Velocity and flow resistance in step-pool streams Amanda J. Lee 1 , Robert I. Ferguson * Department of Geography, University of Sheffield, Winter Street, Sheffield S10 2TN, UK Abstract Flow resistance in steep streams with step-pool morphology consists of form drag as well as skin friction. It therefore alters rapidly as discharge increases and is not expected to show constant Manning’s n or simple log law behaviour, but there is no widely accepted alternative representation. We report measurements of at-a-station hydraulic geometry, n, and (1/f ) 0.5 for a range of discharges at each of six field sites and in flume experiments loosely Froude-scaled to the prototypes. Velocity and resistance vary strongly with discharge in all cases. The flume data extend to formative flows, and when rescaled extend the range of the field data, but plot in line with them. This suggests a single resistance law can describe the full range from trickle to formative flow. Equations based on the log law with k s ~step D 84 perform unexpectedly well, especially when allowance is made for flow blocking and/or the k s /D 84 multiplier is optimised separately for each site. The latter suggests step D 84 is not a good summary representation of effective roughness, but none of a variety of alternative grain-size and microtopographic measures performed much better. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Velocity; Flow resistance; Steps and pools; Froude scaling; Hydraulic geometry; Microtopography 1. Introduction Small steep streams in which individual clasts protrude through most or all of the flow depth are mor- phologically and hydraulically distinctive (Judd and Peterson, 1969; Church, 1992; Bathurst, 1993; Mont- gomery and Buffington, 1997; Wohl, 2000). They usually have closely spaced bed steps formed by a single layer of the biggest clasts and separated by pools whose bed material is relatively finer. Flow is resisted not only by the shear drag or skin resistance which is quantified by the well-known logarithmic ‘law of the wall,’ but also by form drag associated with pressure differences around individual large bed elements (LBEs) and manifested in frequent wakes, jets and standing waves (Judd and Peterson, 1969; Wohl, 2000). At higher flows, the smaller obstacles become submerged and a faster ‘skimming’ flow can develop over them, so that velocity increases more rapidly with discharge than in larger rivers. Standard flow-resistance formulae used for engi- neering calculations, palaeohydraulic inferences, fish- habitat assessment and other purposes make no explicit allowance for these special circumstances in steep streams and might, therefore, not be expected to perform well. There is, however, no widely accepted alternative approach. Judd and Peterson (1969) argued that whilst flow in steep streams is locally nonuniform and unsteady, it is macroscopically uniform within a reach. Reach-averaged velocity should, therefore, be predictable from depth, slope and one or more resist- 0169-555X/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII:S0169-555X(02)00054-5 * Corresponding author. E-mail address: r.ferguson@shef.ac.uk (R.I. Ferguson). 1 Now with Accenture consultants, Sydney, Australia. www.elsevier.com/locate/geomorph Geomorphology 46 (2002) 59 – 71