[1] Research examining the hydraulics, morphology, and stability of step-pool mountain streams has blossomed in the last decade, resulting in more than a dozen dissertations. These, along with other research projects, have transformed our understanding of step-pool channels. Contributions have been made toward understanding depositional step formation and destruction, scour downstream of steps, step-pool hydraulics, and the effect of sediment transport on step stability. We propose that depositional steps exist in a jammed state whereby the boulders are structurally arranged within the channel and thereby stabilize it. Once a step has formed, a scour pool with a characteristic length and depth develops downstream, creating a zone where additional steps are unlikely to occur. Downstream of the scour hole, steps are more likely to occur as the high energy associated with the plunge pool has dissipated. Data suggest that the presence of cobbles or boulders limits pool scour as well as the degree to which well-defined, channelspanning step-pools form. We propose a state-space for step-pools in which conditions for a step to form include (1) the ratio between width and boulder diameter (the jamming ratio), (2) the ratio between applied shear stress and the stress needed to mobilize the bed (relative Shields number), and (3) the ratio between bed material supply and discharge (bed sediment concentration). Available data suggest this model is plausible. Emerging critical research questions are discussed.

No abstract

[1] We investigate the stability of step-pool channels by examining how the traditional approach to bed stability based on the critical Shields number is modified by particles jamming across the width of the channel. Experiments were conducted in a flume with slopes ranging between 3% and 18% and either smooth or rough walls. By varying the size of sediment and width of the flume we observed that the stability of the bed increases as the jamming ratio (channel width/D 84step is the diameter at which 84% of the step stones are smaller) decreases for jamming ratios less than six. At low jamming ratios both grainon-grain structuring and sediment entrainment phenomena affect the stability of the bed. Actual bed failure, however, depends upon the history of bed development and the chance arrangement of the stone structures in the bed. Thus, the experiments also demonstrate that the inherently stochastic nature of sediment transport affects not only the movement of individual grains but also the stability of the channel as a whole. Since stochastic processes affect the stability of the entire channel, there is no clearly defined separation between stable and unstable beds, rather, an overlapping field where both stable and unstable bed states can exist. This field was modeled using logistic regression to derive a probability of bed failure. A comparison of data from experiments with rough banks and smooth banks showed that rough banks significantly increase the stability of the bed.

[1] Frequently, an assessment of the mean water velocity in a stream is necessary to estimate the discharge associated with a particular flow depth or, conversely, the mean depth associated with a particular discharge. In the absence of a direct measurement of flow velocity, a flow resistance approach, which establishes the relation between depth and velocity, can be applied. Two approaches have been used in the past: traditional approaches based on the use of a resistance coefficient (e.g., Darcy-Weisbach) or dimensionless hydraulic geometry approaches. To examine if one approach is more appropriate for steep streams, data from 31 flume experiments conducted to examine flow resistance in self-formed cascade channels were analyzed. A dimensionless hydraulic geometry approach developed using at-a-station data to characterize the q* exponent and between-site data to characterize the exponent on the channel slope term was more accurate than more traditional approaches. The developed relation was similar to the established rational relation (v a g 0.2 q 0.6 s −0.4 S 0.2 ), suggesting that the rational relation has merit. The approach does not utilize a flow partitioning approach since, in steep streams with small relative depths, the grains themselves generate form and spill resistance. The observation that a single dimensionless hydraulic geometry flow resistance relation can describe measurements across a range of grain sizes and bed slopes (3-21%) suggests that steep streams may follow a single scaling relation similar to the regime equations associated with lowland rivers.

Temporal dynamics of sediment transport in steep channels using two experiments performed in a steep flume (8%) with natural sediment composed of 12 grain sizes are studied. High-resolution (1 s) time series of sediment transport were measured for individual grain-size classes at the outlet of the flume for different combinations of sediment input rates and flow discharges. Our aim in this paper is to quantify (a) the relation of discharge and sediment transport and (b) the nature and strength of memory in grainsize-dependent transport. None of the simple statistical descriptors of sediment transport (mean, extreme values, and quantiles) display a clear relation with water discharge, in fact a large variability between discharge and sediment transport is observed. Instantaneous transport rates have probability density functions with heavy tails. Bed load bursts have a coarser grain-size distribution than that of the entire experiment. We quantify the strength and nature of memory in sediment transport rates by estimating the Hurst exponent and the autocorrelation coefficient of the time series for different grain sizes. Our results show the presence of the Hurst phenomenon in transport rates, indicating long-term memory which is grain-size dependent. The short-term memory in coarse grain transport increases with temporal aggregation and this reveals the importance of the sampling duration of bed load transport rates in natural streams, especially for large fractions.