EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

蜿蜒边界下平面流的线性流动稳定性

冀自青 白玉川 徐海珏

冀自青, 白玉川, 徐海珏. 蜿蜒边界下平面流的线性流动稳定性. 力学学报, 2023, 55(2): 1-13 doi: 10.6052/0459-1879-22-570
引用本文: 冀自青, 白玉川, 徐海珏. 蜿蜒边界下平面流的线性流动稳定性. 力学学报, 2023, 55(2): 1-13 doi: 10.6052/0459-1879-22-570
Ji Ziqing, Bai Yuchuan, Xu Haijue. Linear global instability of the plane flow with meandering wall. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 1-13 doi: 10.6052/0459-1879-22-570
Citation: Ji Ziqing, Bai Yuchuan, Xu Haijue. Linear global instability of the plane flow with meandering wall. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 1-13 doi: 10.6052/0459-1879-22-570

蜿蜒边界下平面流的线性流动稳定性

doi: 10.6052/0459-1879-22-570
基金项目: 国家自然科学基金资助项目(51979185, 51879182, 52109097)
详细信息
    作者简介:

    通讯作者: 冀自青, 主要研究方向: 河流动力学、流体力学、泥沙运动力学. E-mail: jiziqing2008@163.com

    通讯作者: 白玉川, 主要研究方向: 河流动力学、泥沙运动力学、海岸动力学. E-mail: ychbai@tju.edu.cn

    通讯作者: 徐海珏, 主要研究方向: 河流动力学、泥沙运动力学、海岸动力学. E-mail: xiaoxiaoxu_2004@163.com

  • 中图分类号: O352

LINEAR GLOBAL INSTABILITY OF THE PLANE FLOW WITH MEANDERING WALL

  • 摘要: 为便于数值分析, 蜿蜒河流水动力和演变模型中一般隐性假设二次时均流−二次涡的关系与明渠流时均流-明渠湍流的关系相同, 但由于高雷诺数下的DNS算力限制和实验尺度限制, 这种隐含假设是否成立目前尚无相关湍流研究来支撑. 文章试图通过分析明渠湍流和二次湍流发展初期的研究, 侧面揭示其湍流结构的异同. 通过对曲线正交坐标系下的平面二维NS方程使用双参数摄动的方法, 建立了一种求解蜿蜒边界弱非线性层流的摄动解法, 并推导得出一个适用于蜿蜒边界的控制方程EOS以及其特征值问题的解法. 蜿蜒边界下弱非线性层流解为一系列蜿蜒谐波分量的叠加, 其中线性部分使得两壁产生流速差, 非线性部分随着雷诺数增大呈指数增长. 水流的扰动增长率特征谱的第一模态与直道流相似, 由3条曲线、4个波段合成, 但其长波段和短波段的扰动流场与直道流不同, 所有短波段的扰动流速近似于KH涡. 蜿蜒边界对内部水流扰动有一定的选择性. 偏角幅值越大扰动增长越快; 蜿蜒波数的影响则为先增后减, 有一个使扰动增长最快的蜿蜒波数. 扰动流场由一个典型的TS波和一对波包形式的二次涡叠加而成, 波包只有纵向流速分量, 包络线由蜿蜒波数控制, 波包内是与直道扰动波参数相同的TS波.

     

  • 图  1  正弦派生曲线边界平面示意图

    Figure  1.  Sketch of the orthogonal curvilinear coordinate system with meandering wall

    图  2  弱非线性层流解中分解量${\bar {\boldsymbol{q}}_{00}},{\bar {\boldsymbol{q}}_{11}},{\bar {\boldsymbol{q}}_{20}}$

    Figure  2.  The weakly nonlinear laminar solution

    图  3  参数(R, αc)对线性层流解${\bar {\boldsymbol{q}}_{11}}$的影响

    Figure  3.  Counter of the linear laminar solution effected by parameters (R, αc)

    图  4  参数(R, αc)对非线性层流解$ {\bar {\boldsymbol{q}}_{20}} $的影响

    Figure  4.  Counter of the nonlinear laminar solution effected by parameters (R, αc)

    图  5  直道流(OS方程)的扰动增长率特征谱和横向扰动流速分布

    Figure  5.  Spectrum of growth rate and profile of transverse velocity from OS equation

    图  6  蜿蜒边界下(EOS方程)的扰动增长率特征谱和横向扰动流速分布

    Figure  6.  Spectrum of growth rate and profile of transverse velocity from EOS equation

    图  7  蜿蜒边界下扰动增长率和相速度的云图

    Figure  7.  Contour of growth rate and phase speed of disturbance between meandering walls

    图  8  蜿蜒波数αc对扰动特征值的影响

    Figure  8.  Effect of meander wavenumber αc on growth rate and phase speed

    图  9  偏角幅值θc对扰动特征值的影响

    Figure  9.  Effect of angular amplitude θc on growth rate and phase speed

    图  10  平面形态参数(θc, αc)对中性曲线的影响

    Figure  10.  Effect of parameters (θc, αc) on neutral curve

    图  11  扰动波的形状函数

    Figure  11.  Shape function of disturbance velocity components

    图  12  二次涡向下游传播形成的波包

    Figure  12.  Wave pack of the secondary turbulent vortex

    表  1  无量纲参数及其物理意义汇总

    Table  1.   dimensionless parameters and physical significance

    Dimensionless parametersFormulaPhysical significance
    αcB*/M*meandering wavenumber
    θcθcmeandering amplitude
    R$U_m^* $B**Reynolds number
    F$U_m^* $/( g*B*)1/2Froude number
    cmαcθccurvature amplitude
    εu'/ u0disturbance to mean flow
    下载: 导出CSV
  • [1] Leopold LB, Wolman MG. River meanders. Geol Soc A M Bull, 1960, 71: 769-794 doi: 10.1130/0016-7606(1960)71[769:RM]2.0.CO;2
    [2] Langbein WB, Leopold LB. River meanders-theory of minimum variance. Geographical Review, 1967, 57(2): 279
    [3] Hafez Y. Excess energy theory for river curvature and meandering. Journal of Hydrology, 2022, 608(1): 127604
    [4] Ikeda S, Parker G, Kenji Sawai K. Bend theory of river meanders. Part 1. Linear development. Journal of Fluid Mechanics, 1981, 112: 363-377
    [5] Parker G, Sawai K, Ikeda S. Bend theory of river meanders. Part 2. Nonlinear deformation of finite-amplitude bends. Journal of Fluid Mechanics, 1982, 115: 303-314
    [6] Johannesson H, Parker G. Linear theory of river meanders//(Parker G. and Ikeda S eds.) River Meandering. American Geophysical Union, Washington, D. C. 1989
    [7] Seminara G. Meanders. Journal of Fluid Mechanics, 2006, 554: 271-297 doi: 10.1017/S0022112006008925
    [8] Pittaluga BM, Nobile MG, Seminara G. A nonlinear model for river meandering. Water Resources Research. 2009, 45, W04432
    [9] Chen, D, Duan JD. Simulating sine-generated meandering channel evolution with an analytical model. Journal of Hydraulic Research, 2006, 44(3): 363-373 doi: 10.1080/00221686.2006.9521688
    [10] Hooke RB. Distribution of sediment transport and shear stress in a meander bend. Journal of Geology, 1975, 83: 543-565 doi: 10.1086/628140
    [11] Abad JD, Garcia MH. Experiments in a high-amplitude kinoshita meandering channel: 1. implications of bend orientation on mean and turbulent flow structure. Water Resources Research, 2009, 45: W02401
    [12] Abad JD, Garcia MH. Experiments in a high-amplitude Kinoshita meandering channel: 2. Implications of bend orientation on bed morphodynamics. Water Resources Research, 2009, 45: W02402
    [13] 许栋, 白玉川, 谭艳. 正弦派生曲线弯道中水沙运动特性动床试验, 天津大学学报, 2010, 43(9): 762-770

    Xu Dong, Bai Yuchuan, Tan Yan. Experiment on characteristics of flow and sediment movement in sine-generated meandering channels with movable bed. Journal of Tianjin University, 2010, 43(9): 762-770. (in Chinese))
    [14] Pan Y, Liu X, Yang K. Effects of discharge on the velocity distribution and riverbed evolution in a meandering channel. Journal of Hydrology, 2022, 607: 127539 doi: 10.1016/j.jhydrol.2022.127539
    [15] Yalin MS. River Mechanics. UK: Oxford, Pergamon Press, 1992
    [16] Julien P. River Mechanics. UK: Cambridge University Press, 2002
    [17] Duan Y, Chen Q, Li D, et al. Contributions of very large-scale motions to turbulence statistics in open channel flows. Journal of Fluid Mechanics, 2020, 892: A3 doi: 10.1017/jfm.2020.174
    [18] Orszag SA. Accurate solution of the Orr-Sommerfeld stability equation. Journal of Fluid Mechanics, 1971, 50(4): 689-703 doi: 10.1017/S0022112071002842
    [19] Reynolds WC, Potter MC. Finite-amplitude instability of parallel shear flows. Journal of Fluid Mechanics, 1967, 27: 465-492 doi: 10.1017/S0022112067000485
    [20] Nishioka M, Ichikawa Y. An experimental investigation of the stability of plane Poiseuille flow. J Fluid Mech, 1975, 72: 731-751 doi: 10.1017/S0022112075003254
    [21] Stuart JT. Nonlinear stability theory. Annual Review of Fluid Mechanics, 1971, 3: 347-70 doi: 10.1146/annurev.fl.03.010171.002023
    [22] Herbert T. Secondary instability of boundary layers. Annual Review of Fluid Mechanics, 1988, 20: 487-526 doi: 10.1146/annurev.fl.20.010188.002415
    [23] Herbert T. Parabolized stability equations. Annual Review of Fluid Mechanics, 1997, 29: 245-83 doi: 10.1146/annurev.fluid.29.1.245
    [24] Smith FT, Stewart PA. The resonant-triad nonlinear interaction in boundary-layer transition. Journal of Fluid Mechanics, 1987, 179: 227-52 doi: 10.1017/S0022112087001502
    [25] Smith FT, Blennerhassett P. Nonlinear interaction of oblique three-dimensional Tollmien-Schlichting waves and longitudinal vortices, in channel flows and boundary layers. Proceedings of The Royal Society A, 1992, 436: 585-602
    [26] Hall P, Smith FT. Nonlinear Tollmien-Schlichting/vortex interaction in boundary-layers. European Journal of Mechanics - B, 1989, 8: 179-205
    [27] Hall P, Smith FT. On strongly nonlinear vortex/wave interactions in boundary-layer transition. Journal of Fluid Mechanics, 1991, 227: 641-66 doi: 10.1017/S0022112091000289
    [28] Wu X. Viscous effects on fully coupled resonant-triad interactions: an analytical approach. Journal of Fluid Mechanics, 1995, 292: 377-407 doi: 10.1017/S0022112095001571
    [29] Wu X, Stewart PA, Cowley SJ. On the weakly nonlinear development of Tollmien-Schlichting wavetrains in boundary layers. Journal of Fluid Mechanics, 1996, 323: 133-71 doi: 10.1017/S0022112096000870
    [30] Wu X. Nonlinear theories for shear flow instabilities: Physical insights and practical implications. Annu. Rev. Fluid Mech. 2019. 51: 451–85
    [31] Theofilis V. Advances in global linear instability of nonparallel and three-dimensional flows. Progress in Aerospace Sciences, 2003, 39(4): 249-315 doi: 10.1016/S0376-0421(02)00030-1
    [32] Theofilis V. Global linear instability. Annual Review of Fluid Mechanics, 2011, 43: 319-52 doi: 10.1146/annurev-fluid-122109-160705
    [33] Tezuka A, Suzuki K. Three-dimensional global linear stability analysis of flow around a spheroid. AIAA Journal, 2006, 44: 1697-1708 doi: 10.2514/1.16632
    [34] He W, Timme S. Triglobal infinite-wing shock-buffet study. Journal of Fluid Mechanics, 2021, 925: A27 doi: 10.1017/jfm.2021.678
    [35] Thomas C, Andrew P, Bassom PJ, et al. The linear stability of oscillatory Poiseuille flow in channels and pipes. Proceedings of The Royal Society A, 2011, 467: 2643-2662 doi: 10.1098/rspa.2010.0468
    [36] Bai Y, Xu H. A study on the stability of laminar open-channel flow over a sandy rippled bed. Science China Technological Sciences, 2005(1): 83-103
    [37] Xu H, Bai Y. Stability characteristics of the open channel flow above the asymmetrical irregular sand ripples. Science China Physics, Mechanics & Astronomy, 2010, 53(8): 1515-1529
    [38] Cecconi F, Blakaj V, Gradoni G, et al. Diffusive transport in highly corrugated channels. Physics Letters A, 2019, 383(11): 1084-1091 doi: 10.1016/j.physleta.2018.12.041
    [39] Okechi NF, Asghar S. Oscillatory flow in a corrugated curved channel. European Journal of Mechanics - B, 2020, 84: 81-92 doi: 10.1016/j.euromechflu.2020.05.005
    [40] Bai Y, Ji Z, Zhang M. A type of dynamic mechanism of river hydraulic geometry Science China Technological Sciences, 2014, 57(4): 847-855
    [41] 白玉川, 冀自青, 徐海珏. 摆动河槽水动力稳定性特征分析. 力学学报, 2017, 49(2): 274-288 (Bai Yuchuan, Ji Ziqing, Xu Haijue. Hydrodynamic instability characteristics of laminar flow in a meandering channel with moving boundary. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 274-288 (in Chinese) doi: 10.6052/0459-1879-16-105
    [42] 李彬, 徐海珏, 白玉川等. 常曲率弯道二维流动稳定性与非线性演化规律分析. 力学学报, 2021, 53(1): 168-183 (Li Bin, Xu Haijue, Bai Yuchuan, et al. Analysis of hydrodynamic instability and nonlinear evolution characteristics of two dimensional flow in constant curvature bend. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(1): 168-183 (in Chinese)
  • 加载中
图(12) / 表(1)
计量
  • 文章访问数:  58
  • HTML全文浏览量:  21
  • PDF下载量:  8
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-12-01
  • 录用日期:  2023-01-10
  • 网络出版日期:  2023-01-11

目录

    /

    返回文章
    返回