Rates, pathways, and end states of nonlinear evolution in decaying two‐dimensional turbulence: Scaling theory versus selective decay

1992 ◽  
Vol 4 (6) ◽  
pp. 1314-1316 ◽  
Author(s):  
G. F. Carnevale ◽  
J. C. McWilliams ◽  
Y. Pomeau ◽  
J. B. Weiss ◽  
W. R. Young
Keyword(s):  
Nonlinear Evolution ◽  
Scaling Theory ◽  
Two Dimensional ◽  
Theory Versus ◽  
Selective Decay ◽  
Turbulence Scaling

scholarly journals Selective decay and coherent vortices in two-dimensional incompressible turbulence

1991 ◽  
Vol 66 (21) ◽  
pp. 2731-2734 ◽  
Author(s):  
William H. Matthaeus ◽  
W. Troy Stribling ◽  
Daniel Martinez ◽  
Sean Oughton ◽  
David Montgomery
Keyword(s):  
Two Dimensional ◽  
Coherent Vortices ◽  
Selective Decay ◽  
Incompressible Turbulence

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.

Conditional Nonlinear Optimal Perturbations of a Two-Dimensional Quasigeostrophic Model

2006 ◽  
Vol 63 (6) ◽  
pp. 1587-1604 ◽  
Author(s):  
Mu Mu ◽  
Zhiyue Zhang
Keyword(s):  
Singular Vector ◽  
Nonlinear Evolution ◽  
Initial Perturbation ◽  
Nonlinear Effects ◽  
Two Dimensional ◽  
Physical Problems ◽  
Maximum Value ◽  
The Difference ◽  
Quasigeostrophic Model ◽  
The Cost

Abstract Conditional nonlinear optimal perturbations (CNOPs) of a two-dimensional quasigeostrophic model are obtained numerically. The CNOP is the initial perturbation whose nonlinear evolution attains the maximum value of the cost function, which is constructed according to the physical problems of interests with physical constraint conditions. The difference between the CNOP and a linear singular vector is compared. The results demonstrate that CNOPs catch the nonlinear effects of the model on the evolutions of the initial perturbations. These results suggest that CNOPs are applicable to the study of predictability and sensitivity analysis when nonlinearity is of importance.

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.

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