Mode Instability Research Articles

Floquet-based analysis on three-dimensional non-axisymmetric instabilities in oscillatory-driven Taylor–Couette flows and their low-frequency asymptotic behavior using Wentzel–Kramers–Brillouin method

This paper revisits the linear stability analysis of oscillatory-driven flows between two oscillating cylinders against non-axisymmetric disturbances. This study is motivated by the lack of a sufficiently reliable theoretical analysis giving insight into the experimentally observed spiral-like non-axisymmetric patterns when the cylinders are counter-oscillating. A new generalized time-dependent algebraic eigenvalue problem is constructed from the linearized set of the three-dimensional Navier–Stokes equations around the purely azimuthal basic state. Numerical evaluation of the critical eigenvalues combining both Floquet theory and spectral method reveals the existence of frequency ranges where this basic state becomes unstable against three-dimensional non-axisymmetric disturbances before it does so for two-dimensional axisymmetric ones. Indeed, as the oscillation frequency of the cylinders increases, the azimuthal wave number of the critical eigensolution is found to change from 0 to 2 to 1 and then back to 0. The primary bifurcation exchange between two instability modes with different azimuthal wave numbers occurs via different types of codimension-2 bifurcation points giving rise to discontinuities in the critical axial wave number where reversing and non-reversing non-axisymmetric Taylor vortex flows are identified. In addition, by extending our numerical calculations to the co-oscillating case, we show that the axisymmetric disturbances are the most unstable confirming thus existing experimental findings. Furthermore, a Wentzel–Kramers–Brillouin (WKB) analysis is performed to shed light on the asymptotic behavior of these time-dependent flows in the low-frequency limit when the cylinders are slowly oscillating.

The influence of thermal dispersion on the initiation of convective instability in Prats flow through a low permeability porous medium

This study investigates the effect of thermal dispersion on the onset of convective thermal instability in a fluid-saturated porous medium. A horizontal throughflow is considered along the layer, which is bounded by two uniformly heated horizontal rigid impermeable walls from above and below. The two walls are maintained at a constant temperature gradient, which is responsible for the buoyancy to occur and thus making the convection happen. Considering thermal dispersion, we have examined how it affects the natural convective instability occurring due to the thermal buoyancy. This paper proposes an entirely new perspective on the accountability of thermal dispersion in the convective instability. The consideration of Prats flow causes the instability in monotonic and oscillatory modes, where in some of the cases, the convection initiates in the oscillatory modes.

Investigation of longitudinal self-excited combustion instability in a micromix hydrogen combustor

The increasing emphasis on low-carbon energy has heightened investigations into hydrogen combustion. This study focuses on the critical yet underexplored topic of thermoacoustic instabilities in micromix hydrogen combustors. We employ a newly designed micromix burner to explore the intricate relationships among acoustic modes, flame dynamics, and flow-vortex interactions. High-speed particle image velocimetry (PIV) and OH* chemiluminescence, supplemented by dynamic pressure measurements, are employed to capture dynamic behaviors and instability modes of the flame. Through thermoacoustic network analysis, we can identify two primary self-excited modes: a dominant low-frequency mode oscillating between 520 Hz and 565 Hz, and a secondary high-frequency mode surpassing 4400 Hz, originating from the hydrodynamic instability of the nozzle's jet flow. The low-frequency mode significantly influences the flame dynamics, generating a distinct longitudinal flame oscillation behavior. In particular, the inner premixed flame exhibits a periodic pattern of lifting and re-attachment phenomena. The outer diffusion flame, however, dynamically interacts with the outer shear layer (OSL) and the shed outer vortex rings (OVRs), which gives rise to notable deformations in the flame surface, manifesting as neck and swell structures propagating downstream with the OVRs. Furthermore, the dynamics of the OSL and OVRs are attributed to the fluctuations in the bulk flow velocity and local equivalence ratio at the nozzle exit, which are sustained by pressure oscillations induced by thermoacoustics. This presents important insights into the interplay between hydrodynamics and thermoacoustics in the formation of combustion instability in the micromix hydrogen combustor.

Impedance-Based Stability Analysis: Nodal Admittance or Bus Admittance?

Impedance-based stability analysis is widely adopted for small-signal stability demonstration of power electronics dominated power systems. Stability assessment can be performed using either nodal admittance or bus admittance (i.e. equivalent admittance of a network viewed from a specific bus). This paper demonstrates that stability analysis using the bus admittance may not always produce correct results, even though it is easier to implement. Unstable multi-bus systems can be wrongly identified as stable by the single-bus analysis, in the cases where other buses play a dominant role in causing instabilities. A detailed comparison between nodal and bus admittance stability analysis is presented, leading to recommendations for their practical use. A phase-based method is proposed to facilitate the acquisition of eigenloci encirclement around the critical point, which can be used in the stability analysis based on either nodal or bus admittance. Following the conclusion of our work, we recommend multi-bus analysis in white-box model applications for instability mode analysis and stability-oriented design. Single-bus analysis is preferable in black-box model applications due to its simplicity. It is also suggested to select a bus for analysis from those connected to a high share of inverter-based resources, to ensure the correctness of results.

Experimental Research on Abnormal Transverse Mode Instability in High-Power Fiber Lasers

Experimental Research on Abnormal Transverse Mode Instability in High-Power Fiber Lasers

Brightness enhancement on a narrow-linewidth fiber Bragg grating-based master oscillator power amplification fiber laser

Abstract In this paper, we have experimentally demonstrated a high-power and high-brightness narrow-linewidth fiber amplifier seeded by an optimized fiber oscillator. In order to improve the temporal stability, the fiber oscillator consists of a composite fiber Bragg grating-based cavity with an external feedback structure. By optimizing the forward and backward pumping ratio, the nonlinear effects and stimulated Raman scattering-induced mode distortion of the fiber amplifier are suppressed comprehensively, accompanied with the simultaneous improvement of beam quality and output power. The laser brightness is enhanced further by raising the threshold of transverse mode instability by approximately 1.0 kW by coiling the gain fiber with a novel curvature shape. Finally, a 6 kW narrow-linewidth laser is achieved with beam quality (M2) of approximately 1.4. The laser brightness doubled compared to the results before optimization. To the best of our knowledge, it is the highest brightness narrow-linewidth fiber laser based on a one-stage master oscillator power amplification structure.

Theoretical study on radiation effect on threshold of transverse mode instability of Yb-doped fiber amplifiers

<sec>Yb-doped fiber amplifiers and their applications in radiation environments have become more and more attractive in recent years. However, the radiation effect will cause damage to the Yb-doped fibers, which can give negative effect on the output properties of Yb-doped fiber amplifiers. In this work, the influence of radiation effect on the transverse mode instability (TMI) of Yb-doped fiber amplifier is studied. TMI can couple the single light from the fundamental mode to high-order mode, thereby degenerating the beam quality of fiber amplifier. TMI is considered a key limitation of power up-scaling of fiber amplifiers.</sec><sec>In this work, the radiation effect on the TMI is studied theoretically, and a formula of TMI threshold is presented by taking the radiation-induced attenuation (RIA), the most important radiation effect for the TMI, into account. The formula is deduced by introducing the loss of signal light induced by RIA into the formerly reported TMI-threshold formula which can be obtained by the linear stability analysis of the numerical model studying the TMI. Then, the relationship between the TMI and radiation dose is also given with the help of Power-Law describing the relationship between the RIA and radiation dose.</sec><sec>With the formula, the variations of TMI threshold with the radiation dose and RIA are studied. It is found, as expected, that the TMI threshold decreases monotonically with the increase of RIA or radiation dose. Nevertheless, it is unexpectedly found that, to some extent, the gain coefficient of fiber amplifiers will also affect the radiation effect on TMI threshold. The results reveal that the increase of gain coefficient will lower the sensitivity of TMI threshold to the radiation dose. However, it is also implied that the gain coefficient cannot be too large because it can also make the TMI threshold lowered. Therefore, in order to maintain a high TMI threshold in a radiation environment, sufficient radiation resistance of Yb-doped fiber is essential.</sec><sec>Because the RIA can affect not only the TMI threshold but also the output power or efficiency of Yb-doped fiber amplifier, the comparison between two effects of RIA is also discussed. It is found that the threshold of TMI is more sensitive to the radiation than to the output power or efficiency (see the figure attached below), which means that the TMI can exist in the irradiated Yb-doped fiber amplifier, although the output power is reduced because of RIA. This result can be verified by the experimental observation reported formerly. As a result, TMI can become a key limitation to the output power of Yb-doped fiber amplifier in radiation environments. The relevant results can provide significant guidance for the applications of Yb-doped fiber amplifiers in radiation environments.</sec>

Theoretical analysis of effects of ferrite geometrical parameters on tokamak magnetic field perturbations

In this paper, a magneto-dynamic approach has been developed to investigate the probable enhancing effect of a magnetizing material like ferrite on the mitigation of the edge-localized mode instabilities. It has been assumed that the ferrite is placed on the first wall of the tokamak. The Landau–Lifschitz–Gilbert equation has been used to calculate the ferrite contribution to the equilibrium and the perturbed magnetic fields in the plasma. Simulations have shown that the ferrite can alter the magnetic field topology. Investigating the effects of the ferrite geometrical parameters such as the length, the width and the angle have shown that increasing the values of these parameters elevates the ferrite magnetization contribution in the plasma. Because of the type of the perturbation initially defined, this contribution was especially strong at the bottom of the ferrite. Since the ferrite can increase the total perturbation field in the plasma, it can help to mitigate the edge-localized modes by the resonant magnetic perturbation phenomenon. The simulation has shown that for an optimum geometry of the ferrite, the magnetic flux surfaces near the edge can be modified from an opened-line topology to a closed-line topology. Thus, the ferrite can prevent the magnetic flux from touching the wall which is necessary to have a good confinement and to reduce the edge instabilities.

Accurate Modeling of Transverse Mode Instability in Thulium-doped Optical Fiber Amplifiers

Accurate Modeling of Transverse Mode Instability in Thulium-doped Optical Fiber Amplifiers

Coexistence and Coevolution of Wrinkle and Ridge Patterns in the Film-Substrate System by Uniaxial Compression.

Homogeneous wrinkles and localized patterns are ubiquitous in nature and are useful for a wide range of practical applications. Although various strain-driven surface instability modes have been extensively investigated in the past decades, understanding the coexistence, coevolution, and interaction of wrinkles and localized patterns is still a great challenge. Here, we report on the formation and evolution of coexisting wrinkle and ridge patterns in metal films deposited on poly(dimethylsiloxane) (PDMS) substrates by uniaxial compression. It is found that the evolving surface patterns show unique features of morphological transition from stages I to III: namely, transition from localized ridges to coexisting wrinkles and ridges, and finally to sinusoidal-like structures, as the compression increases. Based on the compressive strain-driven surface instability theory and finite element numerical simulation, the morphological features, transition behaviors, and underlying mechanisms of such complex patterns are investigated in detail, and the changes of amplitude and wavelength versus the strain are consistent with our experiments. This work could promote a better understanding of the effect of strain localization and the interaction of multiple surface patterns in hard film-soft substrate systems.

Numerical Evaluation of Lateral Torsional Buckling of PFRP Channel Beams under Pure Bending

The use of pultruded fiber reinforced polymers (PFRPs) in strengthening and sustainable design of bridges and other structures exposed to corrosion and resistance reduction factors is growing rapidly. However, a comprehensive understanding of the structural behavior of these materials under various loading conditions is crucial to unlock their full potential and promote their wider use in diverse structural and industrial applications. Pultrusion profiles can be also used as beams in bridges. One important aspect of the structural behavior of PFRPs is their buckling behavior, particularly in thin-walled open cross sections. Lateral torsional buckling is a probable instability mode for beams with thin-walled open cross sections that are not laterally restrained along their span. Therefore, research on the buckling behavior of PFRP members is essential. In this study, the analytical responses of channel-shaped PFRP beams in bridges under pure bending are calculated using an equation in the Eurocode 3 regulation. The buckling behavior of these beams is then investigated through numerical modeling using the finite element package Abaqus. A total of 75 specimens of PFRP channel profiles with different thicknesses in various spans and lateral restraint conditions are studied for their lateral-torsional buckling behavior. This study uniquely explores the behavior of PFRP beams with lateral restraints, a novel aspect in the field of lateral-torsional buckling research of PFRP beams. The results show that the analytical equation used for these beams needs to be modified to more accurately estimate the buckling loads of FRP beams under the conditions studied in this paper.

One-Dimensional Gap Soliton Molecules and Clusters in Optical Lattice-Trapped Coherently Atomic Ensembles via Electromagnetically Induced Transparency

In past years, optical lattices have been demonstrated as an excellent platform for making, understanding, and controlling quantum matters at nonlinear and fundamental quantum levels. Shrinking experimental observations include matter-wave gap solitons created in ultracold quantum degenerate gases, such as Bose–Einstein condensates with repulsive interaction. In this paper, we theoretically and numerically study the formation of one-dimensional gap soliton molecules and clusters in ultracold coherent atom ensembles under electromagnetically induced transparency conditions and trapped by an optical lattice. In numerics, both linear stability analysis and direct perturbed simulations are combined to identify the stability and instability of the localized gap modes, stressing the wide stability region within the first finite gap. The results predicted here may be confirmed in ultracold atom experiments, providing detailed insight into the higher-order localized gap modes of ultracold bosonic atoms under the quantum coherent effect called electromagnetically induced transparency.

Measurement and analysis of crossflow instability modes on a 7-degree yawed cone at Mach 6

In this work, the crossflow instability modes on a 7° half-angle cone with 6° angle of attack at Mach 6 have been experimentally studied. To begin with, the complete laminar-to-turbulence transition process is acquired by infrared thermography, and the heat flux streaks caused by the stationary crossflow vortices are distinct over the areas of leeward side. Further wavelet analysis reveals a dominant wavenumber of the stationary crossflow vortices, which is centered at about k = 50. Subsequently, the spatial distribution characteristics of the traveling crossflow instability (f = 20–50 kHz) and high-frequency instabilities (f = 100–500 kHz) are acquired between the azimuthal angle Φ = 90°–150° (windside to leeside) through wall mounted pressure sensors. The results of spectral and wavelet analysis indicate that the two types of instability are the traveling crossflow instability and its secondary instability, respectively. Further bispectral analysis is used to show that these high-frequency waves undergo several quadratic phase-coupled interactions with themselves to produce harmonics, as well interact with low-frequency waves that results in spectral broadening.

Penetrative and Marangoni convection in a fluid film over a phase boundary

We study the effects of buoyancy, surface-tension gradients and phase boundary on the stability of a layer of water that is confined between air at the top and a layer of ice at the bottom. The temperature of the overlying air and flux condition at the free surface of the water layer are such that the layer is susceptible to both thermal and thermocapillary instabilities. We perform a linear stability analysis to identify these modes of instability and investigate the effects of the phase boundary on them. We find that with increasing thickness of the ice layer, the critical Rayleigh and Marangoni numbers for the instabilities are found to first decrease and then asymptote to constant values for ice thicknesses much larger than the thickness of the water layer. In the case of thermocapillary instability, we find that the thickness of the ice layer has negligible influence on the stability threshold for dimensionless wavenumber $k \gg 1$ , and that the presence of an unstably stratified liquid layer significantly alters the stability threshold for $k = O (1)$ . Furthermore, the inclusion of Marangoni stresses reduces the stability threshold of the thermal instability.

Electrothermal instability in different modes of underwater electrical wire explosion

Electrothermal instability and its effect on the uniformity of discharge channels during underwater electrical wire explosions at different energy deposition rates have been investigated. According to the liquid–vapor transition mechanism, we classified underwater electrical explosion into “phase explosion mode” and “supercritical mode.” Two sets of experiments corresponding to the two modes were conducted, and the exploding wires were observed by a shadow imaging system. Results showed that a bamboo-shaped discharge channel was formed in the phase explosion mode, whereas the discharge channel in the supercritical mode was a uniform cylinder. Self-consistent magnetohydrodynamic simulation results indicated that exploding wires transfer into liquid–vapor coexistence phase in the phase explosion mode, accompanied by a rapid increase in the density perturbation and the formation of bamboo-shaped structures. Moreover, a small perturbation model was derived to analyze the electrothermal instability in different thermodynamic states. It was indicated that the density perturbation is easier to grow in the liquid–vapor coexistence state than the supercritical state, which provides a theoretical explanation for the differences between the two electrical explosion modes.

Cumulative damage evolution of jointed slopes subject to continuous earthquakes: Influence of joint type on dynamic amplification effect and failure mode of slopes

This work investigates the dynamic response characteristics and cumulative damage evolution of jointed slopes under continuous earthquakes. Three jointed slope discrete-element models were created using a new fracture formation method to avoid particle overlap. The effects of joint types on dynamic amplification and failure mode are investigated. The results show that joints amplify the seismic response, with bedded jointed slopes exhibiting the highest magnification effect, followed by parallel jointed slopes and anti-dip jointed slopes. Cracks gradually increase under continuous earthquakes, with an increasing rate characterized by increase–decrease-increase–decrease. The failure scale of the bedded jointed slopes is the largest, followed by the parallel jointed slopes, and the anti-dip jointed slopes have the smallest failure scale. Seismic cumulative damage evolution encompasses stages of local damage (priming effect), expansion of local damage (accumulative effect), slip body formation, and instability (acceleration effect). Discontinuous joints affect the damage characteristics and instability modes of slopes by controlling fracture initiation and expansion. They have minimal impact on intrinsic frequency and frequency spectrum characteristics but significantly affect marginal spectrum characteristics. This work provides insights into the behaviour of jointed slopes under continuous earthquakes and the influence of joint types on their cumulative damage evolution process.

Polarization-resolved mode evolution in TMI-limited Yb-doped fiber amplifiers using a novel high-speed Stokes polarimeter.

In this work we have developed a high-speed Stokes polarimeter method based on simultaneous 4-channel imaging with a high-speed camera. Thus, current speed limitations of imaging polarimeters for wavelengths around 1 µm can be overcome, allowing a sub-ms polarization-resolved characterization of transverse mode instability (TMI). Additionally, the Stokes parameters of each individual mode are calculated by a simultaneous 4-beam mode reconstruction algorithm during post-processing and can be analyzed with unprecedented temporal resolution. We demonstrate the measurement capabilities of this polarimeter setup by characterizing TMI of a large-mode-area Yb-doped polarization maintaining (PM) fiber amplifier with 30 kHz video frame rate. Upon thorough characterization, we have found for the first time that at the onset of TMI in a PM fiber, the modal polarization states begin to oscillate on circular and elliptical trajectories at the same frequencies as the modal energy transfer occurs. The ability to measure the modal polarization states with sub-ms temporal resolution is key to developing a fundamental understanding and subsequently possible mitigation strategies of TMI in PM-fiber lasers.

Extending Closed-Loop Control of Two-Dimensional Supersonic Boundary-Layer Instabilities Beyond a Single Operating Point

This paper investigates two control strategies to maintain low perturbation amplitudes of second Mack mode instabilities in a two-dimensional boundary layer with freestream velocity variations of ±5% around M∞=4.5: the multimodel synthesis and the gain scheduling method, both based on the structured mixed H2/H∞ synthesis to handle simultaneously, in an optimal way, the problems of nominal performance, stability, and performance robustness. The multimodel synthesis is based on a single linear-time invariant (LTI) controller optimized over multiple operating points, whereas the gain scheduling method results in a control law based on the interpolation of multiple LTI controllers designed at the various operating points. Both methods are compared with simple LTI controllers based solely on the nominal operating point in two sensor–actuator architectures: in feedforward (respectively, feedback) the estimation sensor is located upstream (respectively, downstream) of the actuator. In the feedforward case, significant performance loss is observed in off-design conditions, regardless of the method used. In the feedback case, multimodel synthesis enhances slightly performance robustness (but improvement is weak because of the wide range of freestream velocity variation), while the gain scheduling approach succeeds in strongly reducing the perturbation amplitude over the entire range of variation.

TESS Cycle 2 observations of roAp stars with 2-min cadence data

ABSTRACT We present the results of a systematic search of the Transiting Exoplanet Survey Satellite (TESS) 2-min cadence data for new rapidly oscillating Ap (roAp) stars observed during the Cycle 2 phase of its mission. We find seven new roAp stars previously unreported as such and present the analysis of a further 25 roAp stars that are already known. Three of the new stars show multiperiodic pulsations, while all new members are rotationally variable stars, leading to almost 70 per cent (22) of the roAp stars presented being α2 CVn-type variable stars. We show that targeted observations of known chemically peculiar stars are likely to overlook many new roAp stars, and demonstrate that multiepoch observations are necessary to see pulsational behaviour changes. We find a lack of roAp stars close to the blue edge of the theoretical roAp instability strip, and reaffirm that mode instability is observed more frequently with precise, space-based observations. In addition to the Cycle 2 observations, we analyse TESS data for all-known roAp stars. This amounts to 18 further roAp stars observed by TESS. Finally, we list six known roAp stars that TESS is yet to observe. We deduce that the incidence of roAp stars amongst the Ap star population is just 5.5 per cent, raising fundamental questions about the conditions required to excite pulsations in Ap stars. This work, coupled with our previous work on roAp stars in Cycle 1 observations, presents the most comprehensive, homogeneous study of the roAp stars in the TESS nominal mission, with a collection of 112 confirmed roAp stars in total.

Effects of the resonance modification by electron cyclotron current drive on the linear and nonlinear dynamics of energetic particle driven magnetohydrodynamics modes in Heliotron J

This study investigates the effects of electron cyclotron current drive (ECCD) on the linear and nonlinear dynamics of energetic-particle (EP)-driven magnetohydrodynamics (MHD) instability (mode) in Heliotron J (HJ), using MEGA, a nonlinear hybrid EP-MHD simulation code. The effects of ECCD are included through the modification of the equilibrium magnetic field. Five MHD equilibria with plasma currents ( Ip ) of −2.00, −1.00, 0.00, 0.50, and 1.00 kA are considered, where negative and positive Ip represent counter and co-ECCD, respectively. To account for the EP finite charge-exchange loss observed in HJ, a bump-on-tail velocity distribution is assumed for EP. The study finds that the stabilization trends in terms of the linear growth rate ( γωA−1 ) are qualitatively similar to the FAR3D linear simulation and experimental results. In addition to the enhancements of the local magnetic shear and continuum damping by ECCD as proposed in previous studies, the study suggests that changes in the linear EP and shear Alfvén wave resonance are another important factor, especially for the n/m=1/2 mode. The study shows that in the currentless equilibrium, the high-velocity toroidicity-induced resonance between the n/m=1/2 mode and the co-passing EP ( L=−1 ) has the highest EP energy transfer rate, but is located slightly below the NBI injection velocity. The co-ECCD and cntr-ECCD can shift this resonance into higher and lower velocity regions, respectively. This can lead to resonance removal for co-ECCD, while cntr-ECCD can initially increase the number of resonant EPs for a small value of shift. If the shift of the resonance by cntr-ECCD is sufficiently large, the study observes stabilization due to the reduction in the EP population in the low-velocity region. The study also finds that changes in resonance affect nonlinear dynamics such as EP transport and frequency chirping. The convective transport of the co- and counter-passing EPs can be controlled, which can only be achieved for energetic-particle-mode due to the asymmetry in the resonance velocity between co- and cntr-passing EPs. The changes in the frequency chirping from the downward chirping branch to the upward chirping branch can also be explained by the changes in the resonance velocity caused by ECCD.