A series of simulations with a circular cylinder of diameter $D$ placed in an open channel flow of depth $H$ are conducted in both purely oscillatory flow (one-mode forcing with maximum orbital velocity, $U_m$) and in combined oscillatory and current flow regime (mean velocity, $U_s$). The paper discusses how the phase-averaged flow, the coherent structures generated around the cylinder, and the forces induced on the cylinder change with the ratio between the steady current velocity and the oscillatory velocity ($0\le U_s/U_m\le 1.4$) and with the Keulegan-Carpenter number, $\mathrm{KC}=U_{m}T/D$ ($1.5\le \mathrm{KC}\le 30.8$), where $T$ is the period of the oscillatory flow. Results show that for constant $U_s/U_m$, the capacity of the horseshoe vortex to erode the bed increases with the KC number. For constant KC number, the overall coherence and lifespan of the main horseshoe vortex forming during each oscillatory cycle increase with $U_s/U_m$. The same is true for the number and initial circulation of the wake vortices shed on the downstream side of the cylinder in the simulations conducted with $\mathrm{KC}=15.4$ and 30.8. An instability in the form of large-scale hairpin-like vortices develops along the vertical cores of the wake vortices in the $\mathrm{KC}=1.5$ simulations with $U_s/U_m\ge 1.0$. For combined wave-current flows with $U_s/U_m\ge 0.4$, the regions of relatively high bed shear stress magnitude and the peak values inside these regions increase monotonically with the KC number for constant $U_s/U_m$. Results show that even for cases with a steady current, the oscillatory component of the phase-averaged in-line force is reasonably well described by Morisson's equation. A drag coefficient can be defined for the steady component of the in-line force with $U_s$ as the velocity scale. For high KC numbers and $U_s/U_m>1$ this drag coefficient is comparable to the standard drag coefficient in steady flow. The phase lag between the in-line force and the oscillatory velocity component decreases with increasing KC and is independent of $U_s/U_m$. For cases where the number of vortices shed in the wake is the same during all cycles, the phase-averaged spanwise force remains small. However, at times, the cylinder is subject to instantaneous forces of comparable magnitude along the streamwise and spanwise directions for $\mathrm{KC}\ge 15.4$, which has important consequences for the design of piles in combined wave-current flow.

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• Channel flow
• Complex fluids
• Turbulence
• Vortex dynamics
• Vortex shedding