Waves and instabilities in rotating free surface flows

The stability properties of the rotating free surface flow in a cylindrical container is studied using a global stability approach, considering succesively three models. For the case of solid body rotation (Newton’s bucket), all eigenmodes are found to be stable, and are classified into three families : gravity waves, singular inertial modes, and Rossby waves. For the case of a potential flow, an instability is found. The mechanism is explained as a resonance between gravity waves and centrifugal waves, and is thought to be at the origin of the ”rotating polygon instability” observed in experiments where the flow is driven by rotation of the bottom plate (see [9]). Finally, we give some preliminary results concerning a third model : the Rankine vortex

New AMS (14)C dates from the early Upper Paleolithic sequence of Raqefet Cave, Mount Carmel, Israel

Raqefet Cave (35°04'21"N, 32°39'17"W) is situated in the southeastern side of Mount Carmel in Israel (Figure 1) on the left bank of wadi Raqefet (230 m asl), ~50 m above the wadi bed. It is 50 m long with an area of ~500 m2 (Figure 2). Eric Higgs of Cambridge University and Tamar Noy of the Israel Museum conducted excavations at the site between 1970 and 1972 (Higgs et al. 1975). New excavations at the cave began in 2004 (Lengyel et al. 2005)

Prediction of microgeometrical influences on micropitting fatigue damage on 32CrMoV13 steel

Dr Fabre's sabbatical period at the Cardiff School of Engineering allowed the research to be conducted. Thanks are due to the M2P department of Arts et Métiers ParisTech, to Arts et Métiers ParisTech—Aix en Provence, and to the MécaSurf laboratory for supporting the visit financially, and to Cardiff University for provision of research facilities. Dr Sharif's contribution to the research was supported financially by UK Engineering & Physical Sciences Research Council (EPSRC) with Grant no. EP/G06024X/1.Micropitting is a form of surface fatigue damage that occurs in the gear teeth. It is due to the effect of variation in the mechanical loading in the contact zone between the two teeth, induced especially by flank roughness. In this study, generic roughness profiles were built with geometrical parameters to simulate the contact between two rough surfaces. Using elastohydrodynamic lubrication code and Crossland’s fatigue criteria, the influence on fatigue lifetime was analysed for changes in each parameter. The relevant parameters were determined that influence(i) the conventional pitting,(ii) the extent to which the von Mises equivalent stress exceeds the material yield stress in the zone where micropitting occurs, and(iii) the fatigue lifetime for steel teeth. With nitriding benefits, the same trends were shown with weaker effects

Waves and instabilities in rotating free surface flows

The stability properties of the rotating free surface flow in a cylindrical container is studied using a global stability approach, considering successively three models. For the case of solid body rotation (Newton’s bucket), all eigenmodes are found to be stable, and are classified into three families: gravity waves, singular inertial modes, and Rossby waves. For the case of a potential flow, an instability is found. The mechanism is explained as a resonance between gravity waves and centrifugal waves, and is thought to be at the origin of the “rotating polygon instability” observed in experiments where the flow is driven by rotation of the bottom plate (see L. Tophøj, J. Mougel, T. Bohr, D. Fabre, The Rotating Polygon Instability of a Swirling Free Surface Flow, Phys. Rev. Lett. 110 (2013) 194502). Finally, in the case of the Rankine vortex which in fact consists in the combination of the two first cases, we report a new instability mechanism involving Rossby and gravity waves

Waves in Newton's bucket

The motion of a liquid in an open cylindrical tank rotating at a constant rate around its vertical axis of symmetry, a configuration called Newton’s bucket, is investigated using a linear stability approach. This flow is shown to be affected by several families of waves, all weakly damped by viscosity. The wave families encountered correspond to: surface waves which can be driven either by gravity or centrifugal acceleration, inertial waves due to Coriolis acceleration which are singular in the inviscid limit, and Rossby waves due to height variations of the fluid layer. These waves are described in the inviscid and viscous cases by means of mathematical considerations, global stability analysis and various asymptotic methods; and their properties are investigated over a large range of parameters (a, Fr), with a the aspect ratio and Fr the Froude number

Instability of a potential swirling flow with a free surface

Rotating flows with free surface are commonly observed in everyday-life, the most popular example being the drain vortex observed in bathtubs and sinks. These flows are known to support spectacular patterns arising from breaking of the axial symmetry. A situation which has been particularly investigated through experiments is the case of a partially filled container with a rotating bottom. In this situation, an instability leads to the appearance of rotating polygons along the free surface. The axisymmetric base flow preexisting the instability is rather complex, involving strong recirculations, but includes a region where the rotation is approximately potential, suggesting that the potential vortex may be a relevant model to investigate the instability mechanism. Consequently, we investigate here the linear inviscid stability of the potential swirling flow with a free surface; namely, the flow defined Vθ = Γ/(2πr), with a free surface given by h0 (r) ∼ R2 − r12 , where R1 corresponds to the radius of the dry area. For the study, we use both a global stability approach based on the finite element software Freefem++ and a shallow water approach. Our results show that unstable modes exist in narrow ranges of the Froude number (defined by F r = Γ/2π (gR0 ), R0 being the radius of the cylinder), for all non-zero values of the azimuthal wavenumber m (see figure 1). The instability seems to be related to the ”strato-rotational” instability mechanism existing in stratified rotating fluids

Experimental evidence of spontaneous symmetry breaking in intracavity type-II second harmonic generation with triple resonance

We describe an experiment showing a spontaneous symmetry breaking phenomenon between the intensities of the ordinary and extraordinary components of the fundamental field in intracavity type-II harmonic generation. It is based on a triply resonant dual cavity containing a type II phase matched $\chi^{(2)}$ crystal pumped at the fundamental frequency $\omega_0$. The pump beam generates in the cavity a second harmonic mode at frequency $2\omega_0$ which acts as a pump for frequency degenerate type II parametric down conversion. Under operating conditions which are precisely symmetric with respect to the ordinary and extraordinary components of the fundamental wave, we have observed a breaking of the symmetry on the intensities of these two waves in agreement with the theoretical predictions.Comment: submitte

Mise en place d'un nouveau système d'obtention de viande d'impala au Zimbabwe : comparaison avec les systèmes existants : amélioration des conditions de production

Le Zimbabwe souffre de malnutrition et particulièrement d'un manque de protéines animales. Pour contribuer à résoudre ce problème, le CIRAD a développé deux projets en association avec les collectivités locales qui utilisent la faune sauvage et particulièrement l'impala (Aepyceros melampus) afin de fournir de la viande de brousse de bonne qualité sanitaire, vendue à un prix assez bas pour être accessible à tout le monde. Ainsi, la viande d'impala est obtenue, soit par la chasse de troupeaux sauvages présents en abondance dans certaines zones, soit par leur élevage extensif au sein d'un ranch communal. L'analyse des performances de chasse au ranch a permis de montrer que la chasse de nuit était pour le moment la meilleure technique mais qu'elle ne suffisait pas pour satisfaire pleinement les objectifs. La mise en place d'une boucherie fixe et de protocoles sanitaires ont permis d'exécuter toutes les étapes allant de l'abattage jusqu'à la vente dans le respect de l'hygiène. Toutefois, dans ces deux systèmes, il a fallu s'adapter à la situation et aux besoins locaux. La comparaison de ces deux projets montre que le ranch permet un meilleur contrôle sanitaire de la viande et une meilleure gestion des troupeaux

Experimental investigation of amplitude and phase quantum correlations in a type II OPO above threshold: from the non-degenerate to the degenerate operation

We describe a very stable type II optical parametric oscillator operated above threshold which provides 9.7 $\pm$ 0.5 dB (89%) of quantum noise reduction on the intensity difference of the signal and idler modes. We also report the first experimental study by homodyne detection of the generated bright two-mode state in the case of frequency degenerate operation obtained by introducing a birefringent plate inside the optical cavity