Inertia–gravity waves in a liquid-filled, differentially heated, rotating annulus

International audienceDirect numerical simulations based on high-resolution pseudospectral methods are carried out for detailed investigation into the instabilities arising in a differentially heated, rotating annulus, the baroclinic cavity. Following previous works using air (Randriamampianina et al., J. Fluid Mech., vol. 561, 2006, pp. 359–389), a liquid defined by Prandtl number Pr=16 is considered in order to better understand, via the Prandtl number, the effects of fluid properties on the onset of gravity waves. The computations are particularly aimed at identifying and characterizing the spontaneously emitted small-scale fluctuations occurring simultaneously with the baroclinic waves. These features have been observed as soon as the baroclinic instability sets in. A three-term decomposition is introduced to isolate the fluctuation field from the large-scale baroclinic waves and the time-averaged mean flow. Even though these fluctuations are found to propagate as packets, they remain attached to the background baroclinic waves, locally triggering spatio-temporal chaos, a behaviour not observed with the air-filled cavity. The properties of these features are analysed and discussed in the context of linear theory. Based on the Richardson number criterion, the characteristics of the generation mechanism are consistent with a localized instability of the shear zonal flow, invoking resonant over-reflection

Numerical evidence of inertia gravity waves in a baroclinic cavity

International audienc

High resolution method for direct numerical simulation of the instability and transition in a baroclinic cavity

International audienc

Annular and spiral patterns in flows between rotating and stationary discs

International audienceDifferent instabilities of the boundary layer flows that appear in the cavity between stationary and rotating discs are investigated using three-dimensional direct numerical simulations. The influence of curvature and confinement is studied using two geometrical configurations: (i) a cylindrical cavity including the rotation axis and (ii) an annular cavity radially confined by a shaft and a shroud. The numerical computations are based on a pseudo-spectral Chebyshev{Fourier method for solving the incompressible Navier{Stokes equations written in primitive variables. The high level accuracy of the spectral methods is imperative for the investigation of such instability structures. The basic flow is steady and of the Batchelor type. At a critical rotation rate, stationary axisymmetric and/or three-dimensional structures appear in the B¨odewadt and Ekman layers while at higher rotation rates a second transition to unsteady flow is observed. All features of the transitions are documented. A comparison of the wavenumbers, frequencies, and phase velocities of the instabilities with available theoretical and experimental results shows that both type II (or A) and type I (or B) instabilities appear, depending on flow and geometric control parameters. Interesting patterns exhibiting the coexistence of circular and spiral waves are found under certain conditions

Instabilité tridimensionnelle dans une cavité inter-disque de type rotor-stator

International audienc

Square patterns in rotating Rayleigh-Bénard convection

International audienc

Geometry effects on the onset of rotating Rayleigh-Bénard convection in annuli

International audienceRayleigh-Bénard convection is investigated in rotating annular cavities at a moderate rotationrate (square root of the Taylor number) Omega= 60. The onset of convection is in the form of azimuthaltraveling waves that set in at the sidewalls and at values of the Rayleigh number significantly belowthe value of the onset of convection in an infinitely extended layer. When curvature effect becomessignificant, the waves traveling along the sidewalls have different critical Rayleigh numbers and com-plex Guinzburg-Landau equations are no longer applicable. The present study addresses the effectsof curvature and confinement on the onset of sidewall convection by using three-dimensional spectralsolutions of the Oberbeck-Boussinesq equations. Such solutions demonstrate that the curvature ofthe outer boundary promotes the onset of the wall mode, while the opposite curvature of the innerboundary tends to delay the onset of the wall mode. When radial confinement is increased the twoindependent traveling waves can interact and eventually merge to form a nearly steady pattern ofconvection

Instabilité tridimensionnelle de la couche d'Ekman dans une configuration annulaire avec flux forcé

International audienceThe three-dimensional time-dependent flow, which develops in a rotating finite annular cavity with an imposed radial throughflow, is studied using a pseudospectral numerical method. The topic of this paper is to present, for the first time by direct numerical simulation, a fully three-dimensional investigation of the temporal and spatial regimes occurring in the Ekman boundary layer flow. The basic flow corresponds to the Ekman layer solution and is axisymmetric. At high enough values of the mass flow rate, the flow becomes oscillatory and spatial structures appear in the boundary layers under the form of circular or spiral rolls with characteristic parameters of type II instability. The radial component of the wave number in spiral patterns remains the same as in circular patterns but in these structures also arises an azimuthal component in a similar way to the zig-zag instability that is observed in weakly confined natural convection.On considère des écoulements tridimensionnels dans une cavité annulaire de dimension finie en rotation d'ensemble autour de son axe, et soumise à un flux forcé radial. L'objectif est l'étude des régimes spatiaux et temporels se développant comme conséquence de l'instabilité de la couche limite d'Ekman. Pour des nombres de Reynolds suffisamment grands, on met en évidence des structures instationnaires, axisymétriques et tridimensionnelles composées de rouleaux circulaires ou de structures en spirale, dont le nombre d'onde et la fréquence correspondent à la gamme des valeurs caractéristiques de l'instabilité de type II. Les résultats indiquent que les stmetures spirales sont atteintes à partir de la structure axisymétrique et suivant un processus similaire à celui de l'instabilité en zigzag. Il s'agit des premières simulations numériques directes reproduisant les structures tridimensionnelles en spirale

Axisymmetric and three-dimensional instabilities in an Ekman boundary layer flow

International audienc