Irregular bed forms in steep, rough channels: 1. Stability analysis
Irregular bed forms in steep, rough channels: 1. Stability analysis
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陡峭、崎岖河道中的不规则河床形态： 1. 稳定性分析
DOI：
10.1029/98wr02339
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发表时间：
1998
影响因子：
5.4
通讯作者：
D. Furbish
中科院分区：
文献类型：
--
作者：
D. Furbish
针对山区河流粗糙河床条件对深度积分动量方程进行的尺度分析表明，由深度积分产生的某些速度相关项，在较为平滑的冲积河道情况下通常可被忽略，但在这些陡坡河道中却可能是动量平衡的重要组成部分。通过引入时均运动的动能方程来处理这些相关项（这些相关项涉及速度分量相对于深度平均值的局部偏差的乘积），得到了一个能恰当表征顺流加速度的水流模型。利用保留顺流相关项的水流模型进行的线性稳定性分析表明，它们的作用是强化河床形态波长的初始选择，这体现在增长率与河床形态波长曲线的峰值变尖上。迁移率为零的波长接近具有最大增长率的波长；因此固定沙坝的选择作用很强。河床形态生长所需的临界宽深比明显小于忽略相关项时所预测的临界比。此外，在给定的宽深比下，更宽范围的波数可被激活，而且代表河心洲的河床形态模式在比原本预测更窄的河道中也可被激活。因此，交错沙坝最初可与河心洲“竞争”，特别是在低泥沙输移率的情况下。这种竞争可能导致了粗糙的山区河道典型的河床地形的复杂性。
A scaling analysis of the depth‐integrated momentum equations tailored to the rough bed conditions of mountain streams suggests that certain velocity correlation terms that arise from depth integration, and which normally can be neglected in the case of smoother alluvial channels, can be a significant part of the momentum balance in these steep channels. By introducing the kinetic energy equation of the time‐averaged motion to treat these correlation terms, which involve products of local deviations in velocity components about depth‐averaged values, a flow model that suitably characterizes streamwise accelerations is obtained. A linear stability analysis using a flow model that retains the streamwise correlation terms suggests that their effect is to strengthen the initial selection of bed form wavelengths, as reflected by sharpened peaks in curves of growth rate versus bed form wavelength. Wavelengths with zero migration rate are close to wavelengths having the largest growth rate; thus selection of fixed bars is strong. Critical width‐depth ratios necessary for bed form growth are significantly less than the critical ratios that are predicted when correlation terms are neglected. Moreover, a broader band of wavenumbers can be activated at a given width‐depth ratio, and bed form modes representing midchannel bars can be activated in a narrower channel than would otherwise be predicted. Thus alternate bars can initially “compete” with midchannel bars, particularly at low sediment transport rates. This competition probably contributes to the complexity of bed topography that is typical of rough, mountain channels.