Impact of Kelvin–Helmholtz instability on a circular cylinder placed in a trench

This study presents a systematic investigation of hydrodynamic forces on a stationary circular cylinder inside relatively wide and deep trapezoidal trenches in steady flows, representing subsea power cables laid in seabed valleys or artificial trenches, with particular emphasis on the role of Kelvin–Helmholtz (K–H) instability. Using high-fidelity three-dimensional (3-D) implicit large-eddy simulation (iLES), the influences of trench geometry and the incoming flows on hydrodynamic forces were examined. The parametric space includes the trench-width-to-cylinder-diameter ratio ( $ W^{*}$ $\leq$ 20), trench-depth-to-cylinder-diameter ratio ( $H^{*} \leq 5$ ), trench side slope ( $15^{\circ}\leq \theta \leq 60^{\circ}$ ) and the streamwise offset of the cylinder centre from the trench centreline ( ${L}_{p}^{*}$ ). The large-scale cavity-type flows generated by trench geometry and K–H shear-layer dynamics originating at the leading edge of the trench are found to be the dominant mechanisms affecting hydrodynamic forces on the cylinder. Narrow, deep and steep-sided trenches are shown to provide a sheltering effect, reducing forces on the cylinder; whereas wide, shallow trenches promote the generation of strong K–H instabilities that interact directly with the cylinder, leading to periodic force fluctuations. Notably, when the cylinder is positioned downstream of the shear-layer reattachment point in a wide, shallow trench, the mean drag and/or lift forces can exceed those experienced over a flat seabed, accompanied by substantial fluctuations. Increasing Reynolds number ( Re ) from 500 to 3900, as defined based on the diameter of the cylinder, enhances fluctuations of hydrodynamic forces, primarily due to the upstream migration of the onset of K–H instability and the intensified interactions of shed vortices with the cylinder within the trench. A hydrodynamic regime map, constructed from mean force reduction factors and peak fluctuation intensities, is proposed to classify the flow into four distinct regimes: no interaction, transitional, interaction and strong interaction. These findings offer new physical insights and provide practical guidance for evaluating hydrodynamic responses on unburied subsea cables in complex seabed topographies.