechanics,2011,667: 586-606.
    [33]
    Batiste O, Knobloch E, Alonso A, et al. Spatially localized binary-fluid convection[J]. Journal of Fluid Mechanics,2006,560: 149-158.
    [34]
    Bensimon D, Kolodner P, Surko C M, et al. Competing and coexisting dynamical states of travelling-wave convection in an annulus[J]. Journal of Fluid Mechanics,1990,217: 441-467.
    [35]
    胡彪, 宁利中, 宁碧波, 等. 水平来流对扰动成长和对流周期性的影响[J]. 应用数学和力学, 2017,38(10): 1103-1111.(HU Biao, NING Li-zhong, NING Bi-bo, et al. Effects of horizontal flow on perturbation growth and convection periodicity[J]. Applied Mathematics and Mechanics,2017,38(10): 1103-1111.(in Chinese))
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