Axisymmetric propagating vortices in centrifugally stable Taylor–Couette flow

2013 ◽  
Vol 728 ◽  
pp. 458-470 ◽  
Author(s):  
C. Hoffmann ◽  
S. Altmeyer ◽  
M. Heise ◽  
J. Abshagen ◽  
G. Pfister
Keyword(s):  
Hopf Bifurcation ◽  
Shear Flow ◽  
Couette Flow ◽  
Instability Threshold ◽  
Experimental Results ◽  
Centrifugal Instability ◽  
Taylor Couette ◽  
Steady Vortices ◽  
Ekman Cells ◽  
Taylor Couette Flow

AbstractWe present numerical as well as experimental results of axisymmetric, axially propagating vortices appearing in counter-rotating Taylor–Couette flow below the centrifugal instability threshold of circular Couette flow without additional externally imposed forces. These propagating vortices are periodically generated by the shear flow near the Ekman cells that are induced by the non-rotating end walls. These axisymmetric vortices propagate into the bulk towards mid-height, where they get annihilated by rotating, non-propagating defects. These propagating structures appear via a supercritical Hopf bifurcation from axisymmetric, steady vortices, which have been discovered recently in centrifugally stable counter-rotating Taylor–Couette flow (Abshagen et al., Phys. Fluids, vol. 22, 2010, 021702). In the nonlinear regime of the Hopf bifurcation, contributions of non-axisymmetric modes also appear.

Nonlinear Taylor–Couette flow of helium II

1995 ◽  
Vol 283 ◽  
pp. 329-340 ◽  
Author(s):  
Karen L. Henderson ◽  
Carlo F. Barenghi ◽  
Chris A. Jones
Keyword(s):  
Couette Flow ◽  
Equations Of Motion ◽  
Experimental Results ◽  
Second Sound ◽  
Helium Ii ◽  
Vortex Lines ◽  
Taylor Couette ◽  
First Time ◽  
Two Fluid ◽  
Taylor Couette Flow

We solve the nonlinear two-fluid Hall–Vinen–Bekharevich–Khalatnikov equations of motion of helium II for the first time and investigate the configuration of quantized vortex lines in Taylor–Couette flow. The results are interpreted in terms of quantities which can be observed by measuring the attenuation of second sound. Comparison is made with existing experimental results.

Interaction between Ekman pumping and the centrifugal instability in Taylor–Couette flow

2003 ◽  
Vol 15 (2) ◽  
pp. 467-477 ◽  
Author(s):  
Olivier Czarny ◽  
Eric Serre ◽  
Patrick Bontoux ◽  
Richard M. Lueptow
Keyword(s):  
Couette Flow ◽  
Ekman Pumping ◽  
Centrifugal Instability ◽  
Taylor Couette ◽  
Taylor Couette Flow

The onset of steady vortices in Taylor-Couette flow: The role of approximate symmetry

2012 ◽  
Vol 24 (6) ◽  
pp. 064102 ◽  
Author(s):  
K. A. Cliffe ◽  
T. Mullin ◽  
D. Schaeffer
Keyword(s):  
Couette Flow ◽  
Approximate Symmetry ◽  
Taylor Couette ◽  
Steady Vortices ◽  
Taylor Couette Flow

Centrifugal instability of pulsed Taylor-Couette flow in a Maxwell fluid

2016 ◽  
Vol 39 (8) ◽  
Author(s):  
Mehdi Riahi ◽  
Saïd Aniss ◽  
Mohamed Ouazzani Touhami ◽  
Salah Skali Lami
Keyword(s):  
Couette Flow ◽  
Maxwell Fluid ◽  
Centrifugal Instability ◽  
Taylor Couette ◽  
Taylor Couette Flow

Instabilities and transient growth of the stratified Taylor–Couette flow in a Rayleigh-unstable regime

2017 ◽  
Vol 822 ◽  
pp. 80-108 ◽  
Author(s):  
Junho Park ◽  
Paul Billant ◽  
Jong-Jin Baik
Keyword(s):  
Couette Flow ◽  
Density Stratification ◽  
Rotational Instability ◽  
Transient Growth ◽  
Unstable Regime ◽  
Stable Regime ◽  
Energy Growth ◽  
Centrifugal Instability ◽  
Taylor Couette ◽  
Taylor Couette Flow

The stability of the Taylor–Couette flow is analysed when there is a stable density stratification along the axial direction and when the flow is centrifugally unstable, i.e. in the Rayleigh-unstable regime. It is shown that not only the centrifugal instability but also the strato-rotational instability can occur. These two instabilities can be explained and well described by means of a Wentzel–Kramers–Brillouin–Jeffreys asymptotic analysis for large axial wavenumbers in inviscid and non-diffusive limits. In the presence of viscosity and diffusion, numerical results reveal that the strato-rotational instability becomes dominant over the centrifugal instability at the onset of instability when the axial density stratification is sufficiently strong. Linear transient energy growth is next investigated for counter-rotating cylinders in the stable regime of the Froude number–Reynolds number parameter space. We show that there exist two types of transient growth mechanism analogous to the lift up and the Orr mechanisms in homogeneous fluids but with the additional effect of density perturbations. The dominant mechanism depends on the stratification: when the stratification is strong, non-axisymmetric three-dimensional perturbations achieve the optimal energy growth through the Orr mechanism while for moderate stratification, axisymmetric perturbations lead to the optimal transient growth by a lift-up mechanism involving internal waves.

Organized structures in turbulent Taylor-Couette flow

1984 ◽  
Vol 143 ◽  
pp. 429-449 ◽  
Author(s):  
A. Barcilon ◽  
J. Brindley
Keyword(s):  
Couette Flow ◽  
Eigenvalue Problems ◽  
Annular Region ◽  
Circular Cylinders ◽  
Coherent Motion ◽  
Marginal Stability ◽  
Centrifugal Instability ◽  
Wide Range ◽  
Taylor Couette ◽  
Taylor Couette Flow

A simple mathematical model is constructed to describe the regime of flow, extending over a wide range of values of Taylor number, in which turbulent Taylor–Couette flow in the annular region between two coaxial circular cylinders is characterized by the coexistence of steady coherent motion on two widely separated scales. These scales of motion, corresponding to the gap width of the annular region and to a boundary-layer thickness, are each identified as the consequence of a centrifugal instability, and are described as Taylor vortices and Görtler vortices respectively.The assumption that both scales of motion are near marginal stability gives a closure to a pair of coupled eigenvalue problems, and the results of a linear analysis are shown to be in good agreement with many features of experimental observations.

Non-axisymmetric subcritical bifurcations in viscoelastic Taylor–Couette flow

1994 ◽  
Vol 447 (1929) ◽  
pp. 135-153 ◽  
Keyword(s):  
Hopf Bifurcation ◽  
Couette Flow ◽  
Reynolds Numbers ◽  
Gap Size ◽  
Ginzburg Landau ◽  
Hopf Bifurcation Point ◽  
Stable Pattern ◽  
Flow Parameters ◽  
Taylor Couette ◽  
Taylor Couette Flow

Recently, an account of the linear and nonlinear analysis of the viscoelastic Taylor–Couette flow between independently rotating cylinders against axisymmetric disturbances was presented (Avgousti & Beris 1993 a ). However, more recent linear stability analysis has shown that for the range of geometric and kinematic parameters studied and for high enough values of flow elasticity, the critical instabilities are caused by non-axisymmetric, time-dependent disturbances (Avgousti & Beris 1993 b ). In this work, we calculate the bifurcating families corresponding to each one of the two possible non-axisymmetric patterns emerging at the point of criticality, namely the spirals and ribbons and determine their stability. It is shown that for a narrow gap size, for upper convected Maxwell and Oldroyd-B fluids, at least one of the non-axisymmetric families bifurcates subcritically. This result, in conjunction with the theoretical analysis of Hopf bifurcation in presence of symmetries (Golubitsky et al . 1988), implies that neither of the bifurcating families is stable. Consequently, there is a finite transition corresponding to infinitesimal changes of the flow parameters in the vicinity of the Hopf bifurcation point. Although a change in the ratio of the Deborah and Reynolds numbers has not been found to qualitatively affect this behaviour, calculations with a wider gap size have shown that both bifurcating families become supercritical. There, a Ginzburg–Landau analysis shows that the ribbons are the stable pattern. This behaviour is qualitatively similar to that seen for the newtonian fluid, but for counterrotating cylinders, albeit there, spirals have been found to be stable (Golubitsky & Langford 1988).

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