J. E. Wesfreid

On the spatial structure of global modes in wake flow

Numerical simulations of wake flow behind an equilateral triangular obstacle are presented. The form of global modes and their dependence on the Reynolds number found in this study are in accordance with recent experimental results of Goujon–Durand et al. [Phys. Rev. E 50, 308 (1994)]. A scaling law of the amplitude oscillating with the fundamental frequency corresponding to the maximum of the global mode is found to agree with the Landau model in a range of Reynolds Re numbers larger than in previous studies. The position of the maximum amplitude of the fundamental modes scales as (Re−Rec)−1/2. The amplitude of the second harmonic of the longitudinal component of the velocity as well as the correction to the mean flow have different critical behavior than the velocity components oscillating with fundamental frequency. During linear growth the position of the maximum of the global modes is constant and moves only in the nonlinear regime. The effects of the blockage and the boundary conditions on the side ...

Drag reduction of a bluff body using adaptive control methods

A classical actuator is used to control the drag exerted on a bluff body at large Reynolds number (Re=20000). The geometry is similar to a backward-facing step whose separation point is modified using a rotating cylinder at the edge. The slow fluctuations of the total drag are directly measured by means of strain gauges. As shown by visualizations, the actuator delays the separation point. The size of the low-pressure region behind the body is decreased and the drag reduced. It is found that the faster the rotation of the cylinder, the lower the drag. In a first study, the goal of the control is for the system to reach a drag consign predetermined by the experimentalist. The control loop is closed with a proportional integral correction. This adaptive method is shown to be efficient and robust in spite of the large fluctuations of the drag. In the second method, the system finds itself its optimal set point. It is defined as the lowest cost of global energy consumption of the system (drag reduction versus...

The normal field instability in ferrofluids: hexagon–square transition mechanism and wavenumber selection

When a ferrofluid layer is subjected to a uniform and vertically oriented magnetic eld, an interfacial instability occurs, above a critical value of the magnetic eld, giving rise to a hexagonal array of peaks. On increasing the magnetic eld, a smooth morphological transition from the hexagonal array to a square array was observed above a second threshold. The hexagon{square transition phenomenology, in addition to the role of penta{hepta defects initially present in the hexagonal pattern, was investigated. Furthermore, the pattern and wavenumber selection was studied by two dierent procedures: rst by imposing jumps in eld intensity and second by varying the magnetic eld in a quasi-static way. The results obtained were very dierent for the two procedures. They indicated that the square pattern was a metastable state induced by the compression of the hexagonal pattern on increasing the control parameter. This hypothesis was conrmed by performing an additional experiment where the pattern was isotropically compressed. In this experiment, the transition was induced at a constant magnetic eld lower than the transition onset value. However, the theoretical values for stability domains of hexagons and squares proposed in the literature were found to not agree with the experimental values.

Centrifugal instability of pulsed flow

The stability of a pulsed flow in a Taylor–Couette geometry with both cylinders rotating at the same angular velocity Ω(t)=Ω0 cos (ωt) is investigated. The first experimental evidence showing that the flow is less unstable in the limit of low and high frequency while destabilization is maximum for an intermediate frequency ω0 is reported. A detailed analysis of the restabilization at frequencies just above ω0 reveals a behavior not accounted for by previous theoretical analysis. Thus, the linear stability analysis is reconsidered by using a different implementation of the Floquet theory and a satisfactory agreement with the present experimental results is found.

Spatial Evolution of Gortler Instability in a Curved Duct of High Curvature

The Gortler instability is investigated experimentally in a water channel of high curvature. Two different kinds of experiments are presented. The first one corresponds to an experiment where the flow rate increases and where we study the instability in a given longitudinal position along the concave wall. We find a law for the full nonlinear behavior as a correlation for the velocity perturbation as a function of the Gortler number. In the second set of experiments, we follow the spatial evolution of the instability along the concave wall for a given flow rate. We observe the saturation due to the nonlinearities and to the diminution of the thickness of the boundary layer. We show the importance of the initial conditions and of the wavelength in the evolution of the instability.

Coriolis instability of pulsed flow

The linear stability of a time‐periodic flow is considered. The fluid motion is taking place in a Hele–Shaw cell made of two vertical rectangular parallel plates separated by a gap of small extent compared to the dimensions of the plates. The flow is generated by oscillating the cell about its vertical symmetry axis. Our stability analysis was motivated by the experimental results reported some years ago by Bolton and Maurer [Bull. Am. Phys. Soc. 32, 2097 (1987)] who observed the onset of longitudinal rolls in this configuration. The inviscid stability criterion for steady flow subjected to Coriolis force is applied at different times to assess the instability mechanism in the two opposite regimes of respectively low and high frequency of oscillation. For moderate values of the frequency, implementation of Floquet theory is used to find the critical values of the instability parameters. Finally a connection is established between the present results and those we obtained recently for a pulsed flow in a Ta...