HU Biao, NING Li-zhong, NING Bi-bo, TIAN Wei-li, WU Hao, NING Jing-hao. Effects of Horizontal Flow on Perturbation Growth and Convection Periodicity[J]. Applied Mathematics and Mechanics, 2017, 38(10): 1103-1111. doi: 10.21656/1000-0887.370314
Citation: HU Biao, NING Li-zhong, NING Bi-bo, TIAN Wei-li, WU Hao, NING Jing-hao. Effects of Horizontal Flow on Perturbation Growth and Convection Periodicity[J]. Applied Mathematics and Mechanics, 2017, 38(10): 1103-1111. doi: 10.21656/1000-0887.370314

Effects of Horizontal Flow on Perturbation Growth and Convection Periodicity

doi: 10.21656/1000-0887.370314
Funds:  The National Natural Science Foundation of China(10872164)
  • Received Date: 2016-10-17
  • Rev Recd Date: 2016-12-01
  • Publish Date: 2017-10-15
  • Numerical simulation of the 2D fully hydrodynamic equations for the pure fluid in a rectangular channel with horizontal flow for Prandtl number Pr=0.0272 was conducted. Growth and spatiotemporal evolution of the 1D traveling wave patterns in the RayleighBenard convection of the pure fluid were investigated. It is found that the convective growth process can be divided into 3 stages: the development stage, the exponential growth stage and the periodic variation stage. Through analysis on the variation of the maximum vertical velocity field with time for different relative Rayleigh numbers Rar in the exponential growth stage, a formula of variation of linear growth rate γm was obtained with respect to Rar. Furthermore, the traveling wave convection periodicity and its dependence on the horizontal flow Reynolds number were revealed.
  • loading
  • [1]
    Chandrasekhar S. Hydromagnetic Stability [M]. Oxford: Oxford University Press, 1961: 1-100.
    [2]
    Cross M C, Hohenberg P C. Pattern formation outside of equilibrium[J]. Reviews of Modern Physics, 1993,65(3): 998-1011.
    [3]
    Assenheimer M, Steinberg V. Transition between spiral and target states in Rayleigh-Bénard convection[J]. Nature,1994,367: 345-347.
    [4]
    NING Li-zhong, Harada Y, Yahata H, et al. Fully-developed traveling wave convection in binary fluid mixtures with lateral flow[J]. Progress of Theoretical Physics,2001,106(3): 503-512.
    [5]
    NING Li-zhong, Harada Y, Yahata H, et al. The spatio-temporal structure of binary fluid convection with horizontal flow[J]. Journal of Hydrodynamics,2004,16(2): 151-157.
    [6]
    Barten W, Lucke M, Kamps M. Localized traveling-wave convection in binary fluid mixtures[J]. Physical Review Letters,1991,66(20): 2621-2624.
    [7]
    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.
    [8]
    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.
    [9]
    Jung D, Lücke M. Localized waves without the existence of extended waves: oscillatory convection of binary mixtures with strong soret effect[J]. Physical Review Letters,2002,89(5): 054502-1-054502-4.
    [10]
    Batiste O, Knobloch E, Mercader I, et al. Simulations of oscillatory binary fluid convection in large aspect ratio containers[J]. Physical Review E,2001,65(1): 016303.
    [11]
    Taraut A V, Smorodin B L, Lücke M. Collisions of localized convection structures in binary fluid mixtures[J]. New Journal of Physics,2012,14(9): 093055.
    [12]
    Knobloch E, Mercader I, Batiste O, et al. Convectons in periodic and bounded domains[J]. Fluid Dynamics Research,2010,42: 025505-1-025505-10.
    [13]
    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.
    [14]
    Jung C, Lücke M, Büchel P. Influence of through-flow on linear pattern formation properties in binary mixture convection[J]. Physical Review E,1996,54(2): 1510-1529.
    [15]
    Buchel P, Lucke M. Influence of through flow on binary fluid convection[J]. Physical Review E,2000,61(4): 3793-3810.
    [16]
    LI Guo-dong. Traveling-wave patterns in binary mixture convection with through flow[J]. Progress of Theoretical Physics,2001,106(2): 293-313.
    [17]
    LI Guo-dong, Ogawa A, Harada Y. Nonlinear convective states in a fluid mixture with through flow[J]. Progress of Theoretical Physics,2001,106(6): 1115-1128.
    [18]
    李国栋, 黄永念. 有水平流时双流体混合物对流的时空演变[J]. 力学进展, 2004,34(2): 263-269.(LI Guo-dong, HUANG Yong-nian. Spatiotemporal evolution in binary fluid mixture convection with through-flow[J]. Advances in Mechanics,2004,34(2): 263-269.(in Chinese))
    [19]
    赵秉新. 水平流作用下的混合流体行进波对流[J]. 水动力学研究与进展, 2012,27(3): 264-274.(ZHAO Bing-xin. Traveling wave convection in binary fluid mixtures with lateral flow[J]. Chinese Journal of Hydrodynamics,2012,27(3): 264-274.(in Chinese))
    [20]
    宁利中, 周洋, 王思怡, 等. Poiseuille-Rayleigh-Benard流动中的局部行波对流[J]. 水动力学研究与进展, 2010,25(3): 299-306.(NING Li-zhong, ZHOU Yang, WANG Si-yi, et al. Localized traveling wave convection in Poiseuille-Rayleigh-Benard flows[J]. Chinese Journal of Hydrodynamics,2010,25(3): 299-306.(in Chinese))
    [21]
    NING Li-zhong, QI Xin, Harada Y, et al. A periodically localized traveling wave state of binary fluid convection with horizontal flows[J]. Journal of Hydrodynamics(Ser B),2006,18(2): 199-205.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (760) PDF downloads(1069) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return