Three-dimensional linear instability of parallel shear flows

1986 ◽  
Vol 29 (2) ◽  
pp. 364 ◽  
Author(s):  
Michael Magen ◽  
Anthony T. Patera
Keyword(s):  
Shear Flows ◽  
Three Dimensional ◽  
Linear Instability ◽  
Parallel Shear Flows

Extension of classical stability theory to viscous planar wall-bounded shear flows

2019 ◽  
Vol 877 ◽  
pp. 1134-1162 ◽  
Author(s):  
Harry Lee ◽  
Shixiao Wang
Keyword(s):  
Boundary Conditions ◽  
Shear Flows ◽  
Early Stage ◽  
Linear Instability ◽  
Slip Condition ◽  
Translation Invariant ◽  
Alternative Derivation ◽  
Wall Boundary ◽  
Wall Boundary Conditions ◽  
Parallel Shear Flows

A viscous extension of Arnold’s inviscid theory for planar parallel non-inflectional shear flows is developed and a viscous Arnold’s identity is obtained. Special forms of the viscous Arnold’s identity have been revealed that are closely related to the perturbation’s enstrophy identity derived by Synge (Proceedings of the Fifth International Congress for Applied Mechanics, 1938, pp. 326–332, John Wiley) (see also Fraternale et al., Phys. Rev. E, vol. 97, 2018, 063102). Firstly, an alternative derivation of the perturbation’s enstrophy identity for strictly parallel shear flows is acquired based on the viscous Arnold’s identity. The alternative derivation induces a weight function. Thereby, a novel weighted perturbation’s enstrophy identity is established, which extends the previously known enstrophy identity to include general streamwise translation-invariant shear flows. Finally, the validity of the enstrophy identity for parallel shear flows is rigorously examined and established under global nonlinear dynamics imposed with two classes of wall boundary conditions. As an application of the enstrophy identity, we quantitatively investigate the mechanism of linear instability/stability within the normal modal framework. The investigation reveals a subtle interaction between a critical layer and its adjacent boundary layer, which determines the stability nature of the disturbance. As an implementation of the relaxed wall boundary conditions imposed for the enstrophy identity, a control scheme is proposed that transitions the wall settings from the no-slip condition to the free-slip condition, through which a flow is stabilized quickly in an early stage of the transition.

A note on an algebraic instability of inviscid parallel shear flows

1980 ◽  
Vol 98 (2) ◽  
pp. 243-251 ◽  
Author(s):  
M. T. Landahl
Keyword(s):  
Kinetic Energy ◽  
Wide Class ◽  
Shear Flows ◽  
Three Dimensional ◽  
Turbulent Shear ◽  
Constant Density ◽  
Disturbed Region ◽  
Streaky Structure ◽  
Algebraic Instability ◽  
Parallel Shear Flows

It is shown that all parallel inviscid shear flows of constant density are unstable to a wide class of initial infinitesimal three-dimensional disturbances in the sense that, according to linear theory, the kinetic energy of the disturbance will grow at least as fast as linearly in time. This can occur even when the disturbance velocities are bounded, because the streamwise length of the disturbed region grows linearly with time. This finding may have implications for the observed tendency of turbulent shear flows to develop a longitudinal streaky structure.

scholarly journals On the role of vortex stretching in energy optimal growth of three-dimensional perturbations on plane parallel shear flows

2012 ◽  
Vol 707 ◽  
pp. 369-380 ◽  
Author(s):  
H. Vitoshkin ◽  
E. Heifetz ◽  
A. Yu. Gelfgat ◽  
N. Harnik
Keyword(s):  
Shear Flows ◽  
Plane Waves ◽  
Three Dimensional ◽  
Energy Growth ◽  
Plane Parallel ◽  
Optimal Energy ◽  
Parallel Shear Flows ◽  
Spanwise Vorticity ◽  
Background Shear

AbstractThe three-dimensional linearized optimal energy growth mechanism, in plane parallel shear flows, is re-examined in terms of the role of vortex stretching and the interplay between the spanwise vorticity and the planar divergent components. For high Reynolds numbers the structure of the optimal perturbations in Couette, Poiseuille and mixing-layer shear profiles is robust and resembles localized plane waves in regions where the background shear is large. The waves are tilted with the shear when the spanwise vorticity and the planar divergence fields are in (out of) phase when the background shear is positive (negative). A minimal model is derived to explain how this configuration enables simultaneous growth of the two fields, and how this mutual amplification affects the optimal energy growth. This perspective provides an understanding of the three-dimensional growth solely from the two-dimensional dynamics on the shear plane.

scholarly journals Exact coherent structures in an asymptotically reduced description of parallel shear flows

2014 ◽  
Vol 47 (1) ◽  
pp. 015504 ◽  
Author(s):  
Cédric Beaume ◽  
Edgar Knobloch ◽  
Gregory P Chini ◽  
Keith Julien
Keyword(s):  
Coherent Structures ◽  
Shear Flows ◽  
Parallel Shear Flows

On Some Transition Processes in Three-Dimensional Shear Flows

1985 ◽  
pp. 479-486
Author(s):  
S. Y. Gertsenstein ◽  
V. A. Zheligowsky ◽  
N. V. Nikitin ◽  
A. Y. Rudnitsky ◽  
A. N. Sukhorukov ◽  
...  
Keyword(s):  
Shear Flows ◽  
Three Dimensional ◽  
Transition Processes
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