Session PD: Instabilities in Wakes

Wakes of Self-propelled Bodies in Stratified Fluids

Using high Reynolds number (Re=10$^{4}$-10$^{5})$ experiments, the dynamics of stratified momentum wakes of self-propelled underwater and surface bodies were studied in (i) deep linearly stratified (deep ocean pycnocline), (ii) two layer (shallow pycnocline), and (iii) surface stratified (turbocline) fluids, and theoretical models wee advanced to explain the flow behavior. These models: (i) predict conditions under which submerged wakes signatures penetrate to the water surface, as expressed by the Confinement and Contrast numbers, and (ii) describe IR (infra-red) surface wakes signatures, as expressed by the Contrast and modified Froude numbers. If decaying turbulence is present surrounding the wake, the penetration of wake signature to the surface is still possible. Estimates for typical oceanic cases are given. PIV, LIF and high sensitivity Infrared Imaging cameras were employed for flow diagnostics.   

Dynamic 3-D vortex structure of the laminar separation bubble on SD7003 airfoil

Recent increasing interest in laminar separation bubble (LSB) is aroused by the development of the micro air vehicles (MAVs), which normally cruise in the Reynolds number range of 50,000-200,000. This paper studies the LSB over the SD 7003 airfoil at the angle of attack $\alpha $=4$^{\circ}$ and at \textit{Re}=60,000 using the time-resolved PIV technique. A Nd:Yag laser operated at 1000 Hz and a high speed CMOS camera was synchronized to capture the particle images with the full resolution of 1504 x 1128 pixels at 1000 fps. Measurements were carried out from two orthogonal views: in the stream-wise wall-normal plane and the quasi-surface-parallel plane. 3-D disturbance was observed to start even prior to the point of transition. Vortex shedding in transition near the reattachment region of the LSB was clearly identified in the span-wise wall-normal plane, with the dominant K-H frequency of around 10.7 Hz. And subsequent vortex evolution in the reattached turbulent boundary layer was found to be characterized by paired positive and negative vorticity packets transported downstream.   

Experiments and nonlinear evolution of instabilities in the sphere wake

We performed precise and systematic experiments with PIV in order to measure the velocity field in the wake of a solid sphere in a water channel, in the range of Reynolds number between 200 and 400, where stationary and oscillatory instabilities appear, including hairpin shedding regime. From these experimental data, we are studying the modal decomposition of the streamwise vorticity in an instationnary case with standing waves and we describe the full nonlinear evolution of the bifurcation branches. We are comparing these results with recent theoretical and numerical studies on instability in the spherical wake at these intermediate Reynolds numbers.   

Hydrodynamics of an oscillating sphere in water

We have studied the flow patterns and damping of a one inch steel ball oscillating in water. The suspension was a 120 cm copper wire which allowed electrical connection to the water bath providing visualization by means of the Baker technique. The ball could be set into motion by means of a linear motor arranged to oscillate in the horizontal direction at the top of the suspension. Alternatively the bob could be set in motion and allowed to decay freely. The range of Reynolds numbers based on the maximum velocity ranged from $<$100 to over 2500 and the Carpenter-Keulegan numbers from 0.3 to 10. The period of oscillation was 2.5 sec. For Reynolds numbers up to about 400 we observed a boundary layer on the ball with a suggestion of a laminar wake spreading from the equator in the direction of oscillation. At higher Reynolds numbers around 550 we began to see periodic structure developing on the wake. By Re$\sim $700 it is clear the disturbances are a series of vortex rings which form on the rear of the sphere during an oscillation, and leapfrog over the sphere and propagate away when the direction of oscillation is reversed.   

Slowing of Vortex Rings

We have investigated the slowing of vortex rings in water which are created with very thin cores. We find that these rings propagate with no measurable change in diameter or core size. The drag appears to be the result of viscous forces on the core. A simple model for this drag describes experimental data in terms of a drag coefficient, which depends only on Reynolds number. Barenghi's group at Newcastle found that the translational velocity of a ring in an \textit{inviscid} fluid perturbed by Kelvin waves decreases with increasing amplitude of Kelvin waves. This suggests that the velocity of vortex rings in a viscous fluid may well depend on the amplitude of Kelvin waves at the time of formation. Rings with substantial amplitude of Kelvin waves will be expected to move more slowly than rings with little or no Kelvin wave amplitude. We present experimental data confirming this suggestion.   

Convective instability in inhomogeneous media: the impulse response in a subcritical cylinder wake

We study experimentally the impulse response of a cylinder wake below the critical Reynolds number of the B\'enard-von K\'arman instability. In this subcritical regime, a localized region of convective instability exists which determines an initial perturbation to be transiently amplified. Previous experimental works [Le Gal and Croquette, Phys. Rev. E 62, 4424 (2000)] have used the spatiotemporal evolution of streaklines from dye visualizations to analyze the evolution of a wave packet, but this has not permitted to give a correct picture of the transient energy growth. The aim of this work is to quantify the evolution of this convective instability using 2D particle image velocimetry in a hydrodynamic tunnel experiment. The velocity fields allow us to describe the evolution of the wave packet in terms of two control parameters: the Reynolds number and the strength of the imposed perturbation. The energy exhibits a transient algebraic growth followed by an exponential decay. A scaling law with respect to the Reynolds number was evidenced for the later decay, but not for the initial growth, which is consistent with the picture of transient growth in inhomogeneous media governed by the interaction of non-normal modes.   

Secondary instability in the wake of the flow around two circular cylinders in tandem arrangements

The stability of three-dimensional perturbations about two-dimensional time-periodic vortex wakes of the flow around two identical circular cylinders in tandem arrangements is investigated. The centre-to-centre separation is varied from 1.5 to 5 cylinder diameters. Direct linear stability analysis is employed to determine the shape, wavelength and onset of unstable three-dimensional perturbations. In addition the non-linear character of the bifurcations is identified through three-dimensional direct numerical simulations performed in the vicinity of the critical points. It is found that, for configurations with large cylinder separations, the first stages of the wake transition are similar to those observed in the flow around an isolated cylinder, although the onset of the secondary instability occurs at a lower Reynolds number. In contrast, for small separations the transition route is significantly different, resembling that of the flow in a periodically driven cavity. For these configurations the onset of the first instability arises at a higher Reynolds number than in the case of an isolated cylinder.