Papers by Christiane Normand
Effets de courbure sur l'instabilité en ondes hydrothermales d'un écoulement thermocapillaire radial
The stability of a thermocapillary flow in an extended cylindrical geometry is analyzed. This flo... more The stability of a thermocapillary flow in an extended cylindrical geometry is analyzed. This flow occurs in a thin liquid layer with a disk shape when a radial temperature gradient is applied along the horizontal free surface. Besides the aspect ratio, a second parameter related to the local curvature is introduced to describe completely the geometrical effects. We recover classical hydrothermal waves as predicted by Smith and Davis, but the properties of these waves are shown to evolve with the curvature parameter, thus leading to a nonuniform pattern over the cell. Moreover, it is shown that the problem is not invariant with respect to the exchange of the hot and cold sides.
Comptes Rendus de l'Académie des Sciences - Series IV - Physics, 2001
Astronomy and Astrophysics, 2005
We discuss the possibility that astrophysical accretion disks are dynamically unstable to nonaxis... more We discuss the possibility that astrophysical accretion disks are dynamically unstable to nonaxisymmetric 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 a thermocapillary flow in an extended cylindrical geometry is analyzed. This flo... more The stability of a thermocapillary flow in an extended cylindrical geometry is analyzed. This flow occurs in a thin liquid layer with a disk shape when a radial temperature gradient is applied along the horizontal free surface. Besides the aspect ratio, a second parameter related to the local curvature is introduced to describe completely the geometrical effects. We recover classical
Effets de courbure sur l'instabilité en ondes hydrothermales d'un écoulement thermocapillaire radial
The stability of a thermocapillary flow in an extended cylindrical geometry is analyzed. This flo... more The stability of a thermocapillary flow in an extended cylindrical geometry is analyzed. This flow occurs in a thin liquid layer with a disk shape when a radial temperature gradient is applied along the horizontal free surface. Besides the aspect ratio, a second parameter related to the local curvature is introduced to describe completely the geometrical effects. We recover classical hydrothermal waves as predicted by Smith and Davis, but the properties of these waves are shown to evolve with the curvature parameter, thus leading to a nonuniform pattern over the cell. Moreover, it is shown that the problem is not invariant with respect to the exchange of the hot and cold sides.
Journal de Physique, 1978
2014 On montre que les propriétés du phénomène convectif de Rayleigh-Bénard au voisinage de son s... more 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. Tome 39 N° 7 JUILLET Classification Physics Abstracts 47 . 25Q
Gap size effects on centrifugally and rotationally driven instabilities
Physics of Fluids A: Fluid Dynamics, 1992
The rotation effects on centrifugally driven instabilities in curved channel flow with a finite g... more 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 ...
Oscillatory modes in the flow between two horizontal corotating cylinders with a partially filled gap
Physical Review A, 1989
ABSTRACT The linear stability of viscous flow between two rotating coaxial horizontal cylinders w... more ABSTRACT The linear stability of viscous flow between two rotating coaxial horizontal cylinders with a partially filled gap is investigated. It is shown that, for a range of values of the rotation ratio $\mu${}, the stability diagram for stationary modes consists of two separate curves connected by an oscillatory branch. For 0.26<$\mu${}<0.61 the critical point is on the oscillatory branch. Therefore it can be expected that, at onset, the instability will set in as an oscillatory mode. We have established the existence of codimension-2 points for two particular values of the rotation ratio $\mu${}=0.26 and 0.61, where the onset of instability for stationary as well as oscillatory modes occurs for the same value of the Taylor number.
Convective instability: A physicist's approach
Reviews of Modern Physics, 1977
Convective instability: A physicist's approach. Christiane Normand and Yves Pomeau S... more Convective instability: A physicist's approach. Christiane Normand and Yves Pomeau Service de Physique Theorique, CEN de Saclay, 91190 Gif-sur-Yvette (France). Manuel G. Velarde * Departamento de Física C3, Universidad ...
Physics of Fluids, 1994
The stability of a pulsed flow in a Taylor-Couette geometry with both cylinders rotating at the s... more The stability of a pulsed flow in a Taylor-Couette geometry with both cylinders rotating at the same angular velocity fl(t)=O, cos (ot) is investigated. The first experimental evidence showing that the flow is less unstable in the limit of low and high frequency while destabilization is maximum for an intermediate frequency oO is reported. A detailed analysis of the restabilization at frequencies just above wO reveals a behavior not accounted for by previous theoretical analysis. Thus, the linear stability analysis is reconsidered by using a different implementation of the Floquet theory and a satisfactory agreement with the present experimental results is found.
International Communications in Heat and Mass Transfer, 1986
We propose a similarity analysis for the non linear development of Mngers in thermohallne convect... more We propose a similarity analysis for the non linear development of Mngers in thermohallne convection. Their horizontal width grows as the square root of time, and their vertical extension as time to the square, the origin of tlme being the instant when the aspect ratio of the fingers is of order unity.
Comptes Rendus de l'Académie des Sciences - Series IV - Physics, 2001
Parametric instability of the helical dynamo
Physics of Fluids, 2007
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Papers by Christiane Normand