Linear stability of a circular Couette flow under a radial thermoelectric body force

2015 ◽  
Vol 91 (3) ◽  
Author(s):  
H. N. Yoshikawa ◽  
A. Meyer ◽  
O. Crumeyrolle ◽  
I. Mutabazi
Keyword(s):  
Linear Stability ◽  
Couette Flow ◽  
Body Force ◽  
Circular Couette Flow

Numerical simulation of circular Couette flow under a radial thermo-electric body force

2017 ◽  
Vol 29 (11) ◽  
pp. 114105 ◽  
Author(s):  
Changwoo Kang ◽  
Antoine Meyer ◽  
Harunori N. Yoshikawa ◽  
Innocent Mutabazi
Keyword(s):  
Numerical Simulation ◽  
Couette Flow ◽  
Body Force ◽  
Thermo Electric ◽  
Circular Couette Flow

Stratified circular Couette flow: instability and flow regimes

1995 ◽  
Vol 292 ◽  
pp. 333-358 ◽  
Author(s):  
B. M. Boubnov ◽  
E. B. Gledzer ◽  
E. J. Hopfinger
Keyword(s):  
Reynolds Number ◽  
Linear Stability ◽  
Couette Flow ◽  
Flow Instability ◽  
Buoyancy Frequency ◽  
Vertical Wavelength ◽  
Taylor Vortices ◽  
Circular Couette Flow ◽  
Vortex Size ◽  
Gap Width

The stability conditions of the flow between two concentric cylinders with the inner one rotating (circular Couette flow) have been investigated experimentally and theoretically for a fluid with axial, stable linear density stratification. The behaviour of the flow, therefore, depends on the Froude number Fr = Ω/N (where Ω is the angular velocity of the inner cylinder and N is the buoyancy frequency of the fluid) in addition to the Reynolds number and the non-dimensional gap width ε, here equal to 0.275.Experiments show that stratification has a stabilizing effect on the flow with the critical Reynolds number depending on N, in agreement with linear stability theory. The selected, most amplified, vertical wavelength at onset of instability is reduced by the stratification effect and is for the geometry considered only about half the gap width. Furthermore, the observed instability is non-axisymmetric. The resulting vortex motion causes some mixing and this leads to layer formation, clearly visible on shadowgraph images, with the height of the layer being determined by the vertical vortex size. This regime of vertically reduced vortex size is referred to as the S-regime.For larger Reynolds and Froude numbers the role of stratification decreases and the most amplified vertical wavelength is determined by the gap width, giving rise to the usual Taylor vortices (we call this the T-regime). The layers which emerge are determined by these vortices. For relatively small Reynolds number when Fr ≈ 1 the Taylor vortices are stable and the layers have a height h equal to the gap width; for larger Reynolds number or Fr ≈ 2 the Taylor vortices interact in pairs (compacted Taylor vortices, regime CT) and layers of twice the gap width are predominant. Stratification inhibits the azimuthal wavy vortex flow observed in homogeneous fluid. By further increasing the Reynolds number, turbulent motions appear with Taylor vortices superimposed like in non-stratified fluid.The theoretical analysis is based on a linear stability consideration of the axisymmetric problem. This gives bounds of instability in the parameter space (Ω, N) for given vertical and radial wavenumbers. These bounds are in qualitative agreement with experiments. The possibility of oscillatory-type instability (overstability) observed experimentally is also discussed.

Linear stability of modulated circular Couette flow

1976 ◽  
Vol 75 (4) ◽  
pp. 625-646 ◽  
Author(s):  
P. J. Riley ◽  
R. L. Laurence
Keyword(s):  
Linear Stability ◽  
Couette Flow ◽  
Floquet Theory ◽  
Outer Cylinder ◽  
Time Dependent ◽  
Narrow Gap ◽  
Circular Couette Flow ◽  
Steady Rotation ◽  
The Stability ◽  
Axisymmetric Disturbances

The linear stability of modulated circular Couette flow to axisymmetric disturbances is examined in the narrow-gap limit. The outer cylinder is assumed stationary, while the inner is modulated both with and without a mean rotation. The equations governing the disturbance motion are solved by a Galerkin expansion with time-dependent coefficients, and the stability of the motion determined by Floquet theory. Modulation is found, in general, to destabilize the flow due to steady rotation, although weak stabilization is found for some modulation amplitudes at intermediate frequencies.

On the stability of circular Couette flow with radial heating

1990 ◽  
Vol 220 ◽  
pp. 53-84 ◽  
Author(s):  
Mohamed Ali ◽  
P. D. Weidman
Keyword(s):  
Linear Stability ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Boussinesq Approximation ◽  
Base Flow ◽  
Linear Stability Theory ◽  
Critical Stability ◽  
Circular Couette Flow ◽  
Prandtl Numbers ◽  
The Stability

The stability of circular Couette flow with radial heating across a vertically oriented annulus with inner cylinder rotating and outer cylinder stationary is investigated using linear stability theory. Infinite aspect ratio and constant fluid properties are assumed and critical stability boundaries are calculated for a conduction-regime base flow. Buoyancy is included through the Boussinesq approximation and stability is tested with respect to both toroidal and helical disturbances of uniform wavenumber. Symmetries of the linearized disturbance equations based on the sense of radial heating and the sense of cylinder rotation and their effect on the kinematics and morphology of instability waveforms are presented. The numerical investigation is primarily restricted to radius ratios 0.6 and 0.959 at Prandtl numbers 4.35, 15 and 100. The results follow the development of critical stability from Taylor cells at zero heating through a number of asymmetric modes to axisymmetric cellular convection at zero rotation. Increasing the Prandtl number profoundly destabilizes the flow in both wide and narrow gaps and the number of contending critical modes increases with increasing radius ratio. Specific calculations made to compare with the stability measurements of Snyder & Karlsson (1964) and Sorour & Coney (1979) exhibit good agreement considering the idealizations built into the linear stability analysis.

On the linear stability of cellular spiral Couette flow

1993 ◽  
Vol 5 (5) ◽  
pp. 1188-1200 ◽  
Author(s):  
Mohamed E. Ali ◽  
P. D. Weidman
Keyword(s):  
Linear Stability ◽  
Couette Flow
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