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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(5): 1075-1086 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(5): 1075-1086 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(5): 1075-1086 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(5): 1075-1086 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(51979185, 51879182, 52109097), 天津大学水利安全与仿真国家重点实验室开放基金(HESS-2211, HESS-1606)资助项目
详细信息
    作者简介:

    通讯作者: 徐海珏, 教授, 主要研究方向为河流动力学、泥沙运动力学和海岸动力学. 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EOS方程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 ${{\bar{{\boldsymbol{q}}}}_{00}},{{\bar{{\boldsymbol{q}}}}_{11}},{{\bar{{\boldsymbol{q}}}}_{20}} $

    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 ${\bar {\boldsymbol{q}}_{{11}}}$ 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 ${\bar {\boldsymbol{q}}_{{20}}}$ 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
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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
  • 刊出日期:  2023-05-18

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