Linear stability of laminar plane Poiseuille flow of helium II under a nonuniform mutual friction forcing

2001 ◽  
Vol 13 (4) ◽  
pp. 983-990 ◽  
Author(s):  
Simon P. Godfrey ◽  
David C. Samuels ◽  
Carlo F. Barenghi
Keyword(s):  
Linear Stability ◽  
Poiseuille Flow ◽  
Mutual Friction ◽  
Plane Poiseuille Flow ◽  
Helium Ii

scholarly journals Onset of Thermal Instabilities in the Plane Poiseuille Flow of Weakly Elastic Fluids: Viscous Dissipation Effects

Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 432
Author(s):  
Silvia C. Hirata ◽  
Mohamed Najib Ouarzazi
Keyword(s):  
Linear Stability ◽  
Viscous Dissipation ◽  
Viscoelastic Fluid ◽  
Poiseuille Flow ◽  
Hydrodynamic Instability ◽  
Plane Poiseuille Flow ◽  
Volumetric Heating ◽  
Fluid Elasticity ◽  
Different Temperatures ◽  
Elastic Fluids

The onset of thermal instabilities in the plane Poiseuille flow of weakly elastic fluids is examined through a linear stability analysis by taking into account the effects of viscous dissipation. The destabilizing thermal gradients may come from the different temperatures imposed on the external boundaries and/or from the volumetric heating induced by viscous dissipation. The rheological properties of the viscoelastic fluid are modeled using the Oldroyd-B constitutive equation. As in the Newtonian fluid case, the most unstable structures are found to be stationary longitudinal rolls (modes with axes aligned along the streamwise direction). For such structures, it is shown that the viscoelastic contribution to viscous dissipation may be reduced to one unique parameter: γ=λ1(1−Γ), where λ1 and Γ represent the relaxation time and the viscosity ratio of the viscoelastic fluid, respectively. It is found that the influence of the elasticity parameter γ on the linear stability characteristics is non-monotonic. The fluid elasticity stabilizes (destabilizes) the basic Poiseuille flow if γ<γ* (γ>γ*) where γ* is a particular value of γ that we have determined. It is also shown that when the temperature gradient imposed on the external boundaries is zero, the critical Reynolds number for the onset of such viscous dissipation/viscoelastic-induced instability may be well below the one needed to trigger the pure hydrodynamic instability in weakly elastic solutions.

The initial-value problem for three-dimensional disturbances in plane Poiseuille flow of helium II

2008 ◽  
Vol 598 ◽  
pp. 227-244 ◽  
Author(s):  
LARS B. BERGSTRÖM
Keyword(s):  
Poiseuille Flow ◽  
Three Dimensional ◽  
Peak Level ◽  
Minor Effect ◽  
Transient Growth ◽  
Plane Poiseuille Flow ◽  
Mean Flow ◽  
Normal Fluid ◽  
Helium Ii ◽  
Fluid Field

The time development of small three-dimensional disturbances in plane Poiseuille flow of helium II is considered. The study is conducted by considering the interaction of a normal fluid field and a superfluid field. The interaction is caused by a mutual friction forcing between the two flow fields. Specifically, the stability of the normal fluid affected by the mutual forcing is considered. Compared to the ordinary fluid case where the mutual forcing is not present, the presence of the mutual forcing implies a substantial increase of the transient growth of the disturbances. The increase of the transient growth occurs because the mutual forcing reduces the damping of the disturbances. The phase of transient growth becomes thereby more prolonged and higher levels of amplification are reached. There is also a minor effect on the transient growth caused by the modification of the mean flow owing to the mutual forcing. The strongest transient growth occurs for streamwise elongated disturbances, i.e. disturbances with streamwise wavenumber α = 0. When α increases beyond zero, the transient amplification quickly becomes reduced. Striking differences compared to the ordinary fluid case are that the largest transient amplification does not occur when the spanwise wavenumber (β) is close to two and that the peak level of the disturbance energy density amplification does not depend on the square of the Reynolds number.

The Stability of Plane Poiseuille Flow in a Finite-Length Channel

2021 ◽  
Author(s):  
Lei Xu ◽  
Zvi Rusak
Keyword(s):  
Kinetic Energy ◽  
Boundary Conditions ◽  
Linear Stability ◽  
Finite Length ◽  
Poiseuille Flow ◽  
Weak Form ◽  
Plane Poiseuille Flow ◽  
Various Boundary Conditions ◽  
New Perspective ◽  
The Stability

Abstract The linear stability of plane Poiseuille flow through a finite-length channel is studied. A weakly-divergence-free basis finite element method with SUPG stabilization is used to formulate the weak form of the problem. The linear stability characteristics are studied under three possible inlet-outlet boundary conditions and the corresponding perturbation kinetic energy transfer mechanisms are investigated. Active transfer of perturbation kinetic energy at the channel inlet and outlet, energy production due to convection and dissipation at the flow bulk provide a new perspective in understanding the distinct stability characteristics of plane Poiseuille flow under various boundary conditions.

Linear stability of plane Poiseuille flow of two superposed fluids

1988 ◽  
Vol 31 (11) ◽  
pp. 3225 ◽  
Author(s):  
Stergios G. Yiantsios ◽  
Brian G. Higgins
Keyword(s):  
Linear Stability ◽  
Poiseuille Flow ◽  
Plane Poiseuille Flow ◽  
Superposed Fluids

scholarly journals Linear stability of plane Poiseuille flow over a generalized Stokes layer

2011 ◽  
Vol 318 (2) ◽  
pp. 022033
Author(s):  
Maurizio Quadrio ◽  
Fulvio Martinelli ◽  
Peter J Schmid
Keyword(s):  
Linear Stability ◽  
Poiseuille Flow ◽  
Plane Poiseuille Flow ◽  
Stokes Layer

Dual Role of Wall Slip on Linear Stability of Plane Poiseuille Flow

2008 ◽  
Vol 25 (2) ◽  
pp. 601-603 ◽  
Author(s):  
Ren Ling ◽  
Chen Jian-Guo ◽  
Zhu Ke-Qin
Keyword(s):  
Linear Stability ◽  
Poiseuille Flow ◽  
Wall Slip ◽  
Dual Role ◽  
Plane Poiseuille Flow
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