Transition to chaos in a reduced-order model of a shear layer

The present work studies the non-linear dynamics of a shear layer, driven by a body force and confined between parallel walls, a simplified setting to study transitional and turbulent shear layers. It was introduced by Nogueira \& Cavalieri (J. Fluid Mech. 907, A32, 2021), and is here studied using a reduced-order model based on a Galerkin projection of the Navier-Stokes system. By considering a confined shear layer with free-slip boundary conditions on the walls, periodic boundary conditions in streamwise and spanwise directions may be used, simplifying the system and enabling the use of methods of dynamical systems theory. A basis of eight modes is used in the Galerkin projection, representing the mean flow, Kelvin-Helmholtz vortices, rolls, streaks and oblique waves, structures observed in the cited work, and also present in shear layers and jets. A dynamical system is obtained, and its transition to chaos is studied. Increasing Reynolds number $Re$ leads to pitchfork and Hopf bifurcations, and the latter leads to a limit cycle with amplitude modulation of vortices, as in the DNS by Nogueira \& Cavalieri. Further increase of $Re$ leads to the appearance of a chaotic saddle, followed by the emergence of quasi-periodic and chaotic attractors. The chaotic attractors suffer a merging crisis for higher $Re$, leading to chaotic dynamics with amplitude modulation and phase jumps of vortices. This is reminiscent of observations of coherent structures in turbulent jets, suggesting that the model represents dynamics consistent with features of shear layers and jets.Comment: 28 pages, 18 figure

Drift waves and transport

Drift waves occur universally in magnetized plasmas producing the dominant mechanism for the transport of particles, energy and momentum across magnetic field lines. A wealth of information obtained from quasistationary laboratory experiments for plasma confinement is reviewed for drift waves driven unstable by density gradients, temperature gradients and trapped particle effects. The modern understanding of Bohm transport and the role of sheared flows and magnetic shear in reducing the transport to the gyro-Bohm rate are explained and illustrated with large scale computer simulations. The types of mixed wave and vortex turbulence spontaneously generated in nonuniform plasmas are derived with reduced magnetized fluid descriptions. The types of theoretical descriptions reviewed include weak turbulence theory, Kolmogorov anisotropic spectral indices, and the mixing length. A number of standard turbulent diffusivity formulas are given for the various space-time Scales of the drift-wave turbulent mixing. [S0034-6861(99)00803-X].Physic

自励燃焼不安定性に関する数値解析に関する研究

Nowadays, combustion provides more than 80% of the worldwide energy sources. However, practical combustion systems are often susceptible to combustion instabilities characterized by large-amplitude and low-frequency pressure oscillations. This dissertation presents a nonlinear analysis and a Computational Fluid Dynamics (CFD) simulation of those self-excited combustion instabilities with a Rijke tube combustor. It is necessary to learn the mechanisms of combustion instabilities in-depth to prevent combustion instabilities or control them at acceptable levels. The nonlinear analysis of the combustion is implemented first. A model of a one-dimensional (1D) Rijke tube burner with both ends opened is built. The nondimensional momentum equation and energy equation of the acoustic perturbation are derived and solved in the time domain by using the Galerkin technique. A saturated n-τ model is proposed to descript the nonlinear flame heat release rate. The time evolution of the combustion instability is calculated. The stabilities of the systems under given conditions are determined by calculating the eigenvalues. Next, the bifurcation analysis of the dynamics behavior for the Rijke burner is performed for the variation of flame location, flame heat release intensity, and the time lag between heat release and flow velocity perturbation. Nonlinear phenomena, including hysterical, critical bifurcation, and stability switching, were observed, verifying the nonlinear characteristic of the Rijke tube burner. Further, the phase diagram and Poincaré map of the limit cycle oscillations are given, showing the oscillations' periodic character. The growth rates of the onset for the exciting case and decay for the stable case are calculated too. This nonlinear analytical method helps to understand the nature of combustion instability. Second, the self-excited combustion instability in a two-dimensional (2D) Rijke tube burner with a center-stabilized premixed methane-air flame is numerically studied. The simulation considers the reacting flow, flame dynamics, and radiation model to investigate the essential physical processes. A finite volume-based approach is used to simulate reacting flows. Chemical reaction modeling is conducted via the species transport model with one-step reaction mechanisms, and the radiation heat flux is determined by using the P-1 model. The steady-state reacting flow is first simulated for model verification. Then, the dynamic pressure, velocity, and reaction heat evolutions are determined to show the onset and growth rate of self-excited instability in the burner. The growth rates of the acoustic disturbances at the onset stages are calculated by curve fitting. Using the fast Fourier transform (FFT) method, the limit cycle oscillation frequency is obtained, which agrees well with the theoretical prediction. The dynamic pressure and velocity along the tube axis provide the acoustic oscillation mode and amplitude, agreeing well with the prediction. Finally, the unsteady flow field at different times in a limit cycle shows that flame-induced vortices occur inside the combustor. The temperature distribution indicates that the back-and-forth velocity changes in the tube vary the distance between the flame and honeycomb in turn, forming a forward feedback loop in the tube. The results reveal the route of flame-induced thermoacoustic instability and indicate periodical vortex formation and breakdown in the Rijke burner. In summary, the combustion instability in a Rijke type burner is numerically investigated from the nonlinear dynamics analysis and CFD simulation. The nonlinear analysis results show that combustion instability is a nonlinear system. There are bifurcation, stability switching phenomenons that exist, and the systems may have stable and unstable results for a given state. The CFD results verify the predictions of 1D analytical results and reveal details of the dynamics flow field, showing that even in very low Reynold numbers, the coupling of flow perturbation and heat release may induce vortices. These results provide people new perspective in studying the mechanisms of combustion

Exploiting Nonlinear Recurrence and Fractal Scaling Properties for Voice Disorder Detection

Background: Voice disorders affect patients profoundly, and acoustic tools can potentially measure voice function objectively. Disordered sustained vowels exhibit wide-ranging phenomena, from nearly periodic to highly complex, aperiodic vibrations, and increased "breathiness". Modelling and surrogate data studies have shown significant nonlinear and non-Gaussian random properties in these sounds. Nonetheless, existing tools are limited to analysing voices displaying near periodicity, and do not account for this inherent biophysical nonlinearity and non-Gaussian randomness, often using linear signal processing methods insensitive to these properties. They do not directly measure the two main biophysical symptoms of disorder: complex nonlinear aperiodicity, and turbulent, aeroacoustic, non-Gaussian randomness. Often these tools cannot be applied to more severe disordered voices, limiting their clinical usefulness.

Methods: This paper introduces two new tools to speech analysis: recurrence and fractal scaling, which overcome the range limitations of existing tools by addressing directly these two symptoms of disorder, together reproducing a "hoarseness" diagram. A simple bootstrapped classifier then uses these two features to distinguish normal from disordered voices.

Results: On a large database of subjects with a wide variety of voice disorders, these new techniques can distinguish normal from disordered cases, using quadratic discriminant analysis, to overall correct classification performance of 91.8% plus or minus 2.0%. The true positive classification performance is 95.4% plus or minus 3.2%, and the true negative performance is 91.5% plus or minus 2.3% (95% confidence). This is shown to outperform all combinations of the most popular classical tools.

Conclusions: Given the very large number of arbitrary parameters and computational complexity of existing techniques, these new techniques are far simpler and yet achieve clinically useful classification performance using only a basic classification technique. They do so by exploiting the inherent nonlinearity and turbulent randomness in disordered voice signals. They are widely applicable to the whole range of disordered voice phenomena by design. These new measures could therefore be used for a variety of practical clinical purposes.
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Computational studies of multiple-particle nonlinear dynamics in a spatio-temporally periodic potential

The spatio-temporally periodic (STP) potential is interesting in Physics due to the intimate coupling between its time and spatial components. In this paper, we begin with a brief discussion of the dynamical behaviors of a single particle in a STP potential and then examine the dynamics of multiple particles interacting in a STP potential via the electric Coulomb potential. For the multiple particles\u27 case, we focus on the occurrence of bifurcations when the amplitude of the STP potential varies. It is found that the particle concentration of the system plays an important role; the type of bifurcations that occur and the number of attractors present in the Poincaré sections depend on whether the number of particles in the simulation is even or odd. In addition to the nonlinear dynamical approach, we also discuss dependence of the squared fractional deviation of particles\u27 kinetic energy of the multiple particle system on the amplitude of the STP potential which can be used to elucidate certain transitions of states; this approach is simple and useful particularly for experimental studies of complicated interacting systems. © 2014 AIP Publishing LLC

Contributions of plasma physics to chaos and nonlinear dynamics

This topical review focusses on the contributions of plasma physics to chaos and nonlinear dynamics bringing new methods which are or can be used in other scientific domains. It starts with the development of the theory of Hamiltonian chaos, and then deals with order or quasi order, for instance adiabatic and soliton theories. It ends with a shorter account of dissipative and high dimensional Hamiltonian dynamics, and of quantum chaos. Most of these contributions are a spin-off of the research on thermonuclear fusion by magnetic confinement, which started in the fifties. Their presentation is both exhaustive and compact. [15 April 2016

Transverse Patterns in Nonlinear Optical Resonators

The book is devoted to the formation and dynamics of localized structures (vortices, solitons) and extended patterns (stripes, hexagons, tilted waves) in nonlinear optical resonators such as lasers, optical parametric oscillators, and photorefractive oscillators. The theoretical analysis is performed by deriving order parameter equations, and also through numerical integration of microscopic models of the systems under investigation. Experimental observations, and possible technological implementations of transverse optical patterns are also discussed. A comparison with patterns found in other nonlinear systems, i.e. chemical, biological, and hydrodynamical systems, is given. This article contains the table of contents and the introductory chapter of the book.Comment: 37 pages, 14 figures. Table of contents and introductory chapter of the boo