scholarly journals Wave growth patterns in a non-linear dispersive system with instability and dissipation

1997 ◽  
Vol 20 (3) ◽  
pp. 599-604
Author(s):  
Dinesh Gera ◽  
Mridul Gautam ◽  
Hota V. S. Gangarao
Keyword(s):  
Periodic Solution ◽  
Growth Pattern ◽  
Initial Conditions ◽  
Growth Patterns ◽  
Dispersive Equation ◽  
Time Intervals ◽  
One Dimensional ◽  
Non Linear Equation ◽  
Dispersive System ◽  
Non Linear

A simple one-dimensional non linear equation including effects of instability, dissipation, and dispersion is examined numerically. Periodic solution of a non linear dispersive equation is presented for different values ofα,β, andγcharacterizing the constants for instability, dissipation, and dispersion respectively. In this paper, the growth pattern for the wave at different time intervals is discussed. Various equilibrium states with different initial configuration have been observed depending on initial conditions.

A Linear Algorithm of Spatial Straightness for Five Points

2012 ◽  
Vol 490-495 ◽  
pp. 1888-1892
Author(s):  
Fan Wu Meng ◽  
Chun Guang Xu ◽  
Juan Hao
Keyword(s):  
Traditional Method ◽  
Linear Problem ◽  
Initial Conditions ◽  
The Novel ◽  
Novel Approach ◽  
Non Linear Equation ◽  
Non Linear ◽  
Minimum Zone ◽  
Effectiveness And Efficiency ◽  
Straightness Error

It is a non-linear problem to evaluate the minimum zone spatial (3-D) straightness. Because of the disadvantages of evaluating spatial straightness error with traditional method, such as difficulty in solving the non-linear equation, the evaluating precision is lower. This paper develops a solution that can transform the non-linear problem into a linear problem. The solution can obtain more exact results than traditional method using results of LSC as initial conditions. This methodology can also be applied to the problems of computing the minimum circumscribed cylinder and the maximum inscribed cylinder. The effectiveness and efficiency of the novel approach are illustrated by two examples.

scholarly journals Interaction of equivalence ratio fluctuations and flow fluctuations in acoustically forced swirl flames

2021 ◽  
pp. 175682772110155
Author(s):  
Vincent Kather ◽  
Finn Lückoff ◽  
Christian O. Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Equivalence Ratio ◽  
Transfer Functions ◽  
Transport Model ◽  
Mode Conversion ◽  
Fuel Injector ◽  
One Dimensional ◽  
Flow Fluctuations ◽  
Non Linear ◽  
Non Local ◽  
Acoustic Forcing

The generation and turbulent transport of temporal equivalence ratio fluctuations in a swirl combustor are experimentally investigated and compared to a one-dimensional transport model. These fluctuations are generated by acoustic perturbations at the fuel injector and play a crucial role in the feedback loop leading to thermoacoustic instabilities. The focus of this investigation lies on the interplay between fuel fluctuations and coherent vortical structures that are both affected by the acoustic forcing. To this end, optical diagnostics are applied inside the mixing duct and in the combustion chamber, housing a turbulent swirl flame. The flame was acoustically perturbed to obtain phase-averaged spatially resolved flow and equivalence ratio fluctuations, which allow the determination of flux-based local and global mixing transfer functions. Measurements show that the mode-conversion model that predicts the generation of equivalence ratio fluctuations at the injector holds for linear acoustic forcing amplitudes, but it fails for non-linear amplitudes. The global (radially integrated) transport of fuel fluctuations from the injector to the flame is reasonably well approximated by a one-dimensional transport model with an effective diffusivity that accounts for turbulent diffusion and dispersion. This approach however, fails to recover critical details of the mixing transfer function, which is caused by non-local interaction of flow and fuel fluctuations. This effect becomes even more pronounced for non-linear forcing amplitudes where strong coherent fluctuations induce a non-trivial frequency dependence of the mixing process. The mechanisms resolved in this study suggest that non-local interference of fuel fluctuations and coherent flow fluctuations is significant for the transport of global equivalence ratio fluctuations at linear acoustic amplitudes and crucial for non-linear amplitudes. To improve future predictions and facilitate a satisfactory modelling, a non-local, two-dimensional approach is necessary.

scholarly journals Optimal Perturbations of an Oceanic Vortex Lens

Fluids ◽  
2018 ◽  
Vol 3 (3) ◽  
pp. 63 ◽  
Author(s):  
Thomas Meunier ◽  
Claire Ménesguen ◽  
Xavier Carton ◽  
Sylvie Le Gentil ◽  
Richard Schopp
Keyword(s):  
Normal Mode ◽  
Growth Rates ◽  
Time Interval ◽  
Time Intervals ◽  
Horizontal Structure ◽  
Azimuthal Wave ◽  
Wave Numbers ◽  
Non Linear ◽  
Long Time ◽  
Short Time

The stability properties of a vortex lens are studied in the quasi geostrophic (QG) framework using the generalized stability theory. Optimal perturbations are obtained using a tangent linear QG model and its adjoint. Their fine-scale spatial structures are studied in details. Growth rates of optimal perturbations are shown to be extremely sensitive to the time interval of optimization: The most unstable perturbations are found for time intervals of about 3 days, while the growth rates continuously decrease towards the most unstable normal mode, which is reached after about 170 days. The horizontal structure of the optimal perturbations consists of an intense counter-shear spiralling. It is also extremely sensitive to time interval: for short time intervals, the optimal perturbations are made of a broad spectrum of high azimuthal wave numbers. As the time interval increases, only low azimuthal wave numbers are found. The vertical structures of optimal perturbations exhibit strong layering associated with high vertical wave numbers whatever the time interval. However, the latter parameter plays an important role in the width of the vertical spectrum of the perturbation: short time interval perturbations have a narrow vertical spectrum while long time interval perturbations show a broad range of vertical scales. Optimal perturbations were set as initial perturbations of the vortex lens in a fully non linear QG model. It appears that for short time intervals, the perturbations decay after an initial transient growth, while for longer time intervals, the optimal perturbation keeps on growing, quickly leading to a non-linear regime or exciting lower azimuthal modes, consistent with normal mode instability. Very long time intervals simply behave like the most unstable normal mode. The possible impact of optimal perturbations on layering is also discussed.

scholarly journals Production performance of cows raised with different post-weaning growth patterns

2021 ◽  
Author(s):  
Harvey C Freetly ◽  
Robert A Cushman ◽  
Gary L Bennett
Keyword(s):  
Growth Pattern ◽  
Bos Taurus ◽  
Life Time ◽  
Growth Patterns ◽  
Production Performance ◽  
Genetic Population ◽  
Breed Type ◽  
Genetic Types ◽  
Period 2 ◽  
Step Growth

Abstract The period of heifer development is a relatively small fraction of a cow’s life; however, her pattern of growth may have permanent effects on her productivity as a cow. We hypothesized that altering the growth pattern during the peri-pubertal period would increase life-time productivity across genetic types of Bos taurus cows. The objective was to determine the stayability, calf production, and weight of calf weaned across six calf crops. Heifers (n = 685) were placed on one of two developmental programs at 256 ± 1 d of age. Control heifers received a diet that provided 228 kcal ME·(BW, kg) -0.75 daily, and Stair-Step heifers were allocated 157 kcal ME·(BW, kg) -0.75 daily for 84 or 85 d, and then the daily allocation was increased to 277 kcal ME·(BW, kg) -0.75. Stair-Step heifers (0.33 ± 0.02 kg/d) had a lower ADG than Control heifers (0.78 ± 0.02 kg/d; P < 0.001) during Period 1, and Stair-Step heifers (0.93 ± 0.03 kg/d) had a greater ADG than Controls (0.70 ± 0.03 kg/d; P < 0.001) during Period 2. There were no treatment (P = 0.28) or breed type differences (P = 0.42) for the proportion of cows weaning a calf; however, the proportion of cows weaning a calf decreased with cow age (P < 0.001). Calves from Stair-Step dams had heavier weaning weights (193 ± 1 kg) compared to Control calves (191 ± 1 kg; P = 0.007). There was not a treatment (P = 0.25) or breed type differences in cumulative BW weaned (P = 0.59). A diverse genetic population of cattle within Bos taurus was tested and responses in calf production did not differ between Stair-Step growth pattern and a more constant non-obese growth pattern.

scholarly journals Nonlinear Solution to a Non-Fourier Heat Conduction Problem in a Slab Heated by Laser Source

2016 ◽  
Vol 63 (1) ◽  
pp. 129-144
Author(s):  
Mohammad Javad Noroozi ◽  
Seyfolah Saedodin ◽  
Davood Domiri Ganji
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Adomian Decomposition Method ◽  
Laser Source ◽  
Temperature Dependent ◽  
Conduction Model ◽  
Non Linear Equation ◽  
Adomian Decomposition ◽  
Non Linear ◽  
Fourier Heat Conduction

Abstract The effect of laser, as a heat source, on a one-dimensional finite body was studied in this paper. The Cattaneo-Vernotte non-Fourier heat conduction model was used for thermal analysis. The thermal conductivity was assumed temperature-dependent which resulted in a non-linear equation. The obtained equations were solved using the approximate-analytical Adomian Decomposition Method (ADM). It was concluded that the non-linear analysis is important in non-Fourier heat conduction problems. Significant differences were observed between the Fourier and non-Fourier solutions which stresses the importance of non-Fourier solutions in the similar problems.

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