Self-sustained Oscillations Research Articles

Bifurcation-Diagram-Free Postflutter Response Constraint for Design Optimization

This paper introduces a new metric to constrain postflutter responses of aeroelastic systems in design optimization. The new metric aggregates the recovery rate to equilibrium for a range of operating conditions, modes, and amplitudes, resulting in a scalar constraint that does not involve the bifurcation diagram. By generalizing damping-based flutter constraints, the formulation yields mathematical properties oriented toward gradient-based optimization. The approach is demonstrated by optimizing a typical section with a subcritical bifurcation using a gradient-based algorithm and finite-difference derivatives. The postflutter response constraint suppresses self-sustained oscillations below a given flow speed while minimizing the mass penalty, which avoids a conservative solution. This constraint can help design highly efficient aeroelastic systems with feasible postflutter dynamics. Future development of adjoint derivatives will enable large-scale gradient-based optimization.

Ferrite Beads Design to Improve Turn-Off Characteristics of Cascode GaN HEMTs: An Optimum Design Method

In this paper, an optimum ferrite beads design method is proposed to suppress the self-sustained turn-off oscillation of cascode gallium nitride high-electron-mobility transistors (GaN HEMTs). At first, the impacts of gate loop beads and power loop beads on the turn-off oscillation of cascode GaN HEMTs are analyzed. The analysis reveals the weak damping effect of gate loop beads on the turn-off oscillation. Next, an analytical method is proposed to design the power loop beads that can achieve maximum effective damping on the turn-off oscillation. The power loop beads introduce extra stray inductance in the power loop, which can induce high voltage overshoot. To tackle the problem, an optimum design method is proposed so that the power loop beads can suppress the oscillation while mitigating the voltage overshoot. The accuracy of the proposed model is validated by the experimental data in the end.

Computation and prediction of intrinsic thermoacoustic oscillations associated with autoignition fronts

A sequential combustor architecture consists of two longitudinally staged combustion zones featuring a propagation-stabilized flame in the first stage and an autoignition-stabilized flame in the second (reheat) stage. This layout allows for increased fuel flexibility compared to single-stage systems and enables clean and efficient combustion of carbon-free fuels such as hydrogen. Interactions between the autoignition-stabilized flame and the acoustic field created by the unsteady ignition front and the surrounding boundaries can result in self-sustained (thermoacoustic) flame oscillations in the reheat stage of the sequential burner, causing performance losses and structural damage. In this paper, an intrinsic flame-acoustic feedback mechanism causing self-sustained thermoacoustic oscillations in a reheat combustor is studied. The intrinsic thermoacoustic feedback is established when an acoustic wave generated by the unsteady ignition front travels upstream and introduces local temperature, pressure and velocity perturbations in the unburnt mixture. These modulate the ignition chemistry and the front kinematics and thus, in turn, act as a new source of perturbation for the ignition front that generates heat release rate oscillations and upstream-traveling acoustic disturbances, closing the feedback loop. Compressible reactive Euler equation computations of autoignition fronts in a simple one-dimensional reheat combustor configuration with fully non-reflecting boundaries are first performed to demonstrate and characterize the intrinsic thermoacoustic oscillations associated with autoignition fronts. These computations show that the autoignition front exhibits distinct harmonic thermoacoustic oscillations which tend to become unstable at some conditions. Next, frequencies and growth rates of the intrinsic thermoacoustic oscillations in the linear regime are predicted using a hybrid approach with flame response transfer functions taken from a forced Euler calculation and using a linearized Euler equation framework to describe the combustor acoustic field. The predictions of the intrinsic thermoacoustic eigenvalue from the linearized Euler equation framework show good agreement with the linear behaviour of these oscillations observed in the Euler computations. The findings of the present work are useful both from a fundamental standpoint for prediction of intrinsic thermoacoustic instabilities and from an industrial perspective for prevention of thermoacoustic instabilities in staged combustion systems.

Imaging Interface and Particle Size Effects by In Situ Correlative Microscopy of a Catalytic Reaction.

The catalytic behavior of Rh particles supported by three different materials (Rh, Au, and ZrO2) in H2 oxidation has been studied in situ by correlative photoemission electron microscopy (PEEM) and scanning photoemission electron microscopy (SPEM). Kinetic transitions between the inactive and active steady states were monitored, and self-sustaining oscillations on supported Rh particles were observed. Catalytic performance differed depending on the support and Rh particle size. Oscillations varied from particle size-independent (Rh/Rh) via size-dependent (Rh/ZrO2) to fully inhibited (Rh/Au). For Rh/Au, the formation of a surface alloy induced such effects, whereas for Rh/ZrO2, the formation of substoichiometric Zr oxides on the Rh surface, enhanced oxygen bonding, Rh-oxidation, and hydrogen spillover onto the ZrO2 support were held responsible. The experimental observations were complemented by micro-kinetic simulations, based on variations of hydrogen adsorption and oxygen binding. The results demonstrate how correlative in situ surface microscopy enables linking of the local structure, composition, and catalytic performance.

New Viewpoint on the Mechanism of Laminar Separation Flutter

At transitional Reynolds numbers, an elastically supported airfoil oscillating in pitch can undergo laminar separation flutter (LSF), which is characterized by self-sustained small-amplitude oscillations. To gain insight into the mechanism of LSF, we conduct wind tunnel tests for to investigate the LSF response of a freely rotating NACA0015 airfoil with various structural natural frequencies and positions of the elastic axis. The experimental results show that the dominant mode of flow around the NACA0015 airfoil abruptly changes at , resulting in a change in the trend of LSF response. Then, an aeroelastic model is constructed to explain how the instability of LSF arises. This model can accurately predict the LSF frequency of airfoils with various structural natural frequencies. Moreover, based on the aeroelastic model, we perform linear stability analysis on the aeroelastic system and propose the instability criterion for LSF as . This instability criterion is identical to that for rotational galloping of square cylinder, indicating that LSF and rotational galloping of square cylinder are essentially the same aeroelastic phenomenon that appears in different aerodynamic profiles. This finding identifies the underlying cause for the remarkable similarities between the two phenomena.

Bifurcation analysis of a pulsating heat pipe

Heat pipes are being used for transferring a very high amount of heat in electronic devices. The Pulsating Heat Pipe has the advantage of not having a wick structure and, therefore, is a promising candidate for both terrestrial and space applications. However, understanding Pulsating Heat Pipe's operation is somewhat limited due to the multi-physics involved in the process. The presence of self-sustained oscillations can be understood by non-linear dynamics. In order to understand these oscillations, recently a simple phenomenological model is developed. This model explains all the thermodynamic processes of the system. Moreover, the oscillatory behavior of the liquid slug is modeled in a similar way to the spring-mass system. The system of non-linear ordinary differential equations, containing the conservation equations for the liquid slug and vapor bubble separately, has been solved numerically and the bifurcation analysis has been performed using MATCONT. The oscillatory behavior of the position of the liquid slug is identified through Hopf bifurcation. For self-sustained oscillations, the Pulsating Heat Pipe must operate in the region where limit cycles exist, the so-called unstable side of the Hopf bifurcation line. It is observed that the Hopf bifurcation is subcritical throughout the parametric range of operation. The existence of subcritical Hopf bifurcation indicates that limit cycles may exist even in the linearly stable region. However, further analysis reveals that such regions in the parameter space are negligibly small and, hence, may not be of any practical consequence. It is also important to note that heat transfer enhances as one operates in a chaotic regime. Although the presence of the chaotic feature is confirmed by experimental data, the onset of this regime is an important aspect of analysis that has not been addressed in previous works. In the present work, Period-doubling bifurcation and Neimark–Sacker bifurcations have been identified to analyze the onset of chaotic regimes. Therefore, there is a possibility of two different routes to chaos. Further studies with improved models may shed more light on the chaotic regimes.

Study on Relation Between Voltage-induced Switching Behavior and Self-sustained Electrical Oscillations in Vanadium Dioxide Thin Films

Study on Relation Between Voltage-induced Switching Behavior and Self-sustained Electrical Oscillations in Vanadium Dioxide Thin Films

Time delay feedbacks enhanced bifurcation in the birhythmic fractional self-sustained system subjected to correlated noise

The response of the birhythmic fractional Van der Pol (VdP) self-sustained oscillator driven both by time delay feedbacks and correlated noise is considered. We mainly focus on the effects of time-delay feedback parameter and fractional damping on stochastic properties of the birhytmic system, such as P-bifurcation. The minimum mean-square error is used to reduce the system to its equivalent integer-order nonlinear stochastic equation. An analytical approximation is adopted to obtain the system behavior and it is compared with numerical simulation. The delay self-control feedbacks are transformed into state variables without delay by means of the harmonic approximation. The maximum extension of the control parameters to have a birhythmic solution can be thus determined by an appropriated choice of the fractional order and delay time parameters. In particular, when the fractional damping is lowered below 2, the birhythmic region disappears. However, the influence of the fractional damping changes as a function of the correlation noise parameter. Instead, the delay feedback and the fractional derivative are not so effective on the transition. The input delay and fractional derivative can be greatly enhanced by the nonlinear interaction. Specifically, the amplitude of the induced oscillations can be much larger than that of the input fractional with the cooperation of an appropriated time delay and nonlinear terms. It is then shown that the time delay feedback parameters and the fractional damping also act as bifurcation parameters.

Investigation of the do minant Rossiter modal tones at the locked-on state

Rossiter resonance noise, which is flow driven cavity noise involving fluid dynamics processes, was investigated in a low-speed wind tunnel. The experiments include near-field and far-field acoustic field measurements of the rectangular cavity at different depths as well as velocity measurements of the shear layer. The rectangular cavity geometry was also designed to enable the Rossiter mode to interact with the first-order depth resonant mode in a locked-on state. The experimental results showed the variation of frequency and overall sound pressure level (OASPL) when the self-sustained oscillation was in the locked-on state. When the self-sustained oscillatory mode is in the unlocked state, the frequency of the self-sustained oscillatory mode can be predicted well by using the Rossiter formula, whereas the frequency of the dominant Rossiter mode in the locked-on state will be predicted inconsistently. Moreover, the corresponding selection of the dominant mode also depends on the resonant mode, and there are local variations in the OASPL. The results indicate that the ratio of the resonant mode frequency to the self-sustained oscillatory fundamental frequency, Rd, plays a key role in the locked-on state. In this paper, the Rossiter model is modified using the parameter Rd for the prediction of the dominant mode frequency in the locked-on state. The difference between the current formula and previous studies is that the variation of the phase delay coefficient γ with velocity is considered, and γ is related to Rd. Finally, the accuracy of the formulation is verified with experimental data from different models.

Impact of spray dynamics on combustion instabilities investigated by changing the atomizer recess in a swirl combustor

The present article is aimed at identifying the impact of spray-wall interaction on combustion instabilities. This is achieved by systematically modifying the liquid fuel atomizer location with respect to the injector outlet in experiments carried out on a single-injector swirling combustor. The injector is characterized by a high swirl number and a relatively high pressure drop, and features a pressure atomizer that delivers liquid heptane fuel in the form of a fine spray. In the first set of experiments, longitudinal self-sustained oscillations (SSOs) are examined by varying the atomizer recess distance and using three combustion chamber lengths. Three distinct instability regions characterized by jumps in amplitude and frequency are observed as a function of the atomizer recess. At lower SSO frequencies (obtained for longer chambers), the pressure fluctuation amplitude in the chamber decreases as the atomizer recess distance is reduced, tending towards a stable operation. An opposite behavior is observed at comparatively higher SSO frequencies (obtained with a shorter chamber), where the system becomes less unstable at higher atomizer recess distances. The oscillation frequency is also found to change and increases as the recess distance is reduced. Three recess distances corresponding to each zone of operation are selected to further analyze the flow and flame structures and dynamics. It is found that the mean velocity profiles only reveal moderate differences in the air flow field, but there are significant changes in the fuel spray distribution in the neighborhood of the injector axis. Laser sheet images of the spray reveal two patterns—one where the spray predominantly interacts with the injector end piece when the atomizer is recessed, and the other where this interaction is minimal. In the latter case, corresponding to a small recess, the fuel spray is directly conveyed into the chamber. It is next found that the spray distribution affects the flame pattern defining two distinct configurations. Finally, the flame response to external disturbances is characterized by flame describing functions (FDFs) that allow carrying out a stability analysis. FDF results obtained with two independent methods indicate that the gain and phase at the three recess positions vary substantially and that this can be used in combination with a low-order model to interpret the instability behavior of the system. This study might serve to guide the modeling of combustion dynamics and help design injectors that are less sensitive to instabilities.

Energy transfer characteristics of sunroof wind buffeting noise via dynamic mode decomposition

To further investigate the reason contributing to the abrupt increase in pressure fluctuations on the sunroof and the characteristics of energy transfer between velocity and pressure, dynamic mode decomposition (DMD) is performed to investigate the dynamic characteristics of related coherent structures on the sunroof. First, a large eddy simulation is applied to a sports utility vehicle with a fully open sunroof, and the simulation results are verified via wind tunnel tests. Subsequently, the steady-state and transient characteristics of the flow field are investigated. The significant pressure fluctuation in the passenger compartment is discovered to be related to the pressure core at the trailing edge; however, the significant amount of energy exhibited by the pressure core at the trailing edge remains unclear. In addition, important information that explains the significant pressure fluctuations is obfuscated by the relatively random fluctuations in the turbulence. Thus, DMD is performed to extract the main coherent structures, including the fluctuating pressure and velocity. Finally, the relationships among the fluctuating pressure, fluctuating velocity, and their energy properties are investigated simultaneously. The results show that DMD is excellent for extracting the dominant coherent structures. A comparison between the model results for the fluctuating pressure and velocity at f = 15.0 Hz shows that the fluctuating pressure in the passenger compartment is primarily related to the positive and negative fluctuating pressure cores near the trailing edge. The significant pressure fluctuations between the center and trailing edge of the sunroof are caused by the vortices expanding and pushing against each other. In addition, the self-sustained oscillation in the sunroof is caused by the vortex extruded from the trailing edge, which causes the new vortex at the leading edge to collapse rapidly.

Accurate Reduced Models for the pH Oscillations in the Urea–Urease Reaction Confined to Giant Lipid Vesicles

This theoretical study concerns a pH oscillator based on the urea-urease reaction confined to giant lipid vesicles. Under suitable conditions, differential transport of urea and hydrogen ion across the unilamellar vesicle membrane periodically resets the pH clock that switches the system from acid to basic, resulting in self-sustained oscillations. We analyze the structure of the phase flow and of the limit cycle, which controls the dynamics for giant vesicles and dominates the pronouncedly stochastic oscillations in small vesicles of submicrometer size. To this end, we derive reduced models, which are amenable to analytic treatments that are complemented by numerical solutions, and obtain the period and amplitude of the oscillations as well as the parameter domain, where oscillatory behavior persists. We show that the accuracy of these predictions is highly sensitive to the employed reduction scheme. In particular, we suggest an accurate two-variable model and show its equivalence to a three-variable model that admits an interpretation in terms of a chemical reaction network. The faithful modeling of a single pH oscillator appears crucial for rationalizing experiments and understanding communication of vesicles and synchronization of rhythms.

Geometry Controlled Oscillations in Liquid Crystal Polymer Films Triggered by Thermal Feedback.

Light-induced oscillatory behavior of liquid crystal polymer network (LCN) films has been demonstrated by several researchers in the past decade. Similarly, oscillations in LCN films under constant thermal stimulus have been reported recently, although the mechanism and the factors that govern the oscillatory behavior are not well understood. In this work, we study the dynamics of self-sustained oscillations exhibited by LCN films under a constant thermal stimulus through experiments and simulations. Geometrically asymmetric films such as a right triangle and an equilateral triangle are obtained from a twisted nematic square film. A multiphysics computational framework using the finite element method is developed to simulate the oscillatory behavior of the LCN films kept on a hot plate. The framework accounts for a coupling between heat transfer and mechanical deformations during the oscillations. Small temperature fluctuations (≈ 1 °C) coupled with gravity induced torque are shown to drive the oscillatory behavior at a specific plate temperature. We show for the first time that self-sustained oscillations can also be achieved in symmetric shapes, such as square films, by creating a thickness tapering between two opposite edges. The frequency of the oscillations is found to be in the range of 0.5 to 2.5 Hz for different geometries studied. The oscillation temperature depends on the mean thickness, size, and thickness profile of the films. As a possible application, we demonstrate a thermally actuated optical chopper using the oscillatory response of the films.

Identifying the Self-Sustaining Mechanisms of Transonic Airfoil Buffet with Resolvent Analysis

The self-sustaining mechanisms of shock oscillations in transonic airfoil buffet are studied by wall-resolved large-eddy simulation (LES) and resolvent analysis. The LES successfully reproduces the large-scale shock oscillations over a transonic OAT15A airfoil, and the resolvent analysis using the high-fidelity LES data reveals the input–output relations in the self-sustained shock oscillations. Based on the input–output relations revealed by the resolvent analysis, this study identifies two mechanisms of the self-sustained shock oscillations. The first mechanism is closely tied to the periodic variations of the shock-induced separation height, whereas the second mechanism is related to the pressure dynamics around the shock wave. The mechanisms of the self-sustained shock oscillations identified by the input–output relations are examined in detail along with the high-fidelity LES data to aid the understanding of the feedback formulations in transonic airfoil buffet.

From primordial clocks to circadian oscillators

Circadian rhythms play an essential part in many biological processes, and only three prokaryotic proteins are required to constitute a true post-translational circadian oscillator1. The evolutionary history of the three Kai proteins indicates that KaiC is the oldest member and a central component of the clock2. Subsequent additions of KaiB and KaiA regulate the phosphorylation state of KaiC for time synchronization. The canonical KaiABC system in cyanobacteria is well understood3–6, but little is known about more ancient systems that only possess KaiBC. However, there are reports that they might exhibit a basic, hourglass-like timekeeping mechanism7–9. Here we investigate the primordial circadian clock in Rhodobacter sphaeroides, which contains only KaiBC, to elucidate its inner workings despite missing KaiA. Using a combination of X-ray crystallography and cryogenic electron microscopy, we find a new dodecameric fold for KaiC, in which two hexamers are held together by a coiled-coil bundle of 12 helices. This interaction is formed by the carboxy-terminal extension of KaiC and serves as an ancient regulatory moiety that is later superseded by KaiA. A coiled-coil register shift between daytime and night-time conformations is connected to phosphorylation sites through a long-range allosteric network that spans over 140 Å. Our kinetic data identify the difference in the ATP-to-ADP ratio between day and night as the environmental cue that drives the clock. They also unravel mechanistic details that shed light on the evolution of self-sustained oscillators.

Nonlinear Aeroelastic Prediction in Transonic Buffeting Flow by Deep Neural Network

Transonic buffet is an aerodynamic phenomenon of self-sustained shock oscillations. The aeroelastic problem caused by it is very complex, including two different dynamic modes: forced vibration and frequency lock-in. The vibration of the structure has a negative influence on the fatigue life of the aircraft. Especially in the region of frequency lock-in, the limit cycle oscillations occur due to the instability of the structural mode. Researchers have accurately predicted the region of frequency lock-in in transonic buffet and have clarified its mechanism by using a linear aerodynamic model. However, the nonlinear aeroelastic modeling and prediction of the transonic buffet remain to be solved. The long short-term memory (LSTM) deep neural network is suitable for predicting the time-delayed effects of unsteady aerodynamics. And it has achieved remarkable results in sequential data modeling. In the present work, a nonlinear model is developed for the aeroelastic system with NACA0012 airfoil in transonic buffeting flow and validated with the coupled computational fluid dynamics/computational structural dynamics (CFD/CSD) simulation. First, the data set and the loss function are specially designed. Then, the reduced-order model (ROM) based on the LSTM of the flow is built by using unsteady Reynolds-averaged Navier–Stokes computations data in a post-buffet state. By coupling the ROM and the single degree-of-freedom equation for the pitching angle, the nonlinear aeroelastic model is finally produced. The results show that the phenomenon of frequency lock-in and the self-sustained buffeting aerodynamics are precisely reconstructed. And the model has a strong generalization ability and can reproduce complex vibrations caused by competition between different modes. In short, the model can replace the CFD/CSD method in the current case with high efficiency and accuracy. The method can be used for modeling and prediction of other various complex aeroelastic systems.

The Darboux Polynomials and Integrability of Polynomial Levinson–Smith Differential Equations

We provide the necessary and sufficient conditions of Liouvillian integrability for nondegenerate near infinity polynomial Levinson–Smith differential equations. These equations generalize Liénard equations and are used to describe self-sustained oscillations. Our results are valid for arbitrary degrees of the polynomials arising in the equations. We find a number of novel Liouvillian integrable subfamilies. We derive an upper bound with respect to one of the variables on the degrees of irreducible Darboux polynomials in the case of nondegenerate or algebraically degenerate near infinity polynomial Levinson–Smith equations. We perform the complete classification of Liouvillian first integrals for the nondegenerate or algebraically degenerate near infinity Rayleigh–Duffing–van der Pol equation that is a cubic Levinson–Smith equation.

Experimental investigation on the cavitation modulation mechanism in submerged self-sustained oscillating jets

To investigate the cavitation evolution states in chamber and its modulation on the self-sustained oscillation, experimental research is conducted in the nozzles with three different chamber lengths using high-speed photography and high frequency sensors. The experiment results indicate that with the increase of the chamber length of Helmholtz nozzles utilized in this study, the intensity of cavitation gradually decreases and the complex congestion cavitation state will switch to the periodic shedding annular cavitation cloud and even discrete free cavitation. With the increase of inlet pressure, the self-maintenance of Helmholtz vortex ring in the jet shear layer enhances, making the random components in the shear layer and the chaotic degree of the flow field reduce. For the submerged self-sustained oscillating jets, the cavitation structure in the nozzle can be regarded as an accumulator, which shrinks and expands periodically to determine the release and aggregation of energy and modulates the pulsation frequency and intensity of the pulsed jet induced by Helmholtz nozzles. The amplitude of pressure pulsation is positively correlated with the cavitation intensity, which means that the pulsation performance of the self-sustained oscillating pulsed jet gets better with the increase of the cavitation intensity.

A30 EPITHELIAL FUNCTION OF THE CIRCADIAN CLOCK GENE, BMAL1, IS NECESSARY FOR COLONIC REGENERATION

Abstract Background The circadian clock is a self-sustained molecular oscillator which drives 24-hour physiological rhythms. It consists of the genes Bmal1 and Clock that positively regulate Cry and Per, their negative regulators, resulting in a 24-hour transcription/translation feedback loop. Shift work, which causes disruptions to 24-hour physiological rhythms, has been shown to lead to an increased incidence of inflammatory bowel disease (IBD). We have previously established that mice lacking the non-redundant circadian regulator, Bmal1, exhibit more severe colitis compared to controls. Purpose This study aims to investigate the epithelial function of Bmal1 in colonic regeneration during colitis. Method In order to assess the cell-specific role of the clock, we tested the regenerative effects of Bmal1 in intestinal epithelial tissue using Vil+/+;Bmal1flox/flox (control) and VilCre/+;Bmal1flox/flox (conditional mutant) mice. Dextran Sulfate Sodium (DSS) was applied to induce acute colitis. Disease progression was evaluated during colitis and during recovery upon removal of DSS treatment. We hypothesized that the absence of a functional circadian clock disrupts effective proliferation and regeneration of intestinal epithelial cells during colitis remission. Result(s) Vil +/+ ;Bmal1 flox/flox control and VilCre/+;Bmal1flox/flox conditional mutant mice exhibit no significant differences in disease severity or tissue histopathology during colitis. However, after the removal of DSS, VilCre/+;Bmal1flox/flox conditional mutants show increased total lesions and overall inflammation, decreased crypt density as well as a higher propensity of hyperplastic crypts in the tissue. Regenerative ability of the colon is decreased in conditional mutants: phosphorylated-histone H3 and Ki67 show persistent increases in mitosis and overall proliferation near ulcerated lesions. This suggests that, while controls complete the regenerative response, conditional mutants fail to recover from colitis and show inefficient regeneration when Bmal1 is disrupted in intestinal epithelial cells. Conclusion(s) Our results support a critical role for Bmal1 in intestinal epithelial cells during post-colitis regeneration and recovery. Please acknowledge all funding agencies by checking the applicable boxes below CIHR, Other Please indicate your source of funding; OGS, Crohn's & Colitis Canada Disclosure of Interest None Declared

Interaction of shock train with cavity shear layer in a scramjet isolator

The interaction between the self-excited shock train flow and the cavity shear layer in a scramjet isolator is investigated numerically using detached-eddy simulations. The effect of changing the position of the shock train by controlling the back pressure ratio and the effect of changing the cavity front wall angle are analyzed using unsteady statistics and modal analysis. The propagation mechanism of the pressure disturbance was investigated by spatiotemporal cross-correlation coefficient analysis. In the present numerical study, a constant isolator section with a cavity front wall (θ = 90° and 60°) was considered, followed by a diffuser section simulated at Mach number 2.2 with three different back pressure ratios (pb/p∞ = 0.7, 5.0, and 6.0). The change in back pressure provides three different conditions (i.e., no shock train, shock train ends before the leading edge of the cavity, and shock train present above the cavity). To understand the unsteady dynamics of the interaction of the shear layer with the shock train, the spatiotemporal trajectory of the wall pressure and the centerline pressure distribution, the spatiotemporal cross-correlation coefficient, and the modal analysis by dynamic mode decomposition are obtained. The results show that the low-frequency shock train oscillation dominates the self-sustained cavity oscillation. The spatiotemporal cross-correlation between the wall surface and the center of the cavity bottom wall indicates the propagation of local disturbances originating from the separated boundary layer caused by the shock and the recirculation zone in the corners of the cavity. Dynamic mode decomposition analysis shows the shear layer at the leading edge of the cavity and the downstream propagation of large eddies from the cavity. It also shows the pairing of coherent structures between the shock train and the recirculation zone of the cavity.