Onset Of Oscillatory Instability Research Articles

Explosive synchronization in a turbulent reactive flow system.

The occurrence of abrupt dynamical transitions in the macroscopic state of a system has received growing attention. We present experimental evidence for abrupt transition via explosive synchronization in a real-world complex system, namely, a turbulent reactive flow system. In contrast to the paradigmatic continuous transition to a synchronized state from an initially desynchronized state, the system exhibits a discontinuous synchronization transition with a hysteresis. We consider the fluctuating heat release rate from the turbulent flames at each spatial location as locally coupled oscillators that are coupled to the global acoustic field in the confined system. We analyze the synchronization between these two subsystems during the transition to a state of oscillatory instability and discover that explosive synchronization occurs at the onset of oscillatory instability. Further, we explore the underlying mechanism of interaction between the subsystems and construct a mathematical model of the same.

Effect of horizontal aspect ratio on magnetoconvective instabilities in liquid metals

Three-dimesional direct numerical simulations are performed to investigate the effect of the horizontal aspect ratio on magnetoconvective instabilities using plane layer Rayleigh-B\'enard geometry in the presence of an external uniform horizontal magnetic field. The onset of oscillatory instability is found to scale with magnetic field strength with two distinct scaling laws. The scaling exponent gradually decreases with the increment in the aspect ratio. Different transition routes to chaos have been found depending on the aspect ratio and the magnetic field strength. We find that transient chaotic flow reversals eventually lead to persistent chaotic flow reversals.

Dynamic mode decomposition of oscillatory thermo-capillary flow in curved liquid bridges of high Prandtl number liquids under microgravity

• Influence of free surface heat transfer on the onset of oscillatory instability. • Thermo-capillary flow in curved liquid bridges under microgravity conditions. • Critical value for the onset of oscillatory flow instability. • ‘Dynamic mode decomposition’ technique to reveal the inherent flow dynamics. • Quantification of each characteristic mode. Three-dimensional and oscillatory thermo-capillary flow in a liquid bridge of 5 cSt silicone oil ( Pr = 67) has been numerically investigated by performing dynamic mode decomposition (DMD) analysis applied to the time-resolved thermal data generated by the ‘method of snapshots’. For various heat transfer conditions defined on the free surface of the curved liquid bridge, a series of dynamic modes has been extracted to unfold the underlying physical mechanism that governs the considered dynamical system. Unstable and neutral modes primarily accountable for the transition to the supercritical state established in the liquid bridge have been identified by decomposing the acquired temperature disturbances into spatial and temporal coherent structures. Under microgravity conditions, unsteady and three-dimensional computations are carried out in a liquid bridge of different volume ratios ( VR = 0.9 and 1.1) using the finite volume method (FVM) to capture the dynamical evolution of temperature disturbances at the onset of oscillatory instability. The present numerical investigation is mainly aimed at providing broader insight into the complex fluid dynamic processes associated with the oscillatory thermal convection by determining the growth/decay rate and frequency of each characteristic mode with the help of DMD spectra. For each oscillation pattern, the dominant behavior of oscillatory thermo-capillary flow is revealed by its coherent structures. The characteristic modes having more energy content (dominant modes) are also analyzed by the norm of modes || ϕ || by demonstrating the frequency spectra of DMD analysis.

Condensation in the phase space and network topology during transition from chaos to order in turbulent thermoacoustic systems

The emergence of oscillatory dynamics (order) from chaotic fluctuations is a well-known phenomenon in turbulent thermoacoustic, aero-acoustic, and aeroelastic systems and is often detrimental to the system. We study the dynamics of two distinct turbulent thermoacoustic systems, bluff-body and swirl-stabilized combustors, where the transition occurs from the state of combustion noise (chaos) to thermoacoustic instability (order) via the route of intermittency. Using unweighted complex networks built from phase space cycles of the acoustic pressure oscillations, we characterize the topology of the phase space during various dynamical states in these combustors. We propose the use of network centrality measures derived from cycle networks as a novel means to characterize the number and stability of periodic orbits in the phase space and to study the topological transformations in the phase space during the emergence of order from chaos in the combustors. During the state of combustion noise, we show that the phase space consists of several unstable periodic orbits, which influence the phase space trajectory. As order emerges in the system dynamics, the number of periodic orbits decreases and their stability increases. At the onset of oscillatory dynamics, the phase space consists of a stable periodic orbit. We also use network centrality measures to identify the onset of thermoacoustic instability in both the combustors. Finally, we propose that the onset of oscillatory instabilities in turbulent systems is analogous to Bose-Einstein condensation transition observed for bosons, if we define phase space cycles as particles and the periodic orbits as energy levels.

Synchronization transition from chaos to limit cycle oscillations when a locally coupled chaotic oscillator grid is coupled globally to another chaotic oscillator.

Some physical systems with interacting chaotic subunits, when synchronized, exhibit a dynamical transition from chaos to limit cycle oscillations via intermittency such as during the onset of oscillatory instabilities that occur due to feedback between various subsystems in turbulent flows. We depict such a transition from chaos to limit cycle oscillations via intermittency when a grid of chaotic oscillators is coupled diffusively with a dissimilar chaotic oscillator. Toward this purpose, we demonstrate the occurrence of such a transition to limit cycle oscillations in a grid of locally coupled non-identical Rössler oscillators bidirectionally coupled with a chaotic Van der Pol oscillator. Further, we report the existence of symmetry breaking phenomena such as chimera states and solitary states during this transition from desynchronized chaos to synchronized periodicity. We also identify the temporal route for such a synchronization transition from desynchronized chaos to generalized synchronization via intermittent phase synchronization followed by chaotic synchronization and phase synchronization. Further, we report the loss of multifractality and loss of scale-free behavior in the time series of the chaotic Van der Pol oscillator and the mean field time series of the Rössler system. Such behavior has been observed during the onset of oscillatory instabilities in thermoacoustic, aeroelastic, and aeroacoustic systems. This model can be used to perform inexpensive numerical control experiments to suppress synchronization and thereby to mitigate unwanted oscillations in physical systems.

Linear stability of flow in a differentially heated cavity via large‐scale eigenvalue calculations

Locates the onset of oscillatory instability in the fluid flow inside a differentially heated cavity with aspect ratio 2 by computing a steady‐state and analyzing the stability of the system via eigenvalue approximation. Discusses the choice of parameters for the Cayley transformation so that the calculation of selected eigenvalues of the transformed system will reliably answer the question of stability. Also presents an argument that due to the symmetry of the problem, the first two unstable modes will have eigenvalues that are nearly identical, and the numerical experiments confirm this. Finally, locates a co‐dimension 2 bifurcation signifying where there is a switch in the mode of initial instability. The results were obtained using a parallel finite element CFD code (MPSalsa) along with an Arnoldi‐based eigensolver (ARPACK), a preconditioned Krylov method code for the necessary linear solves (Aztec), and a stability analysis library (LOCA).

Predicting Oscillatory Fluid-Elastic Instability of a Tongue-in-Groove Leakage Joint

This paper describes the application of the small boundary displacement model (SBDM) of fluid-structure coupling for predicting oscillatory fluid-elastic instability of a tongue-in-groove leakage joint. This coupling model extends structural small displacement theory to fluid-structure interfaces, eliminating the need for temporally changing meshes when structural motion is small compared with joint dimensions. The SBDM algorithm accurately predicts the onset of oscillatory instability for a tongue-in-groove leakage joint when compared with experimental data. Even though the methodology is specifically applied to a tongue-in-groove joint, the approach is equally suitable for evaluating the fluid-elastic stability of leakage joints in general.

Instability in thin layer of liquid confined between rigid walls at different temperatures

Combined thermocapillary and buoyancy convection in a thin layer of liquid, confined in a rectangular cavity, is investigated numerically. The fluid is heated from one side. Although the aspect ratio is very large, the existence of a thermal boundary layer near the rigid walls gives different results compared with convection in an infinite liquid layer. The temperature drops near the walls are rapidly increasing with the growth of the imposed temperature difference. As a result, in the core of the cavity the horizontal temperature gradient is up to 3 times smaller than the imposed Δ T/ L just before the onset of oscillatory instability. Further study is focused on the return-flow basic state, its transition to a steady multicellular state and the onset of time-dependent flow from the steady multicellular cell.

Onset of oscillatory instabilities under stochastic modulation

We study the effect of external stochastic modulation on a system with O(2) symmetry that exhibits a Hopf or oscillatory instability in the absence of modulation. The study includes a random component in both the control parameter of the bifurcation and in the modulation amplitude. Stability boundaries are computed by either solving the stationary Fokker-Planck equation in the vicinity of the center manifold of the underlying deterministic system whenever possible, or by direct numerical solution otherwise. If the modulation amplitude has a stochastic component, the primary bifurcation is always to standing waves at a value of the control parameter that depends on the intensity of the fluctuations. More precisely, and to contrast our results with the case of a deterministic periodic forcing, the onset of instability in the standing wave regime is shifted from its deterministic location, and the region of primary bifurcation to traveling waves disappears yielding instead standing waves at negative values of the control parameter.

Stability of confined swirling flow with and without vortex breakdown

A numerical investigation of steady states, their stability, onset of oscillatory instability, and slightly supercritical unsteady regimes of an axisymmetric swirling flow of a Newtonian incompressible fluid in a closed circular cylinder with a rotating lid is presented for aspect ratio (height/radius) 1 [les ] γ [les ] 3.5. Various criteria for the appearance of vortex breakdown are discussed. It is shown that vortex breakdown takes place in this system not as a result of instability but as a continuous evolution of the stationary meridional flow with increasing Reynolds number. The dependence of the critical Reynolds number Recr and frequency of oscillations ωcr on the aspect ratio of the cylinder γ is obtained. It is found that the neutral curve Recr(γ) and the curve ωcr(γ) consist of three successive continuous segments corresponding to different modes of the dominant perturbation. The calculated critical parameters are in good agreement with the available experimental and numerical data for γ < 3. It is shown that the onset of the oscillatory instability does not depend on the existence of a separation bubble in the subcritical steady state. By means of a weakly nonlinear analysis it is shown that the axisymmetric oscillatory instability sets in as a result of a supercritical Hopf bifurcation for each segment of the neutral curve. A weakly nonlinear asymptotic approximation of slightly supercritical flows is carried out. The results of the weakly nonlinear analysis are verified by direct numerical solution of the unsteady Navier-Stokes equation using the finite volume method. The analysis of the supercritical flow field for aspect ratio less than 1.75, for which no steady vortex breakdown is found, shows the existence of an oscillatory vortex breakdown which develops as a result of the oscillatory instability.

On the Amplitude Equations Arising at the Onset of the Oscillatory Instability in Pattern Formation

A well-known system of two amplitude equations is considered that describes the weakly nonlinear evolution of many nonequilibrium systems at the onset of the so-called oscillatory instability. Those equations depend on a small parameter, $\varepsilon $, that is a ratio between two distinguished spatial scales. In the limit $\varepsilon \to 0$, a simpler asymptotic model is obtained that consists of two complex cubic Ginzburg–Landau equations, coupled only by spatially averaged terms.

The onset of oscillatory instability in a rotating layer of mercury heated from below and subject to a magnetic field

A comparison is made between the predicted theoretical values of the Rayleigh number at the onset of instability in both the stationary and oscillatory modes with the observed experimental values of Nakagawa’s ( Proc. R. Soc. Lond . A 242, 81‒88 (1957)), when a layer of mercury is heated from below and simultaneously subjected to the effects of a magnetic field and rotation. The theoretical cell sizes and the gyration frequencies for the onset of oscillatory instabilities are also presented.

The effect of convection upon off-eutectic composite growth of Al-Cu alloys

Different convection conditions were achieved during directional solidification of off-eutectic Al-Cu alloys by different arrangements of the thermal and solutal gradients versus the gravity vector. The macrosegregation and the stability of a planar solidification front were studied. Increasing convection was clearly shown to increase the macrosegregation and the difficulties in achieving a stable planar front. The convection, followed by thermal fluctuations in the melt, was studied, and the onset of oscillatory instabilities was found to coincide with the critical Rayleigh number. The theoretical analysis of the results was focused on conditions at fluctuating growth rates, for which an anomalous segregation behaviour was revealed.