The flow around a vertical circular pile exposed to a steady current is studied numerically and experimentally. The numerical model is a three-dimensional model. The model validation was achieved against new experimental data (which include two-component laser-Doppler anemometry (LDA) flow measurements and the hot-film bed shear stress measurements, and reported in the present paper) and the data of others, and a $k$–$\omega $ turbulence model was used for closure. The model does not have a free-surface facility and therefore is applicable only to cases where the Froude number is small ($\hbox{\it Fr}\,{<}\,O(0.2)$). The flow model was used to study the horseshoe vortex and lee-wake vortex flow processes around the pile. The influence on the horseshoe vortex of three parameters, namely the boundary-layer thickness, the Reynolds number and the bed roughness, was investigated. In the latter investigation, the steady solution of the model was chosen. A study of the influence of the unsteady solution on the previously mentioned flow processes was also carried out. The ranges of the parameters covered in the numerical simulations are: The boundary-layer-thickness-to-pile-diameter ratio is varied from 2$\,{\times}\, 10^{-2}$ to 10$^{2}$, the pile Reynolds number from 10$^{2}$ to $2\,{\times}\, 10^{6},$ and the pile diameter-to-roughness ratio from 2 to about 10$^{3}.$ The amplification of the bed shear stress around the pile (including the areas under the horseshoe vortex and the lee-wake region) was obtained for various values of the previously mentioned parameters. The steady-state flow model was coupled with a morphologic model to calculate scour around a vertical circular pile exposed to a steady current in the case of non-cohesive sediment. The morphologic model includes (i) a two-dimensional bed load sediment-transport description, and (ii) a description of surface-layer sand slides for bed slopes exceeding the angle of repose. The results show that the present numerical simulation captures all the main features of the scour process. The equilibrium scour depth obtained from the simulation agrees well with the experiments for the upstream scour hole. Some discrepancy (up to 30%) was observed, however, for the downstream scour hole. The calculations show that the amplification of the bed shear stress around the pile in the equilibrium state of the scour process is reduced considerably with respect to that experienced at the initial stage where the bed is plane.

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A fundamental requirement for any scour assessment and scour protection design is the ability to determine the Shields parameter for combined wave and current conditions. The Shields parameter can be calculated for current combined with monochromatic waves using the approach of Soulsby (1997) in combination with the wave friction factor concept. For current in combination with irregular waves, the same approach is suggested using a wave orbital velocity, Um, for representation of the irregular sea state. Um is defined as 1.41 times the standard deviation of the near bed wave orbital velocity. The Soulsby (2006) expression for Um is compared with a hyperbolic expression and validated using numerical methods and laboratory measurements. A large number of expressions exist for the wave friction factor as a function of relative bed roughness. From a literature study, the paper proposes a combination of existing expressions to cover relative bed roughnesses from sand over gravel to coarse armour rock.

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