Upper flow regime bedform stability - Cyclic steps, their geometry and position in a bedform stability diagram
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Cyclic steps are upstream migrating bedforms of the upper flow regime, associated with slopes. They are characterized by trains of hydraulic jumps. Upstream of the hydraulic jump the flow is supercritical and the bed erodes, while downstream of the hydraulic jump the flow is subcritical and deposition takes place, resulting in an upstream migration of the bedform and the hydraulic jump. The formation of cyclic steps is empirically researched doing experiments using a tilting flume. Chute and Pools are described by Fukuaka et al. as a limiting case of cyclic steps for which the steepest bed slope realized just upstream of the hydraulic jump is still rather mild. Here, the definition of cyclic steps is discussed and a suggestion is made to use the term cyclic steps with the additional information of the state of the hydraulic jump, which can be ‘normal’ or ‘submerged’. The sensitivity of the cyclic step geometry is analyzed by the median sediment grain size and flow characteristics. The geometry of the cyclic step can be described by the length, the height, the slope and the position of the highest point. Per geometry characteristic the following parameters are tested: the flow specific discharge, the flow sediment volume concentration, the median sediment grain size, the average Froude number, the mobility parameter, the streampower, and the relative flow depth. This resulted in two functions using the streampower to obtain the cyclic step’s length and height. Based on the experiments, a bedform stability diagram is created for the upper flow regime using streampower and slope to plot upper plane bed, antidunes, cyclic steps with a normal and with a submerged hydraulic jump.