Nonlinear evolution of instability waves in boundary layers

1998 ◽  
Author(s):  
Sang Lee
Keyword(s):  
Boundary Layers ◽  
Nonlinear Evolution ◽  
Instability Waves

The production of subharmonic waves in the nonlinear evolution of wavepackets in boundary layers

1999 ◽  
Vol 399 ◽  
pp. 301-318 ◽  
Author(s):  
MARCELLO A. F. MEDEIROS ◽  
MICHAEL GASTER
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Nonlinear Interaction ◽  
Strong Influence ◽  
Nonlinear Evolution ◽  
Nonlinear Behaviour ◽  
Two Dimensional ◽  
Tollmien Schlichting ◽  
Acoustic Excitations ◽  
Dimensional Wave

The nonlinear evolution of wavepackets in a laminar boundary layer has been studied experimentally. The packets were generated by acoustic excitations injected into the boundary layer through a small hole in the plate. Various packets with different phases relative to the envelope were studied. It was found that for all the packets the nonlinearity involved the appearance of oblique modes of frequency close to the subharmonic of the dominant two-dimensional wave. Moreover, the results confirmed that the phase had a strong influence on the strength of the nonlinear interaction. The experimental observations also indicated that although a subharmonic resonance appeared to be present in the process, it alone could not explain the nonlinear behaviour. The experiment demonstrated that the process must also involve a mechanism that generates oblique waves of frequency lower than the Tollmien–Schlichting band.

scholarly journals Nonlinear evolution of interacting oblique waves on two-dimensional shear layers

1989 ◽  
Vol 207 ◽  
pp. 97-120 ◽  
Author(s):  
M. E. Goldstein ◽  
S.-W. Choi
Keyword(s):  
Wave Amplitude ◽  
Numerical Solutions ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Shear Layers ◽  
Instability Wave ◽  
Two Dimensional ◽  
Instability Waves ◽  
Downstream Distance ◽  
Parallel Streams

We consider the effects of critical-layer nonlinearity on spatially growing oblique instability waves on nominally two-dimensional shear layers between parallel streams. The analysis shows that three-dimensional effects cause nonlinearity to occur at much smaller amplitudes than it does in two-dimensional flows. The nonlinear instability wave amplitude is determined by an integro-differential equation with cubic-type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. We show that they always end in a singularity at a finite downstream distance.

Nonlinear evolution of a pair of oblique instability waves in a supersonic boundary layer

1995 ◽  
Vol 282 ◽  
pp. 339-371 ◽  
Author(s):  
S. J. Leib ◽  
Sang Soo Lee
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Nonlinear Evolution ◽  
Supersonic Boundary Layer ◽  
Inviscid Limit ◽  
Instability Wave ◽  
Neutral Stability ◽  
Mean Flow ◽  
Number Range ◽  
Instability Waves

We study the nonlinear evolution of a pair of oblique instability waves in a supersonic boundary layer over a flat plate in the nonlinear non-equilibrium viscous critical layer regime. The instability wave amplitude is governed by the same integro-differential equation as that derived by Goldstein & Choi (1989) in the inviscid limit and by Wu, Lee & Cowley (1993) with viscous effects included, but the coefficient appearing in this equation depends on the mean flow and linear neutral stability solution of the supersonic boundary layer. This coefficient is evaluated numerically for the Mach number range over which the (inviscid) first mode is the dominant instability. Numerical solutions to the amplitude equation using these values of the coefficient are obtained. It is found that, for insulated and cooled wall conditions and angles corresponding to the most rapidly growing waves, the amplitude ends in a singularity at a finite downstream position over the entire Mach number range regardless of the size of the viscous parameter. The explosive growth of the instability waves provides a mechanism by which the boundary layer can break down. A new feature of the compressible problem is the nonlinear generation of a spanwise-dependent mean distortion of the temperature along with that of the velocity found in the incompressible case.

On the growth of waves in boundary layers: a non-parallel correction

2000 ◽  
Vol 424 ◽  
pp. 367-377 ◽  
Author(s):  
M. GASTER
Keyword(s):  
Boundary Layers ◽  
Parallel Flow ◽  
Linear Perturbation ◽  
Mean Flow ◽  
Instability Waves ◽  
Laminar Boundary Layers ◽  
Small Correction ◽  
Base Solution ◽  
The Mean ◽  
Sommerfeld Equation

The estimation of the growth of propagating instability waves in laminar boundary layers is considered when the Reynolds number is sufficiently large for the mean flow to deviate only slightly from a truly parallel flow. An approximate solution for the linear perturbation is sought in the form of a scaled solution of the related locally parallel flow problem. The amplitude scaling is chosen so as to satisfy the full linearized perturbation equations as closely as possible by making the mean-square deviation of the remainder a minimum. By re-arranging the terms in the equations so that some of the small correction terms arising from the non-parallel mean flow are contained in the ordinary differential equation (ODE) defining the quasi-parallel flow solution, a useful simplification is obtained for the scaling function. Then a modified Orr–Sommerfeld equation defines the base solution and the differential expression for the scaling that can be integrated forms a simple conservation relation.

scholarly journals On Nonlinear Evolution of C-type Instability in Nonparallel Boundary Layers

2007 ◽  
Vol 20 (4) ◽  
pp. 313-319 ◽  
Author(s):  
Jixue Liu ◽  
Dengbin Tang ◽  
Yingzhao Yang
Keyword(s):  
Boundary Layers ◽  
Nonlinear Evolution
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