scholarly journals Analysis on secondary instability of shear layer based on the concept of phase synchronization

2014 ◽  
Vol 4 (6) ◽  
pp. 062001
Author(s):  
Wubing Yang ◽  
Qing Shen ◽  
Qiang Wang ◽  
Xiangjiang Yuan
Keyword(s):  
Shear Layer ◽  
Phase Synchronization ◽  
Secondary Instability

scholarly journals The baroclinic secondary instability of the two-dimensional shear layer

2000 ◽  
Vol 12 (10) ◽  
pp. 2489 ◽  
Author(s):  
Jean Reinaud ◽  
Laurent Joly ◽  
Patrick Chassaing
Keyword(s):  
Shear Layer ◽  
Secondary Instability ◽  
Two Dimensional

Secondary instability of cross-flow vortices in Falkner–Skan–Cooke boundary layers

1998 ◽  
Vol 368 ◽  
pp. 339-357 ◽  
Author(s):  
MARKUS HÖGBERG ◽  
DAN HENNINGSON
Keyword(s):  
Growth Rate ◽  
Shear Layer ◽  
Boundary Layers ◽  
Growth Rates ◽  
High Frequency ◽  
Cross Flow ◽  
Low Frequency ◽  
Secondary Instability ◽  
The Cross ◽  
Flow Vortex

Linear eigenvalue calculations and spatial direct numerical simulations (DNS) of disturbance growth in Falkner–Skan–Cooke (FSC) boundary layers have been performed. The growth rates of the small-amplitude disturbances obtained from the DNS calculations show differences compared to linear local theory, i.e. non-parallel effects are present. With higher amplitude initial disturbances in the DNS calculations, saturated cross-flow vortices are obtained. In these vortices strong shear layers appear. When a small random disturbance is added to a saturated cross-flow vortex, a low-frequency mode is found located at the bottom shear layer of the cross-flow vortex and a high-frequency secondary instability is found at the upper shear layer of the cross-flow vortex. The growth rates of the secondary instabilities are found from detailed analysis of simulations of single-frequency disturbances. The low-frequency disturbance is amplified throughout the domain, but with a lower growth rate than the high-frequency disturbance, which is amplified only once the cross-flow vortices have started to saturate. The high-frequency disturbance has a growth rate that is considerably higher than the growth rates for the primary instabilities, and it is conjectured that the onset of the high-frequency instability is well correlated with the start of transition.

Numerical Simulation on a Planar Supersonic Free Shear Layer Secondary Instability

2006 ◽  
Author(s):  
Qing Shen ◽  
Fenggan Zhuang ◽  
Faming Guan ◽  
Qiang Wang ◽  
Xiangjiang Yuan
Keyword(s):  
Numerical Simulation ◽  
Shear Layer ◽  
Secondary Instability ◽  
Free Shear Layer

Three-dimensionalization of barotropic vortices on the f-plane

1994 ◽  
Vol 265 ◽  
pp. 25-64 ◽  
Author(s):  
W. D. Smyth ◽  
W. R. Peltier
Keyword(s):  
Time Dependence ◽  
Shear Layer ◽  
Three Dimensional ◽  
Secondary Instability ◽  
Small Scale ◽  
Two Dimensional ◽  
Longitudinal Modes ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
The Stability

We examine the stability characteristics of a two-dimensional flow which consists initially of an inflexionally unstable shear layer on an f-plane. Under the action of the primary instability, the vorticity in the shear-layer initially coalesces into two Kelvin–Helmholtz vortices which subsequently merge to form a single coherent vortex. At a sequence of times during this process, we test the stability of the two-dimensional flow to fully three-dimensional perturbations. A somewhat novel approach is developed which removes inconsistencies in the secondary stability analyses which might otherwise arise owing to the time-dependence of the two-dimensional flow.In the non-rotating case, and before the onset of pairing, we obtain a spectrum of unstable longitudinal modes which is similar to that obtained previously by Pierrehumbert & Widnall (1982) for the Stuart vortex, and by Klaassen & Peltier (1985, 1989, 1991) for more realistic flows. In addition, we demonstrate the existence of a new sequence of three-dimensional subharmonic (and therefore ‘helical’) instabilities. After pairing is complete, the secondary instability spectrum is essentially unaltered except for a doubling of length- and timescales that is consistent with the notion of spatial and temporal self-similarity. Once pairing begins, the spectrum quickly becomes dominated by the unstable modes of the emerging subharmonic Kelvin–Helmholtz vortex, and is therefore similar to that which is characteristic of the post-pairing regime. Also in the context of non-rotating flow, we demonstrate that the direct transfer of energy into the dissipative subrange via secondary instability is possible only if the background flow is stationary, since even slow time-dependence acts to decorrelate small-scale modes and thereby to impose a short-wave cutoff on the spectrum.The stability of the merged vortex state is assessed for various values of the planetary vorticity f. Slow rotation may either stabilize or destabilize the columnar vortices, depending upon the sign of f, while fast rotation of either sign tends to be stabilizing. When f has opposite sign to the relative vorticity of the two-dimensional basic state, the flow becomes unstable to new mode of instability that has not been previously identified. Modes whose energy is concentrated in the vortex cores are shown to be associated, even at non-zero f, with Pierrehumbert's (1986) elliptical instability. Through detailed consideration of the vortex interaction mechanisms which drive instability, we are able to provide physical explanations for many aspects of the three-dimensionalization process.

Effect of carbon content on supersonic shear-layer instability

2012 ◽  
Vol 693 ◽  
pp. 261-296 ◽  
Author(s):  
Luca Massa
Keyword(s):  
Shear Layer ◽  
Chemical Interaction ◽  
Secondary Instability ◽  
Instability Wave ◽  
Vortical Structures ◽  
Carbon Chemistry ◽  
Boundary Layer Instability ◽  
Free Shear Layers ◽  
Endothermic Reactions ◽  
Primary Instability

AbstractCarbon chemistry and the endothermic reactions it supports were previously shown to delay hypersonic boundary-layer instability and transition. The present analysis addresses the analogous problem in free shear layers and arrives at the conclusion that the lack of the acoustic trapping mechanism implies that endothermic chemistry can lead to stabilization or destabilization of the shear layer depending on the free-stream temperature. This study identifies three mechanisms by which carbon chemistry affects instability and transition. The first is rooted in the changes to the inflectional profiles caused by the visco-chemical interaction. The second is due to damping of the perturbation by finite-rate chemistry. The third is linked to streamwise relaxation which delays the onset of secondary instability of vortical structures generated by a saturated primary instability wave. Linear analysis predicts changes in growth rate lower than 30 % for Mach numbers below 5. Nonlinear parabolized stability analysis predicts significantly larger differences, depending on whether the primary or secondary instability triggers the transition onset.

A spanwise structure in the plane shear layer

1983 ◽  
Vol 132 ◽  
pp. 319-336 ◽  
Author(s):  
Javier Jimenez
Keyword(s):  
Flow Field ◽  
Shear Layer ◽  
Secondary Instability ◽  
Experimental Results ◽  
Mean Flow ◽  
Plane Shear ◽  
Lateral Undulation ◽  
The Mean ◽  
Longitudinal Structures

We study experimentally the spanwise structure of the mean flow field of a plane shear layer. The field is dominated by a lateral undulation that persists downstream to form long longitudinal structures. Both the amplitude and spacing of these structures vary in such a way as to suggest that they are due to a secondary instability of the flow field. Some models for this instability are discussed and compared with the experimental results.

Secondary instability analysis of crossflow on a hypersonic yawed straight circular cone

2016 ◽  
Vol 812 ◽  
pp. 370-397 ◽  
Author(s):  
Alexander J. Moyes ◽  
Pedro Paredes ◽  
Travis S. Kocian ◽  
Helen L. Reed
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Angle Of Attack ◽  
Three Dimensional ◽  
Low Frequency ◽  
Secondary Instability ◽  
Circular Cone ◽  
Swept Wing ◽  
Instability Analysis ◽  
Instability Modes

The purpose of this paper is to provide secondary instability analysis of stationary crossflow vortices on a hypersonic yawed straight circular cone with a $7^{\circ }$ half-angle at $6^{\circ }$ angle of attack, free-stream Mach number 6 and unit Reynolds number $10.09\times 10^{6}~\text{m}^{-1}$. At an angle of attack, a three-dimensional boundary layer is developed between the windward and leeward symmetry planes. Under the action of azimuthal pressure gradients, the flow near the surface is deflected more than the flow near the edge of the boundary layer. This results in an inflectional velocity profile that can sustain the growth of crossflow vortices. The stationary crossflow instability is computed by means of the nonlinear parabolized stability equations, including a methodology to predict the stationary-crossflow marching path and variation of the spanwise number of waves in the marching direction solely from the basic state. Secondary instability analysis is performed using spatial BiGlobal equations based on two-dimensional partial differential equations. The secondary instabilities are calculated at different axial locations along two crossflow vortex trajectories selected to complement experiments conducted in the Mach 6 Quiet Tunnel at Texas A&M University and in the Boeing/AFOSR Mach 6 Quiet Tunnel at Purdue University. The secondary instability analysis captures various instability modes. Similar to observations in the low-speed regime for an infinite swept wing, secondary shear-layer instabilities are amplified as a consequence of the three-dimensional shear layer formed by crossflow vortices. Also, low-frequency travelling crossflow and high-frequency second modes coexist with the shear-layer instabilities. These results are shown to be in good agreement with the two sets of hypersonic yawed cone experiments (one with natural surface roughness and one with artificial discrete roughness) and compare well with experimental measurements of an incompressible swept wing.

scholarly journals Characteristics of a Secondary Instability in a Compressible Double Shear Layer

2005 ◽  
Vol 53 (615) ◽  
pp. 182-189 ◽  
Author(s):  
Mikiya Araki ◽  
Jun Osaka ◽  
Osamu Imamura ◽  
Mitsuhiro Tsue ◽  
Michikata Kono
Keyword(s):  
Shear Layer ◽  
Secondary Instability ◽  
Double Shear
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