The linear stability of steady circular Couette flow with a small radial temperature gradient

1990 ◽  
Vol 2 (9) ◽  
pp. 1585-1591 ◽  
Author(s):  
Jyh‐Chen Chen ◽  
Jer‐Yow Kuo
Keyword(s):  
Temperature Gradient ◽  
Linear Stability ◽  
Couette Flow ◽  
Radial Temperature Gradient ◽  
Radial Temperature ◽  
Circular Couette Flow

scholarly journals Short-wavelength local instabilities of a circular Couette flow with radial temperature gradient

2017 ◽  
Vol 818 ◽  
pp. 319-343 ◽  
Author(s):  
Oleg N. Kirillov ◽  
Innocent Mutabazi
Keyword(s):  
Temperature Gradient ◽  
Couette Flow ◽  
Short Wavelength ◽  
Thermal Conductance ◽  
Radial Temperature Gradient ◽  
Radial Temperature ◽  
Circular Couette Flow ◽  
Stable Flow ◽  
Good Heat ◽  
Axisymmetric Perturbations

We perform a linearized local stability analysis for short-wavelength perturbations of a circular Couette flow with a radial temperature gradient. Axisymmetric and non-axisymmetric perturbations are considered and both the thermal diffusivity and the kinematic viscosity of the fluid are taken into account. The effect of asymmetry of the heating both on centrifugally unstable flows and on the onset of instabilities of centrifugally stable flows, including flows with a Keplerian shear profile, is thoroughly investigated. It is found that an inward temperature gradient destabilizes the Rayleigh-stable flow either via Hopf bifurcation if the liquid is a very good heat conductor or via steady state bifurcation if viscosity prevails over the thermal conductance.

Stability of Flow Between Arbitrarily Spaced Concentric Cylindrical Surfaces Including the Effect of a Radial Temperature Gradient

1964 ◽  
Vol 31 (4) ◽  
pp. 585-593 ◽  
Author(s):  
J. Walowit ◽  
S. Tsao ◽  
R. C. DiPrima
Keyword(s):  
Temperature Gradient ◽  
Couette Flow ◽  
Simple Formula ◽  
Negative Temperature ◽  
Radial Temperature Gradient ◽  
Radial Temperature ◽  
Simple Set ◽  
Wide Range ◽  
The Stability ◽  
The Galerkin Method

The stability of Couette flow and flow due to an azimuthal pressure gradient between arbitrarily spaced concentric cylindrical surfaces is investigated. The stability problems are solved by using the Galerkin method in conjunction with a simple set of polynomial expansion functions. Results are given for a wide range of spacings. For Couette flow, in the case that the cylinders rotate in the same direction, a simple formula for predicting the critical speed is derived. The effect of a radial temperature gradient on the stability of Couette flow is also considered. It is found that positive and negative temperature gradients are destabilizing and stabilizing, respectively.

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