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

Linear and nonlinear dynamics of axisymmetric waves in the hollow core vortex

The dynamics of trailing vortices are under constant investigation during last decades since it is of considerable interest to reduce aircraft wakes and associated hazards to forthcoming planes. The isolated axisymmetric vortex is the commonly used simplest elementary model when considering such issue. Although asymptotically stable, recent studies have revealed its sensitiveness to specific perturbations, leading in some cases to considerable gains of energy. Albeit of evident interest, the underlying mechanisms of energy growth are considered in the linear regime. The nonlinear dynamics of such vortices need also to be considered in order to complete the picture. Rather than performing direct numerical simulations3, an interesting way to investigate it is to consider the nonlinear interactions of waves. This approach is motivated by the possible existence of resonance between wave components. For this purpose, the base flow model is simplified by considering the hollow core vortex. Arising naturally when a tank is drained (bath-tube vortex), it presents simpler dynamics than the Lamb-Oseen vortex as it only possesses two families of waves. This point is of crucial importance for the tractability of the problem. In this work, the nonlinear temporal evolution of axisymmetric waves are investigated through numerical integration when the flow is submitted to various initial conditions (travelling or standing wave, pinching of the free surface, wave trains). We focus on wave trains as important energy exchanges between the main component and its sideband waves are observed. This phenomenon is related to the Benjamin-Feir instability4 (triadic resonance) occurring for wave trains on deep water

Crossover from quasi-static to dense flow regime in compressed frictional granular media

We investigate the evolution of multi-scale mechanical properties towards the macroscopic mechanical instability in frictional granular media under multiaxial compressive loading. Spatial correlations of shear stress redistribution following nucleating contact sliding events and shear strain localization are investigated. We report growing correlation lengths associated to both shear stress and shear strain fields that diverge simultaneously as approaching the transition to a dense flow regime. This shows that the transition from quasi static to dense flow regime can be interpreted as a critical phase transition. Our results suggest that no shear band with a characteristic thickness has formed at the onset of instability

Stochastic forcing of the Lamb–Oseen vortex

The aim of the present paper is to analyse the dynamics of the Lamb–Oseen vortex when continuously forced by a random excitation. Stochastic forcing is classically used to mimic external perturbations in realistic configurations, such as variations of atmospheric conditions, weak compressibility effects, wing-generated turbulence injected in aircraft wake, or free-stream turbulence in wind tunnel experiments. The linear response of the Lamb–Oseen vortex to stochastic forcing can be decomposed in relation to the azimuthal symmetry of the perturbation given by the azimuthal wavenumber m. In the axisymmetric case m = 0, we find that the response is characterised by the generation of vortex rings at the outer periphery of the vortex core. This result is consistent with recurrent observations of such dynamics in the study of vortex-turbulence interaction. When considering helical perturbations m = 1, the response at large axial wavelengths consists of a global translation of the vortex, a feature very similar to the phenomenon of vortex meandering (or wandering) observed experimentally, corresponding to an erratic displacement of the vortex core. At smaller wavelengths, we find that stochastic forcing can excite specific oscillating modes of the Lamb–Oseen vortex. More precisely, damped critical-layer modes can emerge via a resonance mechanism. For perturbations with higher azimuthal wavenumber m > 2, we find no structure that clearly dominates the response of the vortex

On the validity of Kraichnan scalings for forced two-dimensional turbulence

We examine the validity of the scaling laws derived by Kraichnan (1967) for forced two-dimensional turbulence. We use a new numerical technique (Dritschel & Fontane 2010) to reach higher Reynolds number than previously accessible with classical pseudo-spectral methods. No large scale friction or hypo-diffusion is used in order to avoid any distortion of the inverse cascade and to be in agreement with the theoretical framework used by Kraichnan. Both spectral and spatial forcing are considered and statistical convergence is obtained through large simulation ensembles. A steeper energy spectrum proportional to k^(-2) is observed for the inverse cascade in place of the classical k^(-5/3) prediction. This steepening is shown to be associated with a faster growth of energy at large scales, scaling like t^(-1) rather than Kraichnan's prediction of t^(-3/2). The deviation from Kraichnan's theory is related to the emergence of a vortex population dominating the distribution of energy across scales, and whose number density and vorticity distribution with respect to vortex area are related to the shape of the enstrophy spectrum

The Regulator and the Judge: The Optimal Mix in TheControl of Environmental Risk

Nous considérons une firme qui génère un risque pour l'environnment via son activité industrielle et qui a une information privée à la fois sur son effort de précaution et sur le montant de ses actifs. Nous étudions l'interaction entre l'audit ex ante de l'effort de précaution par un régulateur et la vérification ex post de la capacité financière par un juge en cas d'accident. Du point de vue des incitations, les deux instruments sont utiles. Le policy-mix optimal dépend de la règle gouvernant l'intervention ex post et de l'efficience de l'intervention ex ante.

Effective Theory of Dark Energy at Redshift Survey Scales

We explore the phenomenological consequences of general late-time modifications of gravity in the quasi-static approximation, in the case where cold dark matter is non-minimally coupled to the gravitational sector. Assuming spectroscopic and photometric surveys with configuration parameters similar to those of the Euclid mission, we derive constraints on our effective description from three observables: the galaxy power spectrum in redshift space, tomographic weak-lensing shear power spectrum and the correlation spectrum between the integrated Sachs-Wolfe effect and the galaxy distribution. In particular, with $\Lambda$CDM as fiducial model and a specific choice for the time dependence of our effective functions, we perform a Fisher matrix analysis and find that the unmarginalized $68\%$ CL errors on the parameters describing the modifications of gravity are of order $\sigma\sim10^{-2}$--$10^{-3}$. We also consider two other fiducial models. A nonminimal coupling of CDM enhances the effects of modified gravity and reduces the above statistical errors accordingly. In all cases, we find that the parameters are highly degenerate, which prevents the inversion of the Fisher matrices. Some of these degeneracies can be broken by combining all three observational probes.Comment: 41 pages, 5 figures, 2 tables, improved analysis of ISW-galaxy correlation, matches published version on JCA

The public management of risk: Separating ex ante and ex post monitors

When a firm undertakes risky activities, the conflict between social and private incentives to exercise safety care requires public intervention. This control takes the form of both monetary incentives but also monitoring taking place either ex ante or ex post, i.e. before or after an accident occurs. We delineate the respective scopes of these monitoring activities when public monitors are either benevolent or corruptible. Separation between the ex ante and the ex post monitors helps to prevent capture, increases the likelihood of ex post investigation and improves welfare.risk regulation ; monitoring ; capture ; integration and separation

Healthy theories beyond Horndeski

We introduce a new class of scalar-tensor theories that extend Horndeski, or "generalized galileon", models. Despite possessing equations of motion of higher order in derivatives, we show that the true propagating degrees of freedom obey well-behaved second-order equations and are thus free from Ostrogradski instabilities, in contrast to the standard lore. Remarkably, the covariant versions of the original galileon Lagrangians-obtained by direct replacement of derivatives with covariant derivatives-belong to this class of theories. These extensions of Horndeski theories exhibit an uncommon, interesting phenomenology: the scalar degree of freedom affects the speed of sound of matter, even when the latter is minimally coupled to gravity.Comment: 5 pages, version accepted in PR