This paper presents three-dimensional (3D) direct numerical simulations (DNS) of flow past a circular cylinder over a range of Reynolds number ($Re$) up to 300. The gradual wake transition process from mode A* (i.e. mode A with large-scale vortex dislocations) to mode B is well captured over a range of $Re$ from 230 to 260. The mode swapping process is investigated in detail with the aid of numerical flow visualization. It is found that the mode B structures in the transition process are developed based on the streamwise vortices of mode A or A* which destabilize the braid shear layer region. For each case within the transition range, the transient mode swapping process consists of dislocation and non-dislocation cycles. With the increase of $Re$, it becomes more difficult to trigger dislocations from the pure mode A structure and form a dislocation cycle, and each dislocation stage becomes shorter in duration, resulting in a continuous decrease in the probability of occurrence of mode A* and a continuous increase in the probability of occurrence of mode B. The occurrence of mode A* results in a relatively strong flow three-dimensionality. A critical condition is confirmed at approximately $Re=265{-}270$, where the weakest flow three-dimensionality is observed, marking a transition from the disappearance of mode A* to the emergence of increasingly disordered mode B structures.

This paper presents the response and the wake modes of a freely vibrating D-section prism with varying angles of attack ( $\alpha = 0^\circ \text {--}180^\circ$ ) and reduced velocity ( $U^* = 2\text {--}20$ ) by a numerical investigation. The Reynolds number, based on the effective diameter, is fixed at 100. The vibration of the prism is allowed only in the transverse direction. We found six types of response with increasing angle of attack: typical vortex-induced vibration (VIV) at $\alpha = 0^\circ \text {--}35^\circ$ ; extended VIV at $\alpha = 40^\circ \text {--}65^\circ$ ; combined VIV and galloping at $\alpha = 70^\circ \text {--}80^\circ$ ; narrowed VIV at $\alpha = 85^\circ \text {--}150^\circ$ ; transition response, from narrowed VIV to pure galloping, at $\alpha = 155^\circ \text {--}160^\circ$ ; and pure galloping at $\alpha = 165^\circ \text {--}180^\circ$ . The typical and narrowed VIVs are characterized by linearly increasing normalized vibration frequency with increasing $U^*$ , which is attributed to the stationary separation points of the boundary layer. On the other hand, in the extended VIV, the vortex shedding frequency matches the natural frequency in a large $U^*$ range with increasing $\alpha$ generally. The galloping is characterized by monotonically increasing amplitude with enlarging $U^*$ , with the largest amplitude being $A^* = 3.2$ . For the combined VIV and galloping, the vibration amplitude is marginal in the VIV branch while it significantly increases with $U^*$ in the galloping branch. In the transition from narrowed VIV to pure galloping, the vibration frequency shows a galloping-like feature, but the amplitude does not monotonically increase with increasing $U^*$ . Moreover, a partition of the wake modes in the $U^*$ – $\alpha$ parametric plane is presented, and the flow physics is elucidated through time variations of the displacement, drag and lift coefficients and vortex dynamics. The angle-of-attack range of galloping is largely predicted by performing a quasi-steady analysis of the galloping instability. Finally, the effects of $m^*$ and ${\textit {Re}}$ , the roles of afterbody and the roles of separation point in determining vibration responses and vortex shedding frequency are further discussed.

Sinusoidally oscillatory flow around four circular cylinders in an in-line square arrangement is numerically investigated at Keulegan–Carpenter numbers ($\mathit{KC}$) ranging from 1 to 12 and at Reynolds numbers ($\mathit{Re}$) from 20 to 200. A set of flow patterns is observed and classified based on known oscillatory flow regimes around a single cylinder. These include six types of reflection symmetry regimes to the axis of flow oscillation, two types of spatio-temporal symmetry regimes and a series of symmetry-breaking flow patterns. In general, at small gap distances, the four structures behave more like a single body, and the flow fields therefore resemble those around a single cylinder with a large effective cylinder diameter. With increasing gap distance, flow structures around each individual cylinder in the array start to influence the overall flow patterns, and the flow field shows a variety of symmetry and asymmetry patterns as a result of vortex and shear layer interactions. The characteristics of hydrodynamic forces on individual cylinders as well as on the cylinder group are also examined. It is found that the hydrodynamic forces respond in a similar manner to the flow field to the cylinder proximity and wake interference.

A numerical analysis of flow around a circular cylinder oscillating in-line with a steady flow is carried out over a range of driving frequencies $(f_{d})$ at relatively low amplitudes $(A)$ and a constant Reynolds number of 175 (based on the free-stream velocity). The vortex shedding is investigated, especially when the shedding frequency $(f_{s})$ synchronises with the driving frequency. A series of modes of synchronisation are presented, which are referred to as the $p/q$ modes, where $p$ and $q$ are natural numbers. When a $p/q$ mode occurs, $f_{s}$ is detuned to $(p/q)f_{d}$, representing the shedding of $p$ pairs of vortices over $q$ cycles of cylinder oscillation. The $p/q$ modes are further characterised by the periodicity of the transverse force over every $q$ cycles of oscillation and a spatial–temporal symmetry possessed by the global wake. The synchronisation modes $(p/q)$ with relatively small natural numbers are less sensitive to the change of external control parameters than those with large natural numbers, while the latter is featured with a narrow space of occurrence. Although the mode of synchronisation can be almost any rational ratio (as shown for $p$ and $q$ smaller than 10), the probability of occurrence of synchronisation modes with $q$ being an even number is much higher than $q$ being an odd number, which is believed to be influenced by the natural even distribution of vortices in the wake of a stationary cylinder.

This paper presents a numerical study of three-dimensional (3D) vortex shedding flow in the wake of four circular cylinders in a square configuration with a constant space-to-diameter ratio of 2. Numerical tests are carried out for Reynolds number (Re) in the range from 100 to 500. Four wake flow regimes are identified at this spacing ratio. Regime 1 ($100 \le {\mathop{\rm Re}\nolimits} \le 220$100≤ Re ≤220) is characterized by the inclination of weak spanwise vortices and weak streamwise vortices, where the wake behind four cylinder array shares similar features to that behind a single cylinder with a large equivalent diameter. It is observed that the onset of three-dimensionality in the wake behind four cylinder array occurs at lower Re than that behind a single cylinder. Regime 2 ($240 \le {\mathop{\rm Re}\nolimits} \le 300$240≤ Re ≤300) is characterized by the appearance of the regular wavy spanwise vortices and rib-shaped streamwise vortices. The wavelength of the spanwise vortices is about 1.2 and the wake flow is similar to the transition mode B of a single cylinder. Regime 3 ($320 \le {\mathop{\rm Re}\nolimits} \le 380$320≤ Re ≤380) is characterized by severe vortex dislocations in the wake of the cylinders and regime 4 ($400 \le {\mathop{\rm Re}\nolimits} \le 500$400≤ Re ≤500) is characterized by the absence of vortex dislocations and the strong streamwise vortices. The flow between the upstream and the downstream cylinders is predominantly two-dimensional in regimes 1, 2, and 3 and becomes 3D in regime 4. Physical mechanisms responsible for different flow regimes are proposed and discussed in details. Significant changes in the root-mean-square force coefficients, wake formation length, and phase angle of the lift coefficients on the downstream cylinders are observed when the flow transits from one regime to another.