Linear Stability of Supersonic Plane Couette Flow of Vibrationally Excited Gas

2017 ◽  
pp. 51-84
Author(s):  
Yurii N. Grigoryev ◽  
Igor V. Ershov
Keyword(s):  
Linear Stability ◽  
Couette Flow ◽  
Plane Couette Flow ◽  
Vibrationally Excited

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.

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

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.

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