HYDRODYNAMIC INSTABILITY CHARACTERISTICS OF LAMINAR FLOW IN A MEANDERING CHANNEL WITH MOVING BOUNDARY
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摘要: 河流形态与水动力结构息息相关，形态约束水动力结构，水动力结构则通过泥沙运动进一步塑造形态，在自然界河流中形成一对辩证互馈关系.天然河流形态形式多样，大致可以分为顺直、微弯、分叉和散乱游荡几种类型，其中微弯及多个弯曲构成的河型为河流动力演化中最重要的一环.多个弯曲构成的河型可用正弦派生曲线来描述，它也是天然河流主槽与水动力结构复杂相互作用的结果.作为探讨这一过程的力学作用机理，构建摆动槽道并研究槽道摆动与其内部流动结构的互馈关系，既是流体力学研究的热点内容，也是目前河流动力过程研究的基础内容.在此重点讨论这一互馈关系前一部分，即水流对摆动边界的响应.文中建立了随体坐标系下摆动河槽与内部水流动力响应理论模型，通过给定摆动弯曲槽道的不同特征参数，研究讨论了正弦派生型摆动边界下的槽道水流动力稳定性特征，明确了弯曲槽道摆动对其内部主流及扰动水流结构的影响，确定弯曲槽道摆动波数、摆动频率对扰动流发展影响的相应参数定量关系，得到了槽道弯曲度和摆动特征对其内部水流不同尺度扰动影响的阈值选择性范围.Abstract: Configuration of river is closely related with hydrodynamic structures of flows, for the shape of a channel influences the flow structures in it, and the flow structures also affect the developing trend of the channel through the movement of sediment, forming a pair of dialectical interactions in the river system. The natural rivers are different in configurations, which can generally be divided into such types as straight, bending, branching and wandering. Among them, the bending river or the river composed of several curved channels, the result configuration of interaction between the natural river and the complex hydrodynamic flow structure in it, become one of the most important types in the study of river dynamics. As the basis of theoretical research, the establishment of model and the study on flows within a moving channel has become the focus not only from researchers of fluid mechanics, but also from investigators of river dynamics. Therefore, this study first established a theoretic model on the flow in a meandering channel with a moving boundary by using a streamwise-transverse coordinate system. It next discussed the hydro-dynamic instability characteristics of the laminar flow within the sine-generated moving boundaries. Then it quantitatively analyzed the influences of various character parameters to the velocity distributions of main flow. Finally, it obtained the selective influences from the curvature and meandering properties to the flow structure.
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图 2 一阶流速沿n方向分布 (复数空间)
Figure 2. Distribution of first-order velocities along n direction (complexspace)
图 3 一阶流速沿n方向分布 (幅值-相位空间)
Figure 3. Distribution of first-order velocities along n direction (amplitude-phase space)
图 4 一阶流速沿n方向分布 (复数空间)
Figure 4. Distributions of first-order velocities along n direction (complexspace)
图 5 一阶流速横向分布 (幅值-相位空间)
Figure 5. Distributions of first-order velocities (amplitude-phase space)
图 6 顺直河道中性曲线计算结果验证
Figure 6. Comparison of numerical results with data of straight channel
图 7 扰动频率$\omega_{Tr}$及扰动增长率$\omega_{Ti}$随摆动波数$\alpha_{\rm c}$的变化
(平面状态参数：$\theta_{\rm m}=0.1$, $\omega_{\rm c}=0$; 拟序扰动参数：$\alpha _{T }=1.02$, $ Re=5 772.222$)
Figure 7. Variation of disturbance frequency $\omega_{Tr}$ and growth rate $\omega_{Ti}$ with swinging wavenumber $\alpha_{\rm c}$
(for: $\theta_{\rm m}=0.1$, $\omega_{\rm c}=0$; $\alpha_{T }=1.02$, $ Re=5 772.222$)
图 8 临界雷诺数随摆动波数$\alpha_{\rm c}$的变化 (平面状态参数: $\theta_{\rm m}=0.1$, $\omega_{\rm c}=0$)
Figure 8. Variation of critical Reynolds number with swinging wave number $\alpha_{\rm c}$(for: $\theta_{\rm m}=0.1$, $\omega_{\rm c}=0$)
图 9 中性曲线随摆动波数$\alpha_{\rm c}$的变化 (平面状态参数：$\theta_{\rm m}=0.1$, $\omega_{\rm c}=0$, $0 \leq \alpha_{\rm c}\leq 0.5$)
Figure 9. Variation of neutral curve with swinging wave number $\alpha_{\rm c}$ (for: $\theta_{\rm m}=0.1$, $\omega_{\rm c}=0$, $0 \leq \alpha_{\rm c}\leq 0.5$)
图 10 临界扰动点随摆动波数$\alpha_{\rm c}$的变化
(平面状态参数：$\theta_{\rm m}=0.1$, $\omega_{\rm c}=0$)
Figure 10. Variation of critical point with swinging wave number $\alpha_{\rm c}$
(for: $\theta_{\rm m}=0.1$, $\omega_{\rm c}=0$)
图 11 扰动频率$\omega_{Tr}$和扰动增长率$\omega_{Ti}$随摆动频率$\omega_{\rm c}$的变化
(平面状态参数：$\theta_{\rm m}=0.1$, $-0.1 \leq \omega_{\rm c} \leq 0.1$; 拟序扰动参数：$\alpha_{T}=1.016$, $ Re=2 307$)
Figure 11. Variation of disturbance frequency $\omega_{Tr}$ and growth rate $\omega _{Ti}$ with swinging frequency $\omega_{\rm c}$
(for: $\theta_{\rm m}=0.1$, $-0.1 \leq \omega_{\rm c} \leq 0.1$; $\alpha _{T }=1.016$, $ Re=2 307$)
图 12 临界雷诺数$Re_{\rm cr}$随摆动频率$\omega_{\rm c}$的变化 (平面状态参数：$\theta_{\rm m}=0.1$, $\alpha_{\rm c}=0.3$)
Figure 12. Variation of critical Reynolds number $Re_{\rm cr}$ with swinging frequency $\omega_{\rm c}$ (for: $\theta_{\rm m}=0.1$, $\alpha_{\rm c}=0.3$)
图 13 中性曲线随摆动频率$\omega_{\rm c}$的变化 (平面状态参数：$\theta_{\rm m}=0.1$, $\alpha _{\rm c}=0.3$, $-0.02 \leq \omega_{\rm c}\leq 0.02$)
Figure 13. Variation of neutral curve with swinging frequency $\omega_{\rm c}$ (for:$\theta_{\rm m}=0.1$, $\alpha_{\rm c}=0.3$, $-0.02 \leq \omega_{\rm c}\leq 0.02$)
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