ROUGHNESS INDUCED TRANSIENT GROWTH: NONLINEAR EFFECTS

2006 ◽  
pp. 237-242 ◽  
Author(s):  
Meelan Choudhari ◽  
Paul Fischer
Keyword(s):  
Nonlinear Effects ◽  
Transient Growth

scholarly journals Convective instability and transient growth in flow over a backward-facing step

2008 ◽  
Vol 603 ◽  
pp. 271-304 ◽  
Author(s):  
H. M. BLACKBURN ◽  
D. BARKLEY ◽  
S. J. SHERWIN
Keyword(s):  
Convective Instability ◽  
Three Dimensional ◽  
Nonlinear Effects ◽  
Expansion Ratio ◽  
Base Flow ◽  
Time Interval ◽  
Transient Growth ◽  
Two Dimensional ◽  
Backward Facing Step ◽  
Transient Energy

Transient energy growths of two- and three-dimensional optimal linear perturbations to two-dimensional flow in a rectangular backward-facing-step geometry with expansion ratio two are presented. Reynolds numbers based on the step height and peak inflow speed are considered in the range 0–500, which is below the value for the onset of three-dimensional asymptotic instability. As is well known, the flow has a strong local convective instability, and the maximum linear transient energy growth values computed here are of order 80×103 at Re = 500. The critical Reynolds number below which there is no growth over any time interval is determined to be Re = 57.7 in the two-dimensional case. The centroidal location of the energy distribution for maximum transient growth is typically downstream of all the stagnation/reattachment points of the steady base flow. Sub-optimal transient modes are also computed and discussed. A direct study of weakly nonlinear effects demonstrates that nonlinearity is stablizing at Re = 500. The optimal three-dimensional disturbances have spanwise wavelength of order ten step heights. Though they have slightly larger growths than two-dimensional cases, they are broadly similar in character. When the inflow of the full nonlinear system is perturbed with white noise, narrowband random velocity perturbations are observed in the downstream channel at locations corresponding to maximum linear transient growth. The centre frequency of this response matches that computed from the streamwise wavelength and mean advection speed of the predicted optimal disturbance. Linkage between the response of the driven flow and the optimal disturbance is further demonstrated by a partition of response energy into velocity components.

Non-normality and its consequences in active control of thermoacoustic instabilities

2011 ◽  
Vol 670 ◽  
pp. 130-149 ◽  
Author(s):  
RAHUL KULKARNI ◽  
KOUSHIK BALASUBRAMANIAN ◽  
R. I. SUJITH
Keyword(s):  
Stability Analysis ◽  
Simple Model ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Nonlinear Effects ◽  
Transient Growth ◽  
Rijke Tube ◽  
Thermoacoustic Instabilities ◽  
Low Amplitude ◽  
Linear Controllers

Non-normality can cause transient growth of perturbations in thermoacoustic systems with stable eigenvalues. This can cause low-amplitude perturbations to grow to amplitudes high enough to make nonlinear effects significant, and the system can become nonlinearly unstable, even though it is stable under classical linear stability. In this paper, we have demonstrated that this feature can lead to the failure of the traditional controllers that were designed on the basis of classical linear stability analysis. We have also shown in a simple model that it is possible to prevent ‘nonlinear driving’ by controlling transient growth, using linear controllers. The analysis is performed in the context of a horizontal Rijke tube.

Multiple Crossover Effects and Nonlinear Effects on Socio-Cultural Adjustment

2004 ◽  
Author(s):  
Riki Takeuchi ◽  
David P. Lepak ◽  
Sophia Marinova ◽  
Seokhwa Yun
Keyword(s):  
Nonlinear Effects ◽  
Cultural Adjustment ◽  
Crossover Effects

Nonlinear effects in a plasma

1966 ◽  
Vol 90 (11) ◽  
pp. 435-489 ◽  
Author(s):  
Vadim N. Tsytovich
Keyword(s):  
Nonlinear Effects

Nonlinear effects in metals under anomalous-skin conditions

1980 ◽  
Vol 130 (2) ◽  
pp. 357 ◽  
Author(s):  
T.S. Velichkina ◽  
O.I. Vasil'eva ◽  
A.N. Izrailenko ◽  
I.A. Yakovlev
Keyword(s):  
Nonlinear Effects ◽  
Skin Conditions

Some problems of investigation of nonlinear effects in elastomers with long cyclic destruction

2019 ◽  
pp. 77-88
Author(s):  
V.I. Dyrda ◽  
◽  
S.M. Grebenyuk ◽  
S.P. Sokol ◽  
S.B. Slobodian ◽  
...  
Keyword(s):  
Nonlinear Effects

Ultrashort pulses propagation through different approaches of the Split-Step Fourier method

2018 ◽  
Vol 1 (3) ◽  
pp. 2
Author(s):  
José Stênio De Negreiros Júnior ◽  
Daniel Do Nascimento e Sá Cavalcante ◽  
Jermana Lopes de Moraes ◽  
Lucas Rodrigues Marcelino ◽  
Francisco Tadeu De Carvalho Belchior Magalhães ◽  
...  
Keyword(s):  
Energy Conservation ◽  
Optical Pulse ◽  
Time Window ◽  
Fourier Method ◽  
Ultrashort Pulses ◽  
Nonlinear Effects ◽  
Single Mode ◽  
Time Algorithm ◽  
Optical Pulses ◽  
Running Time

Simulating the propagation of optical pulses in a single mode optical fiber is of fundamental importance for studying the several effects that may occur within such medium when it is under some linear and nonlinear effects. In this work, we simulate it by implementing the nonlinear Schrödinger equation using the Split-Step Fourier method in some of its approaches. Then, we compare their running time, algorithm complexity and accuracy regarding energy conservation of the optical pulse. We note that the method is simple to implement and presents good results of energy conservation, besides low temporal cost. We observe a greater precision for the symmetrized approach, although its running time can be up to 126% higher than the other approaches, depending on the parameters set. We conclude that the time window must be adjusted for each length of propagation in the fiber, so that the error regarding energy conservation during propagation can be reduced.

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