On the non-linear stability of parallel shear flows

1991 ◽  
Vol 3 (1) ◽  
pp. 1-11 ◽  
Author(s):  
S. Rionero ◽  
G. Mulone
Keyword(s):  
Linear Stability ◽  
Shear Flows ◽  
Non Linear ◽  
Parallel Shear Flows

Global linear stability analysis of weakly non-parallel shear flows

1993 ◽  
Vol 251 ◽  
pp. 1-20 ◽  
Author(s):  
Peter A. Monkewitz ◽  
Patrick Huerre ◽  
Jean-Marc Chomaz
Keyword(s):  
Linear Stability ◽  
Turning Point ◽  
Shear Flows ◽  
Temporal Evolution ◽  
Basic Flow ◽  
Time Harmonic ◽  
Pressure Feedback ◽  
Parallel Shear Flows ◽  
Global Modes ◽  
Linear Disturbance

The global linear stability of incompressible, two-dimensional shear flows is investigated under the assumptions that far-field pressure feedback between distant points in the flow field is negligible and that the basic flow is only weakly non-parallel, i.e. that its streamwise development is slow on the scale of a typical instability wavelength. This implies the general study of the temporal evolution of global modes, which are time-harmonic solutions of the linear disturbance equations, subject to homogeneous boundary conditions in all space directions. Flow domains of both doubly infinite and semi-infinite streamwise extent are considered and complete solutions are obtained within the framework of asymptotically matched WKBJ approximations. In both cases the global eigenfrequency is given, to leading order in the WKBJ parameter, by the absolute frequency ω0(Xt) at the dominant turning pointXtof the WKBJ approximation, while its quantization is provided by the connection of solutions acrossXt. Within the context of the present analysis, global modes can therefore only become time-amplified or self-excited if the basic flow contains a region of absolute instability.

Generalized energetics for inertially stable parallel shear flows

2007 ◽  
Vol 585 ◽  
pp. 117-126 ◽  
Author(s):  
R. C. KLOOSTERZIEL ◽  
G. F. CARNEVALE
Keyword(s):  
Linear Stability ◽  
Shear Flows ◽  
Stability Boundary ◽  
Energy Norm ◽  
Classical Sense ◽  
Unequal Rates ◽  
Parallel Shear Flows

For simple parallel shear flows on the f-plane and the equatorial β-plane we derive an energy norm for zonally invariant perturbations. It is used to derive the linear stability boundary for when these flows are inertially stable in the classical sense but may be destabilized due to unequal rates of diffusion of momentum and heat. The analysis is valid when there are arbitrary, zonally invariant, no-slip boundaries which are perfect thermal conductors.

Non-Linear Stability of Magnetically Focused Particle Beams

2012 ◽  
Author(s):  
Felipe B. Rizzato ◽  
Renato Pakter ◽  
Yan Levin
Keyword(s):  
Linear Stability ◽  
Particle Beams ◽  
Non Linear ◽  
Focused Particle Beams

scholarly journals Spatiotemporal linear stability of viscoelastic free shear flows: Nonaffine response regime

2021 ◽  
Vol 33 (5) ◽  
pp. 054106
Author(s):  
D. Bansal ◽  
D. Ghosh ◽  
S. Sircar
Keyword(s):  
Linear Stability ◽  
Shear Flows
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