The hydraulics of steep mountain streams differ from lower gradient rivers due to shallow and rough flows, energetic subsurface flow, and macro-scale form drag from immobile boulders and channel- and bed-forms. Heightened flow resistance and reduced sediment transport rates in steep streams are commonly attributed to macro-scale form drag; however, little work has explored steep river hydrodynamics in the absence of complex bed geometries. Here we present theory for the vertical structure of flow velocity in steep streams with planar, rough beds that couples surface and subsurface flow. We test it against flume experiments using a bed of fixed cobbles over a wide range of bed slopes (0.4 – 30%). Experimental flows have a nearly logarithmic velocity profile far above the bed; flow velocity decreases less than logarithmically towards the bed and is non-zero at the bed surface. Velocity profiles match theory derived using a hybrid eddy-viscosity model, in which the mixing length is a function of height above the bed and bed roughness. Subsurface flow velocities are large (> 1 m/s) and follow a modified Darcy-Brinkman-Forchheimer relation that accounts for channel slope and shear from overlying surface flow. Near-bed turbulent fluctuations decrease for shallow, rough flows and scale with the depth-averaged flow velocity rather than bed shear velocity. Flow resistance for rough, planar beds closely matches observations in natural steep streams despite the lack of bed- or channel-forms in the experiments, suggesting that macro-scale form drag is smaller than commonly assumed in stress partitioning models for sediment transport.
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机译：陡峭的山间溪流的水力与低坡度的河流不同，这归因于浅，粗糙的水流，高能量的地下水流以及不动的巨石以及河床和河床形式的宏观形式阻力。在陡流中增加的流动阻力和降低的泥沙输送速率通常归因于宏观形式的阻力。然而，在没有复杂的床层几何结构的情况下，很少有工作探索陡河的水动力。在这里，我们介绍了陡峭的水流的垂直结构的理论，陡峭的水流具有耦合地面和地下流的平面粗糙床。我们使用固定的鹅卵石床在较大的床坡度范围内（0.4 – 30％）针对水槽实验进行了测试。实验流在床层上方有接近对数的速度分布；朝向床的流速降低小于对数，并且在床表面非零。速度分布匹配使用混合涡流-粘度模型得出的理论，其中混合长度是床上方高度和床粗糙度的函数。地下流速很大（> 1 m / s），并且遵循修正的Darcy-Brinkman-Forchheimer关系，该关系说明了通道坡度和上覆地表流的剪切力。对于浅水，粗糙水流，近地层湍流波动减小，并且随深度平均流速而不是地层剪切速度成比例变化。尽管实验中缺乏床或通道形式，但粗糙的平面床的流动阻力与自然陡流中的观测结果非常匹配，这表明宏观形式的阻力小于沉积物运输的应力分配模型中通常假定的阻力。
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