Linear stability of viscous supersonic plane Couette flow

1998 ◽  
Vol 10 (3) ◽  
pp. 709-729 ◽  
Author(s):  
Sean Hu ◽  
Xiaolin Zhong
Keyword(s):  
Linear Stability ◽  
Couette Flow ◽  
Plane Couette Flow

scholarly journals On the linear stability of compressible plane Couette flow

1994 ◽  
Vol 258 ◽  
pp. 131-165 ◽  
Author(s):  
Peter W. Duck ◽  
Gordon Erlebacher ◽  
M. Yousuff Hussaini
Keyword(s):  
Linear Stability ◽  
Couette Flow ◽  
Small Amplitude ◽  
Reynolds Numbers ◽  
Inviscid Limit ◽  
Plane Couette Flow ◽  
Moving Wall ◽  
Type Boundary ◽  
The Stability ◽  
Radiation Type

The linear stability of compressible plane Couette flow is investigated. The appropriate basic velocity and temperature distributions are perturbed by a small-amplitude normal-mode disturbance. The full small-amplitude disturbance equations are solved numerically at finite Reynolds numbers, and the inviscid limit of these equations is then investigated in some detail. It is found that instabilities can occur, although the corresponding growth rates are often quite small; the stability characteristics of the flow are quite different from unbounded flows. The effects of viscosity are also calculated, asymptotically, and shown to have a stabilizing role in all the cases investigated. Exceptional regimes to the problem occur when the wave speed of the disturbances approaches the velocity of either of the walls, and these regimes are also analysed in some detail. Finally, the effect of imposing radiation-type boundary conditions on the upper (moving) wall (in place of impermeability) is investigated, and shown to yield results common to both bounded and unbounded flows.

On the Non-linear Stability of Plane Couette Flow

1971 ◽  
pp. 61-64
Author(s):  
T. Ellingsen ◽  
B. Gjevik ◽  
E. Palm
Keyword(s):  
Linear Stability ◽  
Couette Flow ◽  
Plane Couette Flow ◽  
Non Linear

scholarly journals Bioconvection under uniform shear: linear stability analysis

2013 ◽  
Vol 738 ◽  
pp. 522-562 ◽  
Author(s):  
Yongyun Hwang ◽  
T. J. Pedley
Keyword(s):  
Stability Analysis ◽  
Shear Rate ◽  
Linear Stability ◽  
Couette Flow ◽  
Linear Stability Analysis ◽  
Plane Couette Flow ◽  
Shear Rates ◽  
Uniform Shear ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

AbstractThe role of uniform shear in bioconvective instability in a shallow suspension of swimming gyrotactic cells is studied using linear stability analysis. The shear is introduced by applying a plane Couette flow, and it significantly disturbs gravitaxis of the cell. The unstably stratified basic state of the cell concentration is gradually relieved as the shear rate is increased, and it even becomes stably stratified at very large shear rates. Stability of the basic state is significantly changed. The instability at high wavenumbers is drastically damped out with the shear rate, while that at low wavenumbers is destabilized. However, at very large shear rates, the latter is also suppressed. The most unstable mode is found as a pair of streamwise uniform rolls aligned with the shear, analogous to Rayleigh–Bénard convection in plane Couette flow. To understand these findings, the physical mechanism of the bioconvective instability is reexamined with several sets of numerical experiments. It is shown that the bioconvective instability in a shallow suspension originates from three different physical processes: gravitational overturning, gyrotaxis of the cell and negative cross-diffusion flux. The first mechanism is found to rule the behaviour of low-wavenumber instability whereas the last two mechanisms are mainly associated with high-wavenumber instability. With the increase of the shear rate, the former is enhanced, thereby leading to destabilization at low wavenumbers, whereas the latter two mechanisms are significantly suppressed. For streamwise varying perturbations, shear with sufficiently large rates is also found to play a stabilizing role as in Rayleigh–Bénard convection. However, at small shear rates, it destabilizes these perturbations through the mechanism of overstability discussed by Hill, Pedley and Kessler (J. Fluid Mech., vol. 208, 1989, pp. 509–543). Finally, the present findings are compared with a recent experiment by Croze, Ashraf and Bees (Phys. Biol., vol. 7, 2010, 046001) and they are in qualitative agreement.

Linear stability analysis of plane Couette flow with viscous heating

1996 ◽  
Vol 8 (7) ◽  
pp. 1802-1813 ◽  
Author(s):  
Chao‐Sheng Yueh ◽  
Cheng‐I Weng
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Couette Flow ◽  
Linear Stability Analysis ◽  
Viscous Heating ◽  
Plane Couette Flow

The linear stability of viscous compressible plane Couette flow

1989 ◽  
Vol 202 ◽  
pp. 515-541 ◽  
Author(s):  
W. Glatzel
Keyword(s):  
Phase Velocity ◽  
Linear Stability ◽  
Couette Flow ◽  
Normal Modes ◽  
Reynolds Numbers ◽  
Plane Couette Flow ◽  
Phase Velocities ◽  
Viscous Instability ◽  
Supersonic Regime ◽  
Critical Reynolds Numbers

The structure of normal modes in viscous compressible plane Couette flow is investigated. The spectrum is found to consist of two types of modes: the viscous modes, which obtain finite phase velocities by the mechanism of mode pairing; and the sonic modes, whose phase velocity becomes distorted in the supersonic regime. This leads to mode crossings which unfold, depending on the type of crossing modes, either into purely sonic or viscous-sonic instability bands. The latter provide a new example for viscous instability. Both mode pairing of viscous modes and distortion of the phase velocity of sonic modes is caused by the shear. Critical Reynolds numbers for the instabilities are derived.

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