Journal of Fluid Mechanics

Thrust-producing harmonically oscillating foils are studied through force and power measurements, as well as visualization data, to classify the principal characteristics of the flow around and in the wake of the foil. Visualization data are obtained using digital particle image velocimetry at Reynolds number 1100, and force and power data are measured at Reynolds number 40 000. The experimental results are compared with theoretical predictions of linear and nonlinear inviscid theory and it is found that agreement between theory and experiment is good over a certain parametric range, when the wake consists of an array of alternating vortices and either very weak or no leading-edge vortices form. High propulsive efficiency, as high as 87%, is measured experimentally under conditions of optimal wake formation. Visualization results elucidate the basic mechanisms involved and show that conditions of high efficiency are associated with the formation on alternating sides of the foil of a moderately strong leading-edge vortex per half-cycle, which is convected downstream and interacts with trailing-edge vorticity, resulting eventually in the formation of a reverse Kármán street. The phase angle between transverse oscillation and angular motion is the critical parameter affecting the interaction of leading-edge and trailing-edge vorticity, as well as the efficiency of propulsion.

The flow-induced vibrations of an elastically mounted circular cylinder, free to oscillate in the direction parallel to the current and subjected to a forced rotation about its axis, are investigated by means of two- and three-dimensional numerical simulations, at a Reynolds number equal to 100 based on the cylinder diameter and inflow velocity. The cylinder is found to oscillate up to a rotation rate (ratio between the cylinder surface and inflow velocities) close to 2 (first vibration region), then the body and the flow are steady until a rotation rate close to 2.7 where a second vibration region begins. Each vibration region is characterized by a specific regime of response. In the first region, the vibration amplitude follows a bell-shaped evolution as a function of the reduced velocity (inverse of the oscillator natural frequency). The maximum vibration amplitudes, even though considerably augmented by the rotation relative to the non-rotating body case, remain lower than 0.1 cylinder diameters. Due to their trends as functions of the reduced velocity and to the fact that they develop under a condition of wake-body synchronization or lock-in, the responses of the rotating cylinder in this region are comparable to the vortex-induced vibrations previously described in the absence of rotation. The symmetry breaking due to the rotation is shown to directly impact the structure displacement and fluid force frequency contents. In the second region, the vibration amplitude tends to increase unboundedly with the reduced velocity. It may become very large, higher than 2.5 diameters in the parameter space under study. Such structural oscillations resemble the galloping responses reported for non-axisymmetric bodies. They are accompanied by a dramatic amplification of the fluid forces compared to the non-vibrating cylinder case. It is shown that body oscillation and flow unsteadiness remain synchronized and that a variety of wake topologies may be encountered in this vibration region. The low-frequency, large-amplitude responses are associated with novel asymmetric multi-vortex patterns, combining a pair and a triplet or a quartet of vortices per cycle. The flow is found to undergo three-dimensional transition in the second vibration region, with a limited influence on the system behaviour. It appears that the transition occurs for a substantially lower rotation rate than for a rigidly mounted cylinder.

When a pair of tandem cylinders is immersed in a flow the downstream cylinder can be excited into wake-induced vibrations (WIV) due to the interaction with vortices coming from the upstream cylinder. Assi, Bearman & Meneghini (J. Fluid Mech., vol. 661, 2010, pp. 365–401) concluded that the WIV excitation mechanism has its origin in the unsteady vortex–structure interaction encountered by the cylinder as it oscillates across the wake. In the present paper we investigate how the cylinder responds to that excitation, characterising the amplitude and frequency of response and its dependency on other parameters of the system. We introduce the concept ofwake stiffness, a fluid dynamic effect that can be associated, to a first approximation, with a linear spring with stiffness proportional to$\mathit{Re}$and to the steady lift force occurring for staggered cylinders. By a series of experiments with a cylinder mounted on a base without springs we verify that such wake stiffness is not only strong enough to sustain oscillatory motion, but can also dominate over the structural stiffness of the system. We conclude that while unsteady vortex–structure interactions provide the energy input to sustain the vibrations, it is the wake stiffness phenomenon that defines the character of the WIV response.

The mechanism of wake-induced vibrations (WIV) of a pair of cylinders in a tandem arrangement is investigated by experiments. A typical WIV response is characterized by a build-up of amplitude persisting to high reduced velocities; this is different from a typical vortex-induced vibration (VIV) response, which occurs in a limited resonance range. We suggest that WIV of the downstream cylinder is excited by the unsteady vortex–structure interactions between the body and the upstream wake. Coherent vortices interfering with the downstream cylinder induce fluctuations in the fluid force that are not synchronized with the motion. A favourable phase lag between the displacement and the fluid force guarantees that a positive energy transfer from the flow to the structure sustains the oscillations. If the unsteady vortices are removed from the wake of the upstream body then WIV will not be excited. An experiment performed in a steady shear flow turned out to be central to the understanding of the origin of the fluid forces acting on the downstream cylinder.

Measurements are presented of fluid-dynamic instability of a smooth circular cylinder, free to oscillate laterally against linear springs in the wake from an identical stationary neighbouring body. The observations also encompassed determination of static forces on the downstream cylinder as functions of relative position of the cylinder pair. Most of the experiments were performed under two conditions of free-stream turbulence. Static tests indicated that both the drag coefficient and the Strouhal number of the downstream body are continuous functions of its relative position. The drag forces were found to be negative at small gaps. It was observed that the transverse extent of the force field increases with increasing streamwise gap.

In the dynamic experiments, depending on the cylinders’ separation and structural damping, the cylinder exhibited a vortex-resonance, or a galloping, or a combined vortex-resonance and galloping, or a separated vortex-resonance and galloping. Whilst the characteristics of wake-excited motion were found to be essentially unaffected by a limited change in free-stream turbulence intensity, the galloping amplitudes were observed to be sensitive to the cylinders’ aspect ratio. An increase in the stability parameter caused significant effects on the cylinder response in amplitude domain. Wake observations behind the oscillating body indicated that in vortex lock-in the frequency of vortex-shedding locked to vibration frequency, but during small-amplitude galloping motion the shedding frequency behaved as if the cylinder was stationary.

A high-speed video system was used to study the interaction between sediment particles and turbulence in the wall region of an open channel flow with both smooth and transitionally rough beds. In smooth flows, particles immersed within the viscous sublayer were seen to accumulate along low-speed wall streaks; apparently due to the presence of quasi-streamwise vortices in the wall region. Larger particles did not tend to group along streaks, however their velocity was observed to respond to the streaky structure of the flow velocity in the wall region. In transitionally rough flows particle sorting was not observed. Coherent flow structures in the form of shear layers typically observed in the near-wall region interacted with sediment particles lying on the channel bottom, resulting in the particles being entrained into suspension. Although there has been some speculation that this process would not be effective in entraining particles totally immersed in the viscous sublayer, the results obtained demonstrate the opposite. The entrainment mechanism appears to be the same independent of the roughness condition of the bottom wall, smooth or transitionally rough. In the latter case, however, hiding effects tend to preclude the entrainment of particles with sizes finer than that of the roughness elements. The analysis of particle velocity during entrainment shows that the streamwise component tends to be much smaller than the local mean flow velocity, while the vertical component tends to be much larger than the local standard deviation of the vertical flow velocity fluctuations, which would indicate that such particles are responding to rather extreme flow ejection events.

For flood protection against storm tides, barriers of box-like gates hinged along a bottom axis have been designed to span the three inlets of the Venice Lagoon. While on calm days the gates are ballasted to rest horizontally on the seabed, in stormy weather they are raised by buoyancy to act as a dam which is expected to swing to and fro in unison in response to the normally incident sea waves. Previous laboratory experiments with sinusoidal waves have revealed however that neighbouring gates oscillate out of phase, at one half the wave frequency, in a variety of ways, and hence would reduce the effectiveness of the barrier. Extending the linear theory of trapped waves by Mei et al. (1994), we present here a nonlinear theory for subharmonic resonance of mobile gates allowed to oscillate about a vertical plane of symmetry. In this part (1) the evolution equation of the Landau–Stuart type is first derived for the gate amplitude. The effects of gate geometries on the coefficients in the equation are examined. After accounting for dissipation effects semi-empirically the theoretical results on the equilibrium amplitude excited by uniform incident waves are compared with laboratory experiments.

The inverse water wave problem of bathymetry detection is the problem of deducing the bottom topography of the seabed from measurements of the water wave surface. In this paper, we present a fully nonlinear method to address this problem in the context of the Euler equations for inviscid irrotational fluid flow with no further approximation. Given the water wave height and its first two time derivatives, we demonstrate that the bottom topography may be reconstructed from the numerical solution of a set of two coupled non-local equations. Owing to the presence of growing hyperbolic functions in these equations, their numerical solution is increasingly difficult if the length scales involved are such that the water is sufficiently deep. This reflects the ill-posed nature of the inverse problem. A new method for the solution of the forward problem of determining the water wave surface at any time, given the bathymetry, is also presented.

Frequency lock-in can occur on a spring suspended airfoil in transonic buffeting flow, in which the coupling frequency does not follow the buffet frequency but locks onto the natural frequency of the elastic airfoil. Most researchers have attributed this abnormal phenomenon to resonance. However, this interpretation failed to reveal the root cause. In this paper, the physical mechanism of frequency lock-in is studied by a linear dynamic model, combined with the coupled computational fluid dynamics/computational structural dynamics (CFD/CSD) simulation. We build a reduced-order model of the flow using the identification method and unsteady Reynolds-averaged Navier–Stokes computations in a post-buffet state. A linear aeroelastic model is then obtained by coupling this model with a degree-of-freedom equation for the pitching motion. Results from the complex eigenvalue analysis indicate that the coupling between the structural mode and the fluid mode leads to the instability of the structural mode. The instability range coincides with the lock-in region obtained by the coupled CFD/CSD simulation. Therefore, the physical mechanism underlying frequency lock-in is caused by the linear coupled-mode flutter – the coupling between one structural mode and one fluid mode. This is different from the classical single-degree-of-freedom flutter (e.g. transonic buzz), which occurs in stable flows; the present flutter is in the unstable buffet flow. The response of the airfoil system undergoes a conversion from forced vibration to self-sustained flutter. The coupling frequency certainly should lock onto the natural frequency of the elastic airfoil.

The stability of buoyancy-driven propagation of a fluid-filled crack through an elastic solid is studied using a combination of theory and experiments. For the theory, the lubrication approximation is introduced for fluid flow, and the surrounding solid is described by linear elasticity. Solutions are then constructed for a planar fluid front driven by either constant flux or constant volume propagating down a pre-cut conduit. As the thickness of the pre-cut conduit approaches zero, it is shown how these fronts converge to zero-toughness fracture solutions with a genuine crack tip. The linear stability of the planar solutions towards transverse, finger-like perturbations is then examined. Instabilities are detected that are analogous to those operating in the surface-tension-driven fingering of advancing fluid contact lines. Experiments are conducted using a block of gelatin for the solid and golden syrup for the fluid. Again, planar cracks initiated by emplacing the syrup above a shallow cut on the surface of the gelatin develop transverse, finger-like structures as they descend. Potential geological applications are discussed.