The propagation of periodically generated vortex rings (period $T$) is numerically investigated by imposing pulsed jets of velocity $U_{jet}$ and duration $T_{s}$ (no flow between pulses) at the inlet of a cylinder of diameter $D$ exiting into a tank. Because of the step-like nature of pulsed jet waveforms, the average jet velocity during a cycle is $U_{ave}=U_{jet}T_{s}/T$. By using $U_{ave}$ in the definition of the Reynolds number ($Re=U_{ave}D/\unicode[STIX]{x1D708}$, $\unicode[STIX]{x1D708}$: kinematic viscosity of fluid) and non-dimensional period ($T^{\ast }=TU_{ave}/D=T_{s}U_{jet}/D$, i.e. equivalent to formation time), then based on the results, the vortex ring velocity $U_{v}/U_{jet}$ becomes approximately independent of the stroke ratio $T_{s}/T$. The results also show that $U_{v}/U_{jet}$ increases by reducing $Re$ or increasing $T^{\ast }$ (more sensitive to $T^{\ast }$) according to a power law of the form $U_{v}/U_{jet}=0.27T^{\ast 1.31Re^{-0.2}}$. An empirical relation, therefore, for the location of vortex ring core centres ($S$) over time ($t$) is proposed ($S/D=0.27T^{\ast 1+1.31Re^{-0.2}}t/T_{s}$), which collapses (scales) not only our results but also the results of experiments for non-periodic rings. This might be due to the fact that the quasi-steady vortex ring velocity was found to have a maximum of 15 % difference with the initial (isolated) one. Visualizing the rings during the periodic state shows that at low $T^{\ast }\leqslant 2$ and high $Re\geqslant 1400$ here, the stopping vortices become unstable and form hairpin vortices around the leading ones. However, by increasing $T^{\ast }$ or decreasing $Re$ the stopping vortices remain circular. Furthermore, rings with short $T^{\ast }=1$ show vortex pairing after approximately one period in the downstream, but higher $T^{\ast }\geqslant 2$ generates a train of vortices in the quasi-steady state.

An investigation of the flow around an obstacle positioned within the wake of a rotor is described. A flow visualisation survey was performed using a smoke wand and particle image velocimetry, and surface pressure measurements on the obstacle were taken. The flow patterns were strongly dependent upon the rotor height above the ground and obstacle, and the relative position of the obstacle and rotor axis. High positive and suction pressures were measured on the obstacle surfaces, and these were unsteady in response to the passage of the vortex driven rotor wake over the surfaces. Integrated surface forces are of the order of the rotor thrust, and unsteady pressure information shows local unsteady loading of the same order as the mean loading. Rotor blade-tip vortex trajectories are responsible for the generation of these forces.

Two modal decomposition techniques are employed to analyse the stability of wind turbine wakes. A numerical study on a single wind turbine wake is carried out focusing on the instability onset of the trailing tip vortices shed from the turbine blades. The numerical model is based on large-eddy simulations (LES) of the Navier–Stokes equations using the actuator line (ACL) method to simulate the wake behind the Tjæreborg wind turbine. The wake is perturbed by low-amplitude excitation sources located in the neighbourhood of the tip spirals. The amplification of the waves travelling along the spiral triggers instabilities, leading to breakdown of the wake. Based on the grid configurations and the type of excitations, two basic flow cases, symmetric and asymmetric, are identified. In the symmetric setup, we impose a 120° symmetry condition in the dynamics of the flow and in the asymmetric setup we calculate the full 360° wake. Different cases are subsequently analysed using dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD). The results reveal that the main instability mechanism is dispersive and that the modal growth in the symmetric setup arises only for some specific frequencies and spatial structures, e.g. two dominant groups of modes with positive growth (spatial structures) are identified, while breaking the symmetry reveals that almost all the modes have positive growth rate. In both setups, the most unstable modes have a non-dimensional spatial growth rate close to $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\pi /2$ and they are characterized by an out-of-phase displacement of successive helix turns leading to local vortex pairing. The present results indicate that the asymmetric case is crucial to study, as the stability characteristics of the flow change significantly compared to the symmetric configurations. Based on the constant non-dimensional growth rate of disturbances, we derive a new analytical relationship between the length of the wake up to the turbulent breakdown and the operating conditions of a wind turbine.

Interaction of vortex rings with solid is an important research topic of hydrodynamic. In this study, a multiple-relaxation time (MRT) lattice Boltzmann method (LBM) is used to investigate the flow of a vortex ring impacting spheroidal particles. The MRT-LBM is validated through the cases of vortex ring impacting a flat wall. The vortex evolution due to particle size, the aspect ratio of a prolate particle, as well as Reynolds (Re) number are discussed in detail. When the vortex ring impacting a stationary sphere, the primary and secondary vortex rings wrap around each other, which is different from the situation of the vortex ring impacting a plate. For the vortex ring impacting with a prolate spheroid, the secondary vortex ring stretches mainly along the long axis of the ellipsoid particle. However, it is found that after the vortex wrapping stage, the primary vortex recovers along the short axis of the particle faster than that in the long axis, i.e., the primary vortex ring stretches mainly along the short axis of the particle. That has never been address in the literature.

The effect of the body on the lift force in hovering flight is studied here by including the effect of image vortex rings (IVRs) in the inviscid vortex ring model proposed by Rayner (J. Fluid Mech., vol. 91, 1979, pp. 697–730) and used by Wang & Wu (J. Fluid Mech., vol. 654, 2010, pp. 453–472) to study lift force due to wakes. The body is treated simply as an equivalent sphere following the data of Ellington (Phil. Trans. R. Soc. Lond. B, vol. 305, 1984a, pp. 17–40). It is shown that the body image reduces the lift by inducing a further downwash near the wing tip and an additional contraction to the real vortex rings (RVRs). The amount of force reduction due to body image is found to grow cubically with relative body size, defined by the equivalent radius relative to the wing span, and approximately linearly with the feathering parameter. For Apis and Bombus with large relative body size and large feathering parameter, the body images reduce lift by an amount near 8 % according to the present simplified analysis.

Force and particle image velocimetry measurements were conducted on a NACA 0012 aerofoil undergoing small-amplitude high-frequency plunging oscillation at low Reynolds numbers and angles of attack in the range 0–. For angles of attack less than or equal to the stall angle, at high Strouhal numbers, significant bifurcations are observed in the time-averaged lift coefficient resulting in two lift-coefficient branches. The upper branch is associated with an upwards deflected jet, and the lower branch is associated with a downwards deflected jet. These branches are stable and highly repeatable, and are achieved by increasing or decreasing the frequency in the experiments. Increasing frequency refers to starting from stationary and increasing the frequency very slowly (while waiting for the flow to reach an asymptotic state after each change in frequency); decreasing frequency refers to impulsively starting at the maximum frequency and decreasing the frequency very slowly. For the latter case, angle of attack, starting position and initial acceleration rate are also parameters in determining which branch is selected. The bifurcation behaviour is closely related to the properties of the trailing-edge vortices. The bifurcation was therefore not observed for very small plunge amplitudes or frequencies due to insufficient trailing-edge vortex strength, nor at larger angles of attack due to greater asymmetry in the strength of the trailing-edge vortices, which creates a preference for a downward deflected jet. Vortex strength and asymmetry parameters are derived from the circulation measurements. It is shown that the most appropriate strength parameter in determining the onset of deflected jets is the circulation normalized by the plunge velocity.

A Batchelor vortex represents the asymptotic solution of a trailing vortex in an aircraft wake. In this study, an unequal-strength, counter-rotating Batchelor vortex pair is employed as a model of the wake emanating from one side of an aircraft wing; this model is a direct extension of several prior investigations that have considered unequal-strength Lamb–Oseen vortices as representations of the aircraft wake problem. Both solution of the linearized Navier–Stokes equations and direct numerical simulations are employed to study the linear and nonlinear development of a vortex pair with a circulation ratio of . In contrast to prior investigations considering a Lamb–Oseen vortex pair, we note strong growth of the Kelvin mode coupled with an almost equal growth rate of the Crow instability. Three stages of nonlinear instability development are defined. In the initial stage, the Kelvin mode amplitude becomes sufficiently large that oscillations within the core of the weaker vortex are easily observable and significantly affect the profile of the weaker vortex. In the secondary stage, filaments of secondary vorticity emanate from the weaker vortex and are convected around the stronger vortex. In the tertiary stage, a transition in the dominant instability wavelength is observed from the short-wavelength Kelvin mode to the longer-wavelength Crow instability. Much of the instability growth is observed on the weaker vortex of the pair, although small perturbations in the stronger vortex are observed in the tertiary nonlinear growth phase.