scholarly journals Rotating spherical Couette flow in a dipolar magnetic field: experimental study of magneto-inertial waves

2008 ◽  
Vol 604 ◽  
pp. 175-197 ◽  
Author(s):  
DENYS SCHMITT ◽  
T. ALBOUSSIÈRE ◽  
D. BRITO ◽  
P. CARDIN ◽  
N. GAGNIÈRE ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Couette Flow ◽  
Outer Sphere ◽  
Liquid Sodium ◽  
Inertial Waves ◽  
Spherical Couette Flow ◽  
Rotation Rates ◽  
Inertial Characteristic ◽  
Spherical Couette ◽  
Hydromagnetic Waves

The magnetostrophic regime, in which Lorentz and Coriolis forces are in balance, has been investigated in a rapidly rotating spherical Couette flow experiment. The spherical shell is filled with liquid sodium and permeated by a strong imposed dipolar magnetic field. Azimuthally travelling hydromagnetic waves have been put in evidence through a detailed analysis of electric potential differences measured on the outer sphere, and their properties have been determined. Several types of wave have been identified depending on the relative rotation rates of the inner and outer spheres: they differ by their dispersion relation and by their selection of azimuthal wavenumbers. In addition, these waves constitute the largest contribution to the observed fluctuations, and all of them travel in the retrograde direction in the frame of reference bound to the fluid. We identify these waves as magneto-inertial waves by virtue of the close proximity of the magnetic and inertial characteristic time scales of relevance in our experiment.

scholarly journals Driven inertial waves in spherical Couette flow

2006 ◽  
Vol 16 (4) ◽  
pp. 041105 ◽  
Author(s):  
Douglas H. Kelley ◽  
Santiago Andrés Triana ◽  
Daniel S. Zimmerman ◽  
Barbara Brawn ◽  
Daniel P. Lathrop ◽  
...  
Keyword(s):  
Couette Flow ◽  
Inertial Waves ◽  
Spherical Couette Flow ◽  
Spherical Couette

Spherical Couette flow of Oldroyd 8-constant model Part I. Solution up to the second-order approximation

2006 ◽  
Vol 84 (5) ◽  
pp. 345-364 ◽  
Author(s):  
A Abu-El Hassan
Keyword(s):  
Couette Flow ◽  
Order Approximation ◽  
Order Term ◽  
Additional Term ◽  
Outer Sphere ◽  
Second Order ◽  
Spherical Couette Flow ◽  
Second Order Approximation ◽  
First Order ◽  
Spherical Couette

The steady flow of an incompressible Oldroyd 8-constant fluid in the annular region between two spheres, or so-called spherical Couette flow, is investigated. The inner sphere rotates with anangular velocity Ω about the z-axis, which passes through the center of the spheres, while the outer sphere is kept at rest. The viscoelasticity of the fluid is assumed to dominate the inertia such that the latter can be neglected in the momentum equation. An analytical solution is obtained through the expansion of the dynamical variables in a power series of the dimensionless retardation time. The leading velocity term denotes the Newtonian rotation about the z-axis. The first-order term results in a secondary flow represented by the stream function that divides the flow region into four symmetric parts. The second-order term is the viscoelastic contribution to the primary viscous flow. The first-order approximation depends on the viscosity and four of the material time-constants of the fluid. The second-order approximation depends on the eight viscometric parameters of the fluid. The torque acting on the outer sphere has an additional term due to viscoelasticity that depends on all the material parameters of the fluid under consideration. For an Oldroyd-B fluid this contributed term enhances the primary torque but in the case of fluids with higher elasticity the torque components may be enhanced or diminished depending on the values of the viscometric parameters.PACS Nos.: 47.15.Rq

A super-rotating shear layer in magnetohydrodynamic spherical Couette flow

2002 ◽  
Vol 452 ◽  
pp. 263-291 ◽  
Author(s):  
E. DORMY ◽  
D. JAULT ◽  
A. M. SOWARD
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Point Source ◽  
Shear Layer ◽  
Outer Boundary ◽  
Outer Sphere ◽  
Free Shear Layer ◽  
Spherical Couette Flow ◽  
Spherical Couette ◽  
Layer Problem

We consider axisymmetric magnetohydrodynamic motion in a spherical shell driven by rotating the inner boundary relative to the stationary outer boundary – spherical Couette flow. The inner solid sphere is rigid with the same electrical conductivity as the surrounding fluid; the outer rigid boundary is an insulator. A force-free dipole magnetic field is maintained by a dipole source at the centre. For strong imposed fields (as measured by the Hartmann number M), the numerical simulations of Dormy et al. (1998) showed that a super-rotating shear layer (with angular velocity about 50% above the angular velocity of the inner core) is attached to the magnetic field line [Cscr ] tangent to the outer boundary at the equatorial plane of symmetry. At large M, we obtain analytically the mainstream solution valid outside all boundary layers by application of Hartmann jump conditions across the inner- and outer-sphere boundary layers. We formulate the large-M boundary layer problem for the free shear layer of width M−1/2 containing [Cscr ] and solve it numerically. The super-rotation can be understood in terms of the nature of the meridional electric current flow in the shear layer, which is fed by the outer-sphere Hartmann layer. Importantly, a large fraction of the current entering the shear layer is tightly focused and effectively released from a point source at the equator triggered by the tangency of the [Cscr ]-line. The current injected by the source follows the [Cscr ]-line closely but spreads laterally due to diffusion. In consequence, a strong azimuthal Lorentz force is produced, which takes opposite signs either side of the [Cscr ]-line; order-unity super-rotation results on the equatorial side. In fact, the point source is the small equatorial Hartmann layer of radial width M−2/3 ([Lt ]M−1/2) and latitudinal extent M−1/3. We construct its analytic solution and so determine an inward displacement width O(M−2/3) of the free shear layer. We compare our numerical solution of the free shear layer problem with our numerical solution of the full governing equations for M in excess of 104. We obtain excellent agreement. Some of our more testing comparisons are significantly improved by incorporating the shear layer displacement caused by the equatorial Hartmann layer.

scholarly journals Modes and instabilities in magnetized spherical Couette flow

2013 ◽  
Vol 716 ◽  
pp. 445-469 ◽  
Author(s):  
A. Figueroa ◽  
N. Schaeffer ◽  
H.-C. Nataf ◽  
D. Schmitt
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Time Series ◽  
Couette Flow ◽  
Outer Boundary ◽  
Frequency Spectra ◽  
Spherical Couette Flow ◽  
Moderate Reynolds Number ◽  
Inner Sphere ◽  
Spherical Couette

AbstractSeveral teams have reported peculiar frequency spectra for flows in a spherical shell. To address their origin, we perform numerical simulations of the spherical Couette flow in a dipolar magnetic field, in the configuration of the$DTS$experiment. The frequency spectra computed from time-series of the induced magnetic field display similar bumpy spectra, where each bump corresponds to a given azimuthal mode number$m$. The bumps appear at moderate Reynolds number (${\simeq }2600$) if the time-series are long enough (${\gt }300$rotations of the inner sphere). We present a new method that permits retrieval of the dominant frequencies for individual mode numbers$m$, and extraction of the modal structure of the full nonlinear flow. The maps of the energy of the fluctuations and the spatio-temporal evolution of the velocity field suggest that fluctuations originate in the outer boundary layer. The threshold of instability is found at${\mathit{Re}}_{c} = 1860$. The fluctuations result from two coupled instabilities: high-latitude Bödewadt-type boundary layer instability, and secondary non-axisymmetric instability of a centripetal jet forming at the equator of the outer sphere. We explore the variation of the magnetic and kinetic energies with the input parameters, and show that a modified Elsasser number controls their evolution. We can thus compare with experimental determinations of these energies and find a good agreement. Because of the dipolar nature of the imposed magnetic field, the energy of magnetic fluctuations is much larger near the inner sphere, but their origin lies in velocity fluctuations that are initiated in the outer boundary layer.

scholarly journals Spherical Couette flow in a dipolar magnetic field

2007 ◽  
Vol 26 (6) ◽  
pp. 729-737 ◽  
Author(s):  
Rainer Hollerbach ◽  
Elisabeth Canet ◽  
Alexandre Fournier
Keyword(s):  
Magnetic Field ◽  
Couette Flow ◽  
Spherical Couette Flow ◽  
Spherical Couette

scholarly journals Подавление турбулентности в течениях с вращением

2019 ◽  
Vol 45 (17) ◽  
pp. 20
Author(s):  
Д.Ю. Жиленко ◽  
О.Э. Кривоносова
Keyword(s):  
Laminar Flow ◽  
Couette Flow ◽  
Outer Sphere ◽  
Modulation Amplitude ◽  
Flow State ◽  
Turbulence Control ◽  
Spherical Couette Flow ◽  
Rate Modulation ◽  
Narrow Frequency Band ◽  
Spherical Couette

The possibilities of turbulence control in spherical Couette flow were examined experimentally. It was shown, that with increasing of outer sphere rotational rate modulation amplitude, the suppression of turbulence is possible with transition to laminar flow state. The reverse process - turbulence recovery - is available with amplitude decreasing. It was established that turbulence breaking and recovering is accompanied by hysteresis. It was shown, that at small values of modulation amplitude, suppression of turbulence is available only in narrow frequency band.

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