XXXIII. On the stability of the simple shearing motion of a viscous incompressible fluid

1915 ◽  
Vol 30 (177) ◽  
pp. 329-338 ◽  
Author(s):  
Lord Rayleigh
Keyword(s):  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Simple Shearing ◽  
The Stability ◽  
Shearing Motion

scholarly journals Stability Analysis of Symmetrical Rotors Partially Filled with a Viscous Incompressible Fluid

2001 ◽  
Vol 7 (5) ◽  
pp. 301-310 ◽  
Author(s):  
Zhu Changsheng
Keyword(s):  
Stability Analysis ◽  
Incompressible Fluid ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Damping Ratio ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
Navier Stokes Equations ◽  
Rotor Systems ◽  
The Stability

On the basis of the linearized fluid forces acting on the rotor obtained directly by using the two-dimensional Navier-Stokes equations, the stability of symmetrical rotors with a cylindrical chamber partially filled with a viscous incompressible fluid is investigated in this paper. The effects of the parameters of rotor system, such as external damping ratio, fluid fill ratio, Reynolds number and mass ratio, on the unstable regions are analyzed. It is shown that for the stability analysis of fluid filled rotor systems with external damping, the effect of the fluid viscosity on the stability should be considered. When the fluid viscosity is included, the adding external damping will make the system more stable and two unstable regions may exist even if rotors are isotropic in some casIs.

The stability of Poiseuille flow in a pipe

1969 ◽  
Vol 36 (2) ◽  
pp. 209-218 ◽  
Author(s):  
A. Davey ◽  
P. G. Drazin
Keyword(s):  
Incompressible Fluid ◽  
Poiseuille Flow ◽  
Viscous Incompressible Fluid ◽  
Reynolds Numbers ◽  
Numerical Calculations ◽  
Circular Pipe ◽  
Asymptotic Results ◽  
The Stability

Numerical calculations show that the flow of viscous incompressible fluid in a circular pipe is stable to small axisymmetric disturbances at all Reynolds numbers. These calculations are linked with known asymptotic results.

The Hydrodynamic Stability of Two Viscous Incompressible Fluids in Parallel Uniform Shearing Motion

1979 ◽  
Vol 46 (3) ◽  
pp. 499-504 ◽  
Author(s):  
D. T. Tsahalis
Keyword(s):  
Reynolds Number ◽  
Incompressible Fluid ◽  
Viscosity Ratio ◽  
Density Ratio ◽  
Steady Motion ◽  
Wave Number ◽  
Neutral Stability ◽  
The Family ◽  
The Stability ◽  
Shearing Motion

The stability problem of a thin film of a viscous incompressible fluid bounded on one side by another more viscous and less dense incompressible fluid of semi-infinite extent and on the other side by a fixed wall, where both fluids are in steady motion parallel to their interface and each fluid has a linear velocity profile, is solved for large values of the Reynolds number and small values of the viscosity ratio. Neutral stability curves of the Reynolds number versus the wave number are presented, parametrized with either the density ratio or the viscosity ratio as the family parameters.

Energy stability for the flow between rotating, coaxial disks

1979 ◽  
Vol 83 (3-4) ◽  
pp. 255-261
Author(s):  
Alan R. Elcrat
Keyword(s):  
Reynolds Number ◽  
Incompressible Fluid ◽  
Stability Condition ◽  
Viscous Incompressible Fluid ◽  
Rigid Motion ◽  
Deformation Energy ◽  
Core Region ◽  
Energy Stability ◽  
Angular Velocities ◽  
The Stability

SynopsisA stability condition is derived for solutions of the Von Kárman-Batchelor equations for the flow of a viscous, incompressible fluid between rotating, coaxial (infinite) disks. The rigid motion solution which arises when the angular velocities of the disks are equal is stable with respect to perturbations which go to zero sufficiently rapidly at infinity, for all values of the Reynolds number. If the angular velocities are sufficiently close the stability condition derived applies to perturbations whose “deformation energy” is sufficiently confined to a “core” region.

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