On Secondary Instabilities in Boundary Layers

1987 ◽  
pp. 18-42 ◽  
Author(s):  
Ali H. Nayfeh
Keyword(s):  
Boundary Layers ◽  
Secondary Instabilities

Three-dimensional instabilities in steady and unsteady non-parallel boundary layers, including effects of Tollmien-Schlichting disturbances and cross flow

1987 ◽  
Vol 409 (1837) ◽  
pp. 229-248 ◽  
Keyword(s):  
Boundary Layers ◽  
Large Scale ◽  
Three Dimensional ◽  
Steady Motion ◽  
Cross Flow ◽  
Parallel Flows ◽  
Roughness Elements ◽  
Tollmien Schlichting ◽  
Flow Effects ◽  
Secondary Instabilities

Three-dimensional (3D) linear stability properties are considered for steady and unsteady 2D or 3D boundary layers with significant non-parallelism present. Two main examples of such non-parallel flows whose stability is of interest are, firstly, steady motion, over roughness elements, in cross flow, or in large-scale separation and, secondly, unsteady 2D Tollmien-Schlichting (TS) motion, with its associated question of secondary instabilities. A high-frequency stability analysis is presented here. It is found that, for 2DTS or steady boundary layers, there is a swing in the direction of maximum TS spatial growth rate, from 0° for parallel flow towards 64.68° away from the free-stream direction, as the nonparallel flow effects increase. These effects then depend principally on, and indeed are proportional to, the local slope of the boundary-layer displacement. Cross flow can also have a profound impact on TS instabilities. Further implications for higher-amplitude and/or fasterscale disturbances, their secondary instability, and nonlinear interactions, are also discussed.

The influence of harmonic wall motion on transitional boundary layers

2014 ◽  
Vol 760 ◽  
pp. 63-94 ◽  
Author(s):  
M. J. Philipp Hack ◽  
Tamer A. Zaki
Keyword(s):  
Numerical Simulations ◽  
Boundary Layers ◽  
Wall Motion ◽  
Direct Numerical Simulations ◽  
Bypass Transition ◽  
Power Requirement ◽  
Optimal Values ◽  
Wall Oscillation ◽  
Transition Delay ◽  
Secondary Instabilities

AbstractThe influence of harmonic spanwise wall motion on bypass transition in boundary layers is investigated using direct numerical simulations. It is shown that the appropriate choice of the forcing parameters can achieve a substantial stabilization of the laminar flow regime. However, an increase of the forcing amplitude or period beyond their optimal values diminishes the stabilizing effect, and leads to breakdown upstream of the unforced case. For the optimal wall-oscillation parameters, the reduction in propulsion power substantially outweighs the power requirement of the forcing. The mechanism of transition delay is examined in detail. Analysis of the pre-transitional streaks shows that the wall oscillation substantially reduces their average amplitude, and eliminates the most energetic streaks. As a result, the secondary instabilities that precede breakdown to turbulence are substantially weakened – an effect demonstrated by linear stability analyses of flow fields from direct numerical simulations. The outcome is transition delay owing to a significant reduction in the frequency of occurrence of turbulent spots and a downstream shift in their average inception location. Finally, it is shown that the efficiency of the forcing can be further improved by replacing the sinusoidal time dependence of the wall oscillation with a square wave.

Excitation of secondary instabilities in boundary layers

1997 ◽  
Vol 336 ◽  
pp. 245-266 ◽  
Author(s):  
J. D. CROUCH
Keyword(s):  
Boundary Layers ◽  
Free Stream ◽  
Strong Dependence ◽  
Homogeneous System ◽  
Sound Level ◽  
Base Flow ◽  
Surface Variation ◽  
Tollmien Schlichting ◽  
Local Edge ◽  
Secondary Instabilities

The receptivity to fundamental and subharmonic secondary instabilities is analysed for two-dimensional boundary layers. Fundamental modes are excited by the direct scattering of Tollmien–Schlichting (TS) waves over surface variations. The excitation of subharmonic modes stems from the combined scattering of acoustic free-stream disturbances and TS waves over surface variations. The surface variations are localized in their streamwise extent and are the result of roughness or suction. The velocity field is expanded in terms of small parameters characterizing the acoustic disturbance and the surface variation. The TS wave is included as part of the base flow leading to a non-homogeneous system with periodic coefficients governing the receptivity. The receptivity amplitudes show a strong dependence on the TS-wave amplitude, and for subharmonic modes a strong dependence on the TS-wave phase at the location of the surface variation. The receptivity analysis shows a significant bias toward fundamental modes of secondary instability for larger TS-wave amplitudes – except for conditions of extremely high free-stream sound level. A combination of receptivity results and stability results suggests a bias toward subharmonic modes for TS-wave amplitudes below 0.5% and toward fundamental modes for TS-wave amplitudes above 0.5% (normalized by the local edge velocity).

Longitudinal vorticity elements in boundary layers: nonlinear development from initial Görtler vortices as a prototype problem

1991 ◽  
Vol 231 ◽  
pp. 615-663 ◽  
Author(s):  
A. S. Sabry ◽  
J. T. C. Liu
Keyword(s):  
Boundary Layers ◽  
Nonlinear Effects ◽  
Streamwise Velocity ◽  
Streamwise Vorticity ◽  
Cross Sectional ◽  
Peak Region ◽  
Vertical Vorticity ◽  
Görtler Vortices ◽  
Spanwise Vorticity ◽  
Secondary Instabilities

The nonlinear effects of longitudinal vorticity elements in boundary layers are studied via a prototype problem: the development of such vorticity elements from initial Görtler vortices in the amplified regime. While a time-dependent, quasi-two-dimensional formulation greatly simplifies the computational framework, full three-dimensionality of the velocity components is obtained. This temporal analogy for spatially developing flows approximates the nonlinear streamwise advection by a constant convection velocity, but the strong cross-sectional, advective nonlinearities are retained. Such an approximation lacks the stretching effect of the streamwise vorticity, since such elements are lifted into regions of higher streamwise velocities. That the temporal analogy is a good theoretical (and experimental) approximation to real developing flows is shown by a posteriori indications that the streamwise vorticity remains weak throughout the nonlinear region (though it has far-reaching nonlinear effects in upwelling in the peak region) and that the region of strong nonlinearities remains in the cross-sectional plane.The aim of this work is to elucidate the nonlinearities producing sites of secondary instabilities and turbulence generation. The present mushroom-like computed iso-streamwise velocity contours surrounding the peak, as well as the streamwise velocity profiles in the peak and valley regions, agree well with experimental measurements up to the region of expected wavy secondary instabilities. Three local intense vorticity and enstrophy areas are found to be significant and these are thoroughly diagnosed. One such intense vorticity region arises from the upwelling of existing spanwise vorticity and subsequent spanwise stretching in the outer layers, leading to intense local high-shear layers of spanwise vorticity in the vicinity of the peak region, as expected. Primarily through the stretching of the vertical vorticity, intense vertical vorticity (and associated enstrophy) develop (i) in the shoulder regions of the mushroom-like iso-streamwise velocity structures in the outer layers of the boundary layer and (ii) in the inner regions of about thirty viscous lengths from the wall, close to the base of the mushroom-like structures. Of the three regions of intense local ‘free’ shear-layer vorticity, the vertical vorticity in the inner regions near the mushroom stem is dominant. This is entirely consistent with experimental observations of sites of high-frequency secondary and fine-scaled wavy instabilities. This theoretically/computationally obtained ‘parent flow’ essentially sets the stage for continued studies of its wavy instabilities. In order to analyse and control the shear stress at the wall and nonlinear flow development, the effect of initial parameters such as Görtler number, initial amplitudes and wavenumbers is fully explored.

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