Morphology and origin of alluvial step-pools: A synthesis of experimental and field data from formative flows

An understanding of step-pool geometry has important practical applications in ecological restoration, erosion control and hazard assessment in mountain streams. However, published analysis is insufficient: (1) fully to identify the controls on step-pool geometry, and; (2) to allow inference to be made as to the origin of step-pools and the hydraulic conditions during step-pool formation. The choice of length scales used for normalisation in previous studies has often been ad hoc. In addition, formative discharge is likely to be an important morphological control variable, and field investigations are hampered by a lack of direct knowledge of it. This investigation therefore synthesises data from experimental studies of alluvial step-pools, where formative conditions are known, and uses rigorously identified dimensionless variables to identify: (1) the magnitude and mechanism of the stabilising effect of step-pools; (2) the controls on step-pool geometry; (3) the mechanism(s) responsible for step-pool formation and; (4) the formative flow regime(s) and hydraulic domain of step-pool formation. Bed mobility in formative flows is controlled by the quantity D-100/h(c), where D-100 is the diameter of the largest grains in the sediment mixture and hc is the formative critical flow depth, for which we introduce the term "formative roughness". Formative flows are competent to move all grain sizes for D-100/h(c) <= 1.3. There is a limiting channel slope that can be stabilised by step-pools, the central tendency of which is given by the Shields type relationship S-lim = 0.06(D-100/h(c)). This limiting slope indicates that the stabilising effect of step-pools is comparable to that achieved by replacing the bulk sediment mixture in a plane-bed channel with uniform grains of intermediate diameter D-100/2. The stabilising effect appears to be due the grains being arranged in stable configurations rather than the energy dissipation (form roughness) of step-pools. Step height H in experimental step-pools primarily is controlled by the size of the largest transported grains D-100t, such that H approximate to D-100t. Step spacing L appears to scale with hc. Dimensionless step spacing data L/h(c) are collapsed well by the formative flow final Froude number dFr. The relationship between L/h(c) and Fr shows the existence of two regimes: L/h(c) is greater than minimum antidune spacing but decreases rapidly with increasing Fr for Fr < 0.9 (region 1), but is a weak function of Fr and close to the minimum antidune spacing for Fr > 0.9 (region 2). We argue that step formation via substrate-based mechanisms is consistent with step spacing in region 1, and therefore while substrate-based step formation mechanisms alone are active in the low Fr part of region 1, these mechanisms are progressively replaced by the antidune mechanism as Fr increases, with the antidune mechanism being dominant throughout region 2. Thus, we provide a unifying theory for substrate-based mechanisms and the antidune mechanism. Dimensionless step spacing data do not support the jammed state hypothesis (Church and Zimmerman, 2007), the simplified cascade model (Allen, 1983), the upstream-forced cascade model (Marion et al., 2004; Comiti et al., 2005) or the maximum flow resistance model (Abrahams et al., 1995) of step formation. There is an associated transition with increasing Fr in the dominant flow regime during step formation from tumbling flow to standing waves. However, even where standing waves are dominant during step formation, the final flow regime over the stabilised bed depends on dimensionless step height H/h(c): for H/h(c) > 1.1 tumbling flow develops from the standing waves, while for H/h(c) < 1.1 tumbling flow is drowned out and standing waves persist as the final flow regime. There is no lower formative discharge limit to step-pools; rather, step-pools grade into cascades as Fr decreases. The upper formative discharge limit for step-pools is in the range 0.7 < (D-100/h(c))(lim) < 1.0. We suggest that well developed step-pools are anchored and immobilised antidunes, while at formative roughness D-100/h(c) < (D-100/h(c))(lim), antidunes remain unanchored and mobile.