We address the flutter instability of a flexible plate immersed in an axial flow. This instability is similar to flag flutter and results from the competition between destabilising pressure forces and stabilising bending stiffness. In previous experimental studies, the plates have always appeared much more stable than the predictions of two-dimensional models. This discrepancy is discussed and clarified in this paper by examining experimentally and theoretically the effect of the plate aspect ratio on the instability threshold. We show that the two-dimensional limit cannot be achieved experimentally because hysteretical behaviour and three-dimensional effects appear for plates of large aspect ratio. The nature of the instability bifurcation (sub-or supercritical) is also discussed in the light of recent numerical results. IntroductionThe flutter of a flexible plate immersed in an axial flow is a canonical example of flowinduced vibrations. This instability can be experienced in everyday life when one observes a flag flapping in the wind. Because this phenomenon appears in many applications (paper industry, airfoil flutter, snoring), it has motivated a large literature which has been recently reviewed by Païdoussis (2004). This instability can be regarded as a competition between fluid forces and elasticity. Indeed, when the plate experiences a small lateral deflection, a destabilising pressure jump can appear across the plate, while the bending stiffness tends to bring the plate back to the stable planar state.This system can be studied by restricting the analysis to one-dimensional flutter modes as observed in most experiments. In this case, the plate motion obeys the Euler-Bernoulli beam equation with additional pressure forces which are calculated by assuming a potential flow. To simplify the problem further, Shelley et al. (2005) considered a plate infinite in both directions in a similar way to the stability analysis of a jet by Lord Rayleigh (1879) who already noted in his seminal paper the analogy with the problem of flag flutter.In other theoretical studies, the plate length L (or chord) takes a finite value while two asymptotic limits are considered for its span H. If H L, the fluid forces can be calculated using the slender body theory of Lighthill (1960) (e.g. Datta & Gottenberg 1975Lemaitre et al. 2005) and if H L the problem can be treated as two-dimensional (as done by Kornecki et al. 1976;Huang 1995;Watanabe et al. 2002a;Guo & Païdoussis 2000). In this latter case, the flow is entirely described by point-vortices which are distributed within the plate and possibly in its wake. It is known from airfoil theory that this problem does not admit a unique solution (intrinsically because the Laplace equation has to be solved on an open domain). Kornecki et al. (1976) used two approaches to arXiv:0804.0774v2 [physics.flu-dyn]

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This experimental study is devoted to the description of the different patterns resulting from instabilities which appear in the flow between a rotating and a stationary disk enclosed by a stationary sidewall. With the help of visualizations we describe the different flow regimes as functions of two control parameters: the Reynolds number and the aspect ratio of the gap separating the disks, which are varied over large continuous ranges. Moreover, visualizations and ultrasonic anemometry lead to the description of the different instabilities and to the construction of a transition diagram that summarizes the domains of existence of the various patterns. Two different scenarios of transition are mainly followed by the flow. When the gap between the two disks is more than the thickness of the two disk boundary layers, circular and spiral waves destabilize the stationary disk boundary layer. Transition occurs in this case by the mixing of these waves. On the other hand, when the two boundary layers are merged, finite-size turbulent structures can appear. They consist of turbulent spots or turbulent spirals which invade the laminar domains as the Reynolds number of the flow is increased.

The flapping flag instability occurs when a flexible cantilevered plate is immersed in a uniform airflow. To this day, the nonlinear aspects of this aeroelastic instability are largely unknown. In particular, experiments in the literature all report a large hysteresis loop, while the bifurcation in numerical simulations is either supercritical or subcritical with a small hysteresis loop. In this paper, this discrepancy is addressed. First weakly nonlinear stability analyses are conducted in the slender-body and two-dimensional limits, and second new experiments are performed with flat and curved plates. The discrepancy is attributed to inevitable planeity defects of the plates in the experiments.

International audienceFlexibility of marine animal fins has been thought to enhance swimming performance. However, despite numerous experimental and numerical studies on flapping flexible foils, there is still no clear understanding of the effect of flexibility and flapping amplitude on thrust generation and swimming efficiency. Here, to address this question, we combine experiments on a model system and a weakly nonlinear analysis. Experiments consist in immersing a flexible rectangular plate in a uniform flow and forcing this plate into a heaving motion at its leading edge. A complementary theoretical model is developed assuming a two-dimensional inviscid problem. In this model, nonlinear effects are taken into account by considering a transverse resistive drag. Under these hypotheses, a modal decomposition of the system motion allows us to predict the plate response amplitude and the generated thrust, as a function of the forcing amplitude and frequency. We show that this model can correctly predict the experimental data on plate kinematic response and thrust generation, as well as other data found in the literature. We also discuss the question of efficiency in the context of bio-inspired propulsion. Using the proposed model, we show that the optimal propeller for a given thrust and a given swimming speed is achieved when the actuating frequency is tuned to a resonance of the system, and when the optimal forcing amplitude scales as the square root of the required thrust

The mechanism of reconfiguration of broad leaves subjected to wind loading is investigated. Circular plastic sheets cut along a radius are immersed in a water flow. They roll up into cones when held at their centres. The opening angle of the cone and the drag force exerted on the sheet are measured as a function of the flow velocity and of the sheet bending rigidity. The cone becomes sharper when the velocity increases or when the sheet stiffness decreases; the reconfiguration leads to a decrease in the drag coefficient. Scaling laws are derived from the mechanical equilibrium of the sheets – the balance between form drag and elastic forces – and the experimental data collapse onto master curves. Two models for the pressure field yield theoretical curves in semi-quantitative agreement with the experiments.

The periodic wake of a sphere maintained in a uniform flow is experimentally characterized. Visualizations of the vortical structures periodically shed in this regime are presented and measurements of amplitude and frequency of the streamwise velocity fluctuations are performed. The experiments show that the resulting self-sustained oscillations of the wake flow appear via a supercritical Hopf bifurcation. Then, the relevance of a Landau-type equation to describe the temporal dynamics of the shedding modes near the instability threshold is discussed. For this purpose transient experiments of growth of the shedding modes are performed under supercritical conditions. From the evolutions during these transients of the instantaneous growth rate and frequency, the parameters of the Landau model are estimated. Dependence on the Reynolds number of these parameters is also deduced from the measurements.