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Abstract. We discuss the possibility that astrophysical accretion disks are dynamically unstable to non-axisymmetric disturbances with characteristic scales much smaller than the vertical scale height. The instability is studied using three methods: one based on the energy integral, which allows the determination of a sufficient condition of stability, one using a WKB approach, which allows the determination of the necessary and sufficient condition for instability and a last one by numerical solution. This linear instability occurs in any inviscid stably stratified differential rotating fluid for rigid, stress-free or periodic boundary conditions, provided the angular velocity Ω decreases outwards with radius r. At not too small stratification, its growth rate is a fraction of Ω. The influence of viscous dissipation and thermal diffusivity on the instability is studied numerically, with emphasis on the case when d ln Ω/d ln r = −3/2 (Keplerian case). Strong stratification and large diffusivity are found to have a stabilizing effect. The corresponding critical stratification and Reynolds number for the onset of the instability in a typical disk are derived. We propose that the spontaneous generation of these linear modes is the source of turbulence in disks, especially in weakly ionized disks.

The stability of buoyant-thermocapillary-driven flows in a fluid layer subjected to a horizontal temperature gradient is analysed. Our purpose is the modelization of recent experimental results obtained for a fluid of Prandtl number Pr=7, by Daviaud and Vince [Phys. Rev. E, 4432 (1993)] who observed a transition between traveling waves and stationary rolls when the height of fluid is increased. Our model takes into account several effects which were examined separately in previous studies. The relative importance of buoyancy and thermocapillarity is controlled by the ratio W of Marangoni number to Rayleigh number. The fluid layer is bounded below by a rigid plane whose temperature varies linearly along the direction of the thermal gradient. A Biot number is introduced to describe heat transfer at the top free surface. Our stability analysis establishes the existence of a transition between stationary and oscillatory modes when W exceeds a value W0 which is function of the Biot number. Moreover, two types of oscillatory modes have been identified which differ by the range of variation of their critical parameters (wave number, frequency, angle of propagation) versus W .

2014 On montre que les propriétés du phénomène convectif de Rayleigh-Bénard au voisinage de son seuil critique d'instabilité sont ctroitement liées à celles d'une transition de phase du second ordre. Dans le cadre des hypothèses de Landau-Hopf une théorie est développée dont l'ensemble des conséquences est vérifié par les résultats expérimentaux. Abstract. 2014 The properties of the convection Rayleigh-Bénard phenomenon near its critical threshold of instability are shown to be closely related to those of a second order phase transition. A theory is developed in the framework of the Landau-Hopf hypothesis, and all its predictions are verified by experimental results.

We investigate dynamo action by solving the kinematic dynamo problem for velocity fields of the von Kármán type between two coaxial counter-rotating propellers in a cylinder. A Galerkin method is implemented that takes advantage of the symmetries of the flow and their subsequent influence on the nature of the magnetic field at the dynamo threshold. Distinct modes of instability have been identified that differ by their spatial and temporal behaviors. Our calculations give the result that a stationary and antisymmetric mode prevails at the dynamo threshold. We then present a quantitative analysis of the results based on the parametric study of four interaction coefficients obtained by reduction of our initially large eigenvalue problem. We propose these coefficients to measure the relative importance of the different mechanisms at play in the von Kármán kinematic dynamo.

The rotation effects on centrifugally driven instabilities in curved channel flow with a finite gap are investigated. An inviscid criterion of stability is formulated to explain the behavior of the flow when rotation and curvature effects compete to either stabilize or destabilize the flow. The stability of curved Poiseuille flow with finite gap size is studied, and it is shown that the asymmetry between the directions of rotation is enhanced when the gap size increases.

A model for penetrative convection in which a stably stratified layer of fluid is bounded by two unstable layers is considered. This configuration is obtained in a horizontal water layer around its density extremum when a quadratic temperature profile is maintained by internal heating. A linear stability analysis shows that either stationary or oscillatory modes set in at the onset of instability depending on the values of the control parameter. Moreover, two types of stationary modes have been identified that differ by the value of their critical wave number and the number of vertical cells. These results are discussed in the light of recent studies on related topics.

We study the dynamo threshold of a helical flow made of a mean (stationary) plus a fluctuating part. Two flow geometries are studied, either (i) solid body or (ii) smooth. Two well-known resonant dynamo conditions, elaborated for stationary helical flows in the limit of large magnetic Reynolds numbers, are tested against lower magnetic Reynolds numbers and for fluctuating flows (zero mean). For a flow made of a mean plus a fluctuating part the dynamo threshold depends on the frequency and the strength of the fluctuation. The resonant dynamo conditions applied on the fluctuating (resp. mean) part seems to be a good diagnostic to predict the existence of a dynamo threshold when the fluctuation level is high (resp. low).PACS numbers: 47.65.+a arXiv:physics/0703216v1 [physics.flu-dyn]