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Three-dimensional (3-D) wake transitions of a steady flow past two side-by-side circular cylinders are investigated through Floquet analysis and direct numerical simulations (DNS) over the gap-to-diameter ratio $g^*$ up to 3.5 and Reynolds number ${\textit {Re}}$ up to 400. When the flows behind two cylinders form in-phase and anti-phase wakes at large $g^*$ , the wake transition is similar to the isolated cylinder counterpart, with the critical ${\textit {Re}}$ for the onset of 3-D transition (${\textit {Re}}_{cr-1}$) happens at around 180. At small $g^*$ , 3-D transition becomes interestingly complex due to the distinct characteristics formed in base flows. The ${\textit {Re}}_{cr-1}$ suddenly drops to around 60–100 and forms distinct variation trends with $g^*$. Precisely, the ${\textit {Re}}_{cr-1}$ of the single symmetric wake (SS, $g^*\lessapprox 0.25$) is more than half of the isolated cylinder counterpart due to the large length scale of the SS wake. Only mode A is detected in SS. In the asymmetric single wake (ASS, $g^* \approx 0.25\unicode{x2013}0.6$) and flip-flop wake (FF, $g^* \approx 0.6\unicode{x2013}1.8$), the 3-D transition develops at ${\textit {Re}} \approx 103\unicode{x2013}60$ and 75–60, respectively. The decrease in ${\textit {Re}}_{cr-1}$ with increasing $g^*$ is because of the increased level of wake asymmetry in ASS and irregular vortex shedding in FF. Floquet analysis predicts two new unstable modes, namely mode A $'$ and subharmonic mode C $'$ , of ASS. Both modes are transient features in 3-D DNS and the flow eventually saturates into a new 3-D mode, mode ASS. The gap flow of mode ASS is distinctly characterised by its time-independent spanwise waviness structure that is deflected towards different transverse directions with a long wavelength of about $14$ cylinder diameters. The 3-D mode of the FF is irregular both temporally and spatially. Variations of ${\textit {Re}}_{cr-1}$ with $g^*$ , the characteristics and the physical mechanisms of each 3-D mode are discussed in this study. [ABSTRACT FROM AUTHOR]

The flow-induced vibration of a two-degree-of-freedom cylinder near a free surface at low Reynolds number (Re = 200) is numerically investigated using the lattice Boltzmann method and a free-surface model. The effects of the Froude number and submergence depth on the characteristics of the flow field and cylinder vibration are discussed. With the approach of the free surface, the wake behind the cylinder interacts with the free surface, resulting in a switch in the vortex shedding mode and the fluctuation of the free surface, which in turn affects the vibration of the cylinder. Additionally, a decrease in the normalized submergence depth h ∗ results in a decrease in the transverse amplitude of vibration and an increase in the streamwise amplitude. The topology of the cylinder vibration trajectory changes from a curve of eight to a teardrop, half-moon, or ellipse shape and gradually loses symmetry. Seven characteristic parameters are extracted from the trajectory of the cylinder, among which the amplitude of the vibration frequency and the phase difference of the vibration in different directions mainly affect the symmetry and topological structure of the trajectory. [ABSTRACT FROM AUTHOR]