【作者】 徐海珏；

【导师】 白玉川；

【作者基本信息】 天津大学 ， 水力学及河流动力学， 2004， 硕士

【摘要】 水流作用下的床面并非完全平整，往往存在各种不同的形态，最为常见的就是沙纹和沙垄等。它们广泛存在于河道中，决定着床面的阻力、泥沙的运动以及水流的流动结构。 对于理想的平整床面情况，在流动开始不久后，由于外界的扰动作用，层流失稳，床面出现沙纹。而沙纹的出现，又将改变了原来平整床面层流失稳的“轨迹”。 本论文以沙纹状床面为背景，探讨了明渠层流的失稳问题，该研究有助于了解河流底层流动与床面形态发生变化的动力机制。 在理论分析方面，采用了非线性科学中 Floquet 理论。在计算方法方面，采用了谱方法、Muller 法和 QR 方法。 通过理论分析与数值计算，本文得到如下重要结论： (1).对于明渠层流稳定性的特征值问题,无论是平底床面还是波状沙纹床面,层流是否失稳主要与雷诺数有关,而与佛汝德数无关。 (2).床面起伏对明渠层流稳定性特征(扰动波的频率和增长率)都有较大的影响。 (3).床面起伏(沙纹高度)对中性曲线将产生较大的影响。由于沙纹的存在，床面起伏所引起的边界扰动作用致使明渠层流在较低的雷诺数下失稳,而且随着床面起伏(沙纹高度)的增加,中性曲线趋直,对扰动波的波数变得不敏感。 (4).床面起伏(沙纹高度)的大小,对于扰动波频率、增长率等值线的分布特征也有较大的影响。 (5).在沙纹床面情况下，雷诺数对于扰动增长率和扰动波的频率都有影响，随着雷诺数的增加，扰动增长率呈增长趋势；而扰动频率则呈减小趋势。 (6).沙波的传播频率也会影响明渠层流的稳定性状态。对于扰动波频率来说,随着床面沙纹变化频率的增加而呈先增后减的趋势；而对于扰动增长率来说,床面起伏变化频率越大,扰动发展的增长率增长很快。 这些结论为今后深入研究黄河下游河道的河床演变、河床-水流相互作用如“假潮”现象打下了坚实的理论基础。更多还原

【Abstract】 Riverbed is not so even, and it is always accompanied by certain forms, such assand ripple, sand dune and so on, which determine the resistance of the riverbed, themovement of the sediment and the structure of the current etc. Even it is on an even bed, flow will become unstable and sand ripples willappear because of the external disturbances soon after the flow begins, which alsochanges the instability trace of the laminar flow on it. The instability of the laminar flow on the sand ripples in the open channel isdiscussed in this paper, which can help us understand the dynamical principles thatthe flow interacts with the riverbed. Floquet Theory is used to analyze the problem and spectral collocation method,Muller method and QR method are adopted to calculate the model that established. Through the theoretic analyzing and the numerical calculating, some importantconclusions are reached:（1）The characteristics of the laminar instability in the open channel has relationshipwith Reynolds number and has nothing to do with Froude number whether it is on theplane bed or on the sand ripples.（2）The bed amplitude has deep effect on the characteristic of the laminar instability(the circular frequency and the growth rate of the disturbance wave) in the openchannel.（3）The bed amplitude (height of sand ripples) contributes a lot to the neutral curve.The boundary disturbance caused by the bed amplitude can make the laminar flowbecome unstable under a rather lower Reynolds number; moreover the neutral curvewill become straight and not so sensitive to the wave number with the increase of thebed amplitude.（4）The bed amplitude make it different in the distribution of the contour of thecircular frequency and the growth rate of the disturbance wave.<WP=4>（5）Reynolds number has effect on the circular frequency and the growth rate whenit is on sand ripples. With the increase of the Reynolds number, the growth rateincreases significantly, and the circular frequency decreases.（6）The propagation frequency of the sand ripples also effects the stability conditionof the laminar flow in open channel. With the increase of the propagation frequency,the disturbance frequency increases first and then decreases, and the growth rateincreases significantly. These conclusions set a foundation on the later theoretical researches on the bedevolution in the lower reach of Yellow River near estuary and the interaction of theriverbed and the current.更多还原