Benchmark solution for the hydrodynamic stability of plane porous-Couette flow

2020 ◽  
Vol 32 (10) ◽  
pp. 104104
Author(s):  
B. M. Shankar ◽  
I. S. Shivakumara ◽  
Jai Kumar
Keyword(s):  
Couette Flow ◽  
Hydrodynamic Stability ◽  
Benchmark Solution

scholarly journals Benchmark solution for the stability of plane Couette flow with net throughflow

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
B. M. Shankar ◽  
I. S. Shivakumara
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Couette Flow ◽  
Normal Modes ◽  
Base Flow ◽  
Parallel Plates ◽  
Plane Couette Flow ◽  
Benchmark Solution ◽  
Vertical Throughflow ◽  
The Stability

AbstractThis paper investigates the stability of an incompressible viscous fluid flow between relatively moving horizontal parallel plates in the presence of a uniform vertical throughflow. A linear stability analysis has been performed by employing the method of normal modes and the resulting stability equation is solved numerically using the Chebyshev collocation method. Contrary to the stability of plane Couette flow (PCF) to small disturbances for all values of the Reynolds number in the absence of vertical throughflow, it is found that PCF becomes unstable owing to the change in the sign of growth rate depending on the magnitude of throughflow. The critical Reynolds number triggering the instability is computed for different values of throughflow dependent Reynolds number and it is shown that throughflow instills both stabilizing and destabilizing effect on the base flow. It is seen that the direction of throughflow has no influence on the stability of fluid flow. A comparative study between plane Poiseuille flow and PCF has also been carried out and the similarities and differences are highlighted.

Hydrodynamic Stability

1983 ◽  
Vol 50 (4b) ◽  
pp. 983-991 ◽  
Author(s):  
R. C. DiPrima ◽  
J. T. Stuart
Keyword(s):  
Couette Flow ◽  
Hydrodynamic Stability ◽  
Poiseuille Flow ◽  
Plane Poiseuille Flow ◽  
Concentric Cylinders ◽  
The Stability

Theoretical and experimental developments for the stability and transition of plane Poiseuille flow and for Couette flow between rotating concentric cylinders are reviewed. The paper concludes with brief comments on the stability of Hagen-Poiseuille flow in a pipe and brief comments on the stability of slowly varying flows.

Instability due to viscosity stratification

1967 ◽  
Vol 27 (2) ◽  
pp. 337-352 ◽  
Author(s):  
Chia-Shun Yih
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Hydrodynamic Stability ◽  
Poiseuille Flow ◽  
Plane Couette Flow ◽  
Plane Poiseuille Flow ◽  
Neutral Mode ◽  
Usual Theory

The principal aim of this paper is to show that the variation of viscosity in a fluid can cause instability. Plane Couette-Poiseuille flow of two superposed layers of fluids of different viscosities between two horizontal plates is considered, and it is found that both plane Poiseuille flow and plane Couette flow can be unstable, however small the Reynolds number is. The unstable modes are in the neighbourhood of a hidden neutral mode for the case of a single fluid, which is entirely ignored in the usual theory of hydrodynamic stability, and are brought out by the viscosity stratification.

Hydrodynamic stability of a suspension in cylindrical Couette flow

2002 ◽  
Vol 14 (3) ◽  
pp. 1236-1243 ◽  
Author(s):  
Mohamed E. Ali ◽  
Deepanjan Mitra ◽  
John A. Schwille ◽  
Richard M. Lueptow
Keyword(s):  
Couette Flow ◽  
Hydrodynamic Stability ◽  
Cylindrical Couette Flow

Hydrodynamic stability of compressible plane Couette flow

1994 ◽  
Vol 50 (6) ◽  
pp. R4283-R4285 ◽  
Author(s):  
G. D. Chagelishvili ◽  
A. D. Rogava ◽  
I. N. Segal
Keyword(s):  
Couette Flow ◽  
Hydrodynamic Stability ◽  
Plane Couette Flow
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