ABSTRACT
A new formula to predict the scour depth of equilibrium around bridge piers (i.e. ys ) under clear water conditions is derived using principles pertaining to the phenomenological theory of turbulence. The derivation provides insights into the relation between ys and the so-called relative coarseness (i.e. a/d, where a and d are bridge-pier and sediment diameter, respectively), which has been an important matter of debate in the literature. It is suggested that, if the sediment diameter d lies within the range of turbulent inertial length scales of the flow, then https://www.w3.org/1998/Math/MathML"> y s / K ∝ ( a / d ) 2 / 3 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429069246/b59e18fc-9e1d-4389-b000-a1069c1cd27e/content/eq8861.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , where K is the kinetic head of the approach flow. The relation between ys /K and a/d is also discussed for two limiting conditions of d approaching the integral and the Kolmogorov length scale. Overall, it is shown that this relation is dictated by the relative positioning of d within the range of length scales pertaining to the spectrum of turbulent energy.
