Nonlinear Interactions Between Oblique Instability Waves on Nearly Parallel Shear Flows

1994 ◽  
pp. 3-20
Author(s):  
M. E. Goldstein
Keyword(s):  
Shear Flows ◽  
Nonlinear Interactions ◽  
Instability Waves ◽  
Parallel Shear Flows

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

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 proof of Howard’s conjecture in homogeneous parallel shear flows

1994 ◽  
Vol 104 (3) ◽  
pp. 593-595 ◽  
Author(s):  
Mihir B Banerjee ◽  
R G Shandil ◽  
Vinay Kanwar
Keyword(s):  
Shear Flows ◽  
Parallel Shear Flows

Aerodynamic Effects of Inviscid Parallel Shear Flows

AIAA Journal ◽  
1977 ◽  
Vol 15 (8) ◽  
pp. 1159-1166 ◽  
Author(s):  
M. H. Williams ◽  
M. R. Chi ◽  
C. S. Ventres ◽  
E. H. Dowell
Keyword(s):  
Shear Flows ◽  
Parallel Shear Flows
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