Turbulent and Subcritical Flows over Macro-Roughness Elements

Determining the friction coefficients for uniform flows over very rough bottoms is a long-standing problem in open-channel hydraulics and river engineering. This experimental study presents measurements of the surface deformation as well as Darcy–Weisbach and Manning friction coefficients for steady, turbulent (6058 ≤Re≤ 28,502), and subcritical flows (0.14 ≤Fr≤ 0.52) over large roughness elements, where Fr and Re denote the Froude and Reynolds numbers, respectively. The experiments were conducted in a rectangular, inclined flume with a train of half-cylinders mounted on the bed, with radii in the range 20 mm ≤a≤ 50 mm. These obstacles yield a relative submergence 1.45 ≤hN/a≤ 4.41 and a constant spacing ratio e/a=12.8 across all experimental runs, where hN and e denote the normal flow depth and the center-to-center spacing between cylinders, respectively. The relative amplitude of the surface profiles, (Δh/a), was analyzed and found to correlate strongly with hN/a, Re and Fr. The results reveal very high values of the Darcy friction factor, f, which follows scaling laws of the form f∝(hN/a)n^, with n^<0, independent of a, and f∝Reβ, where β<0 is closely linked to a. Scaling relationships for the Manning roughness coefficient, (n), were also investigated and are reported herein.