Time-resolved Schlieren Images Research Articles

Experimental study on acoustic resonance of subsonic and slightly underexpanded impinging jets

The aeroacoustic feedback loops in high-speed circular jets that impinge on a large flat plate are investigated via acoustic measurements and schlieren visualizations. In the present experiments, the nozzle pressure ratio ranges from 1.39 to 2.20, the corresponding ideally expanded jet Mach number $M_j$ is from 0.70 to 1.12 and the nozzle-to-plate distance ( $H$ ) is from 4.0 $D$ to 6.0 $D$ , where $D$ is the nozzle exit diameter. The results of acoustic measurements show that the strongest tones are generated in a limited frequency band. The empirical dispersion relations obtained from the fluctuating greyscales along the jet centreline of time-resolved schlieren images have good agreement with the dispersion relations from the vortex-sheet model. The coherent flow structures at tonal frequencies are extracted by spectral proper orthogonal decomposition and are analysed in detail. For the $M_j<0.82$ jets, the upstream-propagating guided jet mode is progressively confined to the potential core of jets with increasing tonal frequency, which provides the first direct experimental support for theoretical results. The evolution in the structures of acoustic resonance loops is studied along a single frequency stage of axisymmetric impinging tones. When the acoustic resonance between the upstream- and downstream-propagating guided jet modes is formed at tonal frequencies, the impinging tones are intenser. Slightly underexpanded impinging jets can simultaneously produce impingement tones and screech tones. Shock-cell structures have modulatory effects on the downstream-propagating Kelvin–Helmholtz wavepacket and the upstream- and downstream-propagating guided jet modes. Due to the interaction between the flow structures at the frequencies of impinging and screech tones, tones of axisymmetric modes can be produced outside the frequency ranges in which the axisymmetric upstream-propagating guided jet modes are supported by jets.

Temperature evolution characteristics of stem root during dark period in positive long spark discharge

Gas temperature plays an important role in the characterization of plasma parameters. The temperature evolution of stem roots during the dark period is at the heart of our understanding of the physical mechanism of streamer to the leader transition process in a long spark discharge. The quantitative schlieren system with high spatiotemporal resolution was designed to conduct positive leader discharge experiments with a 1.0 m rod-plate gap at atmospheric pressure, and the amplitude and rise time of positive impulse voltage waveforms were 380 kV and 200 μs, respectively. The time-resolved quantitative schlieren images of the discharge channel near the electrode tip can be captured to gather the temperature data of stem roots for case study. Further statistical tests revealed that due to the dispersion of the first streamer discharge, there were three evolutionary trends of gas temperature at the axis of the stem root in the early dark period. Interestingly, the gas temperature at the axis of the stem root was maintained at 1000–1200 K in regardless of the evolutionary trend in the early dark period. In addition, the statistical results indicate that there is a significant positive correlation between the curvature radius of the discharge electrode tip and the critical charge value Qcrit of the first streamer discharge, which leads to a transition in evolutionary trends of gas temperature at the axis of the stem root. This research has important guiding significance for understanding the physical mechanism of leader inception and the whole process modeling of long air gap discharge.

Experimental study on the axial growth characteristics of streamer stem during dark period in long spark discharge

This paper presents an original investigation into the axial evolution of streamer stem during a dark period in long spark discharge. To obtain thermodynamic morphology and temperature distribution of stems, we set up a quantitative schlieren system with the temporal and spatial resolutions of 0.37 μs and 31 μm/pixel, respectively. The quantitative schlieren observation experiments of positive leader discharge with a 1.0 m rod-plate gap were carried out, and the time-resolved quantitative schlieren images were captured. Furthermore, the temperature distribution of stems and its morphology evolution in the axial direction during a dark period were obtained. Due to the dispersion of first streamer discharge, the gas temperature in stem roots shows two evolutionary trends, namely, rising and falling. It was found that the gas temperature in stem decreased along the axis with the increase in the distance from stem root, and the gas temperature of a thermal thin channel was between 400 and 800 K. There is a significant dependency between axial development parameters of thermal thin channels and the first streamer discharge parameters. The phenomenon of channel abrupt elongation triggered by secondary streamer discharge was observed by the schlieren system, and the influence of characteristic parameters on the inception of secondary streamer was statistically analyzed. The ion current waveform in leader relaxation phase was measured, and it is clarified that the generation mechanism of thermal thin channels is due to the energy transfer between positive ions and neutral particles, which finally leads to the increase in gas temperature in the channels.

Dynamics of laser-induced shock wave and cavitation during laser ablation of aliphatic nitroalkanes

Nanosecond time-resolved schlieren imaging is performed to investigate laser-induced breakdown in nitromethane, nitroethane and 1-nitropropane, and the associated dynamics of laser-induced shock waves and cavitation bubbles. The exothermic reactions upon decomposition and the chemical reactions in the vapor plume behind the shock front increase the shock wave velocity. The correlations of oxygen balance with shock wave velocity, bubble radius, lifetime and bubble energy are established. For instance, shock wave velocity is proportional to the negative inverse of oxygen balance. In addition, the bubble energy of nitroethane tends to saturate at high pulse energy.

Effect of Plate Distance on Steady and Unsteady Characteristics of Impinging Rectangular Jet

Acoustic and unsteady characteristics of a rectangular jet impinging on a flat plate were investigated. Experiments were performed at the nozzle pressure ratio of 2 for the impingement distances , 4, 8, and 12. The mean and unsteady flow properties of the impinging jet were studied using the steady and unsteady pressures on the impinging surface, time-resolved schlieren images, and acoustic measurements at different directivity angles. Mean schlieren images elucidate the flow features including redirected flow, and the plate shock for the impingement distance . The mean surface pressures show unidentical pressure profiles in the and planes. The pressure profile in the plane is found to be identical to the free-jet case. Proper orthogonal decomposition performed on the time-resolved schlieren images shows that the impinging jet is dominated by the flapping instability mode for a given range of impingement distances. Flow features such as plate shock and the redirected flow were assessed using proper orthogonal decomposition and time-resolved schlieren images. Synchronized acoustic and unsteady pressure measurements reveal the coupling between the upstream acoustic waves and the unsteadiness arising from the impinging surface.

Acoustic resonance mechanism for axisymmetric screech modes of underexpanded jets impinging on an inclined plate

In this paper, the acoustic resonance mechanism for different axisymmetric screech modes of the underexpanded jets that impinge on an inclined plate is investigated experimentally. The ideally expanded Mach number of jets ( $M_j$ ) ranges from 1.05 to 1.56. The nozzle-to-plate distance at the jet axis and the impingement angle are respectively set as 5.0 $D$ and $30^{\circ }$ , where $D$ is the nozzle exit diameter. The acoustic results show that the $M_j$ range for the A2 screech mode of impinging jets is broader than that of underexpanded free jets, and a new axisymmetric screech mode A3 appears. With the increase of $M_j$ , the effect of the impinging plate on the shock cell structures of jets becomes obvious gradually, and the second suboptimal peaks are evident in the axial wavenumber spectra of mean shock structures. The coherent flow structures at screech frequencies are extracted from time-resolved schlieren images via the spectral proper orthogonal decomposition (SPOD). The axial wavenumber spectra of the selected SPOD modes suggest that the A1, A2 and A3 screech modes are respectively closed by the guided jet modes that are energized by the interactions between the Kelvin–Helmholtz wavepacket and the first three shock wavenumber peaks. The upstream- and downstream-propagating waves that constitute the screech feedback loop are analysed by applying wavenumber filters to the wavenumber spectra of SPOD modes. The frequencies of these three screech modes can be predicted by the phase constraints between the nozzle exit and the rear edge of the third shock cell. For the A3 mode, the inclined plate invades the third shock cell with the increase of $M_j$ , and the phase constraint cannot be satisfied at the lower side of the jets, which leads the A3 mode to fade away. The present results suggest that external boundaries can modulate the frequency and mode of jet screech by changing the axial spacings of shock cells.

Transient characteristics of a typical vacuum ejector—An experimental study

Using simultaneous measurements of unsteady pressures in conjunction with time-resolved Schlieren images and oil flow visualization, we investigate the characteristics of a typical vacuum ejector's starting transient, steady-state, and shut-down transient. With varying primary jet chamber pressure, the pressure evolution in the secondary chamber shows smooth, perturbed, rapid, and steady evacuation stages, as well as hysteresis and rapid filling stages. It is noticed that the evacuation in the secondary chamber is improved during stopping transient just before the unstart event. By using oil flow images, we illustrate the separation bubble characteristics during each stage of the vacuum ejector operation and their influence on the pressure evolution. Through cross correlation, it has been determined that the primary jet flapping during the starting transient causes the jet to attach to one of the diffuser walls. We also demonstrate that the primary jet undergoes both longitudinal and lateral oscillations in the starting transient, the former having a major effect on unsteadiness in the secondary chamber using proper orthogonal decomposition and spectral proper orthogonal decomposition algorithms and power spectral density (PSD). Simultaneous acquisition of unsteady pressures and high-speed Schlieren images allow us to correlate the frequency peaks (PSD spectra) in the flow. Using magnitude-squared coherence and cross correlation analyses, we confirm communication of unsteadiness and its direction of propagation between the secondary chamber and the diffuser. In this study, we demonstrate that a high ramping rate of primary jet chamber pressure reduces the unsteadiness in the secondary chamber during the transient starting phase.

Control effects of a high-frequency pulsed discharge on a hypersonic separated flow

The control effects of a high-frequency pulsed discharge on a hypersonic separated flow induced by a 42° compression ramp are studied with high-speed schlieren imaging. A discharge is generated between an electrode pair upstream of the ramp to introduce strong disturbances into the boundary layer. The discharge frequencies used are fd = 10, 20, 30, and 40 kHz, with corresponding single-pulse energies Esp = 22.2, 20.3, 12.0, and 8.7 mJ. The results show that the discharge can reduce the separation area, especially with relatively low frequencies of 10 or 20 kHz. The flow mechanism induced by the discharge is scrutinized using a reduced-order method based on the information from time-resolved schlieren images, including proper orthogonal decomposition and dynamic mode decomposition. The results identify an unsteady mode representing regular energetic eddies within the shear layer of the separation zone. This mode has the same characteristic frequency as the discharge. These eddies enhance the mixing of the shear layer and the main flow stream, accelerating the destruction of the shear layer and reducing the separation zone size. The control effectiveness correlates with the scale of the energetic eddies. At frequencies of 10 or 20 kHz, the discharge is more conducive to attenuating the separation because large-scale eddies, excited by higher single-pulse energy, are enhanced as they propagate downstream in the shear layer. By contrast, the control effectiveness deteriorates when the discharge frequency is 30 or 40 kHz because the induced eddies have smaller scales and decay during propagation.

Experiments on flow past cavity and the application of modal decomposition techniques

In this work, Mach 1.8 flow over a shallow open cavity is studied through time-resolved schlieren images as well as unsteady pressure measurements respectively. Additionally, the cavity shear layer dynamics are explored using modal decomposition techniques namely; proper orthogonal decomposition (POD) and spectral proper orthogonal decomposition (SPOD). The results display that the cavity undergoes a self-sustaining oscillation with a number of modes/tones that are closely related to the modified Rossiter relation. Depending on the cavity oscillation, the time-resolved images reveal various complex flow features. Through modal analysis, the shear layer structures which are responsible for the cavity oscillation are identified. It is understood that POD requires several hundreds of modes to capture 67.3% of the total intensity for resembling the cavity flow field, while SPOD shows 65.7% of the total intensity is available in the 1st mode to reconstruct the cavity flow field. Further, modal analyses have demonstrated that cavity oscillatory frequencies are very similar to unsteady pressure measurement and the modified Rossiter relation. We confirmed that, both these techniques can be successfully applied to cavity flows and are complementary.

Response characteristics of impinging shock wave/turbulent boundary layer interaction disturbed by arc plasma energy deposition

Experiments and numerical simulations of shock wave/turbulent boundary layer interaction (STBLI) disturbed by arc plasma energy deposition (APED) were carried out in this paper. The experiments were conducted in a M = 2.497 wind tunnel. Both the flow structures and the evolution process of impinging STBLI disturbed by APED were captured by time-resolved schlieren imaging. The disturbance effects of APED on supersonic flow without STBLI were studied with different capacitor stored energies. Furthermore, under the same capacitor stored energy, the impinging STBLI control with APED were explored in different flow deflection angles. The experimental results indicated that thermal bubbles induced by APED had a high penetration depth and impacted the STBLI seriously. Compared to the incident shock wave, the separation shock wave was more sensitive to the influence of APED and showed significant instability. With equivalent energy deposited into the flow, the ability of APED to disturb the impinging STBLI was decreased as the flow deflection angle increased, and the separation shock wave had a smaller position change and shorter recovery time. The direct numerical simulation results showed that the APED added in a flow field can hinder the velocity development of the turbulent boundary layer. The unsteadiness of separation shock waves was induced by both thermal bubbles and blast waves, and the thermal bubbles' effects were dominant. They would modify the compressibility of the boundary layer and enlarge the separation zone, which contributed to the separation shock wave's dispersion and movement.

Imaging-based harmonic frequency analysis of a bluff-body premixed flame under acoustic excitations

The dynamic responses of a bluff-body premixed methane flame under acoustic excitations were studied using high speed color and schlieren imaging techniques. Two excitation frequencies at different amplitudes were tested and analyzed (50 Hz-105, 110, 115 dB and 200 Hz-120, 125, 130 dB). The fast Fourier transform (FFT) analysis reveals the dominant excitation frequency, as well as several harmonic frequencies as nonlinear responses. The dynamic mode decomposition (DMD) analysis was conducted using the time-resolved color and schlieren images to extract the spatial pattern at the dominant and multiplication harmonic frequencies. The results indicate that under these frequencies, the energy distribution has exhibited axisymmetric patterns to the nozzle axis, with positive and negative energy bands appearing alternatively. The spatial distribution has shown great variances under different excitation frequencies and amplitudes. An energy band sub-dividing phenomenon at multiplication frequencies was observed from the DMD results of both color and schlieren images.

Application of Phase-Averaging Methods to Sweeping Supersonic Jets

This paper examines various methods for phase averaging the flowfield of a sweeping supersonic jet emanating from a scaled fluidic oscillator. Determination of the phase-averaged flowfield is challenging, especially at high oscillation frequencies where there is a jitter in the periodicity caused by its inherent fluid dynamics. Several phase-averaging approaches (including mathematical, signal processing, and phase-lock techniques) applied to time-resolved schlieren images of the flowfield are described. Criteria for evaluation are based on the image distribution per phase bin, the centerline intensity profile of the phase-averaged schlieren image, and the cross correlation of the images with the time-averaged reference image. Examination of the different methods based on the criteria shows that the zero-crossing method is sufficiently accurate and most suitable for the naturally oscillating flowfield investigated in this study. Although the phase-locked approach works well at specific phase angles, overall, it is found unsuitable for the current test conditions. The zero-crossing method applied to a sweeping supersonic jet schlieren reveals shock structure distortion when switching directions in the oscillation cycle. Results indicate that the zero-crossing method described in this study can also be extended to other non-time-resolved quantitative and qualitative flowfield measurement techniques using a simultaneously acquired time-resolved reference signal.

Experimental investigation of start/unstart process during hypersonic intake at Mach 6 and its control

Hypersonic intake with 20 and 30% blockage struts is experimentally investigated in Mach 6 flow. Initially the experiments are conducted with full opening of the cowl at fixed condition. The results show that the intake is started for 20% blockage struts while it is unstarted for 30% blockage struts. The unstart process for 30% blockage struts is due to large separation bubble in the engine flow path which is corroborated through steady pressure measurements, time average schlieren images, and oil flow visualization. To understand the separation bubble behaviour associated with start as well as unstart cases, a cowl opening mechanism is indigenously designed, and the experiments are performed using different cowl opening times from closed to fully opened condition. To quantify the separation bubble behaviour, unsteady pressure measurements, time-resolved schlieren images, and spectral analyses are done. For 20% blockage struts, irrespective of cowl opening time, the separation bubble size remains unaltered. In this case, increasing cowl opening time (110, 185, 350, and 700 ms) delays the separation bubble movement, and a maximum delay in the separation bubble movement is noted for 350 ms cowl opening time. It can be concluded that there exists an optimum cowl opening time at which the separation bubble movement can be restricted. Conversely, un-start process is noted for 30% blockage struts regardless of the cowl opening time where the pressure rise because of the separation bubble is found to be twice that of the 20% blockage struts, indicating a substantial increase in the separation bubble size. To alleviate the un-start process, experiments are further carried out using partial cowl opening with fixed as well as dynamic conditions. The results reveal that the un-start process is eased by opening the cowl below 90% of its full opening.

An Optimization and Parametric Study of a Schlieren Motion Estimation Method

Schlieren imaging is a widely used technique for flow visualization in turbulence and combustion investigations due to its high sensitivity, flexibility and easiness in use. With the development of digital imaging and image processing techniques, it is possible to retrieve velocity measurements using time-resolved schlieren imaging sequences. In this paper, an optimization and parametric study has been conducted on a newly proposed schlieren motion estimation (SME) algorithm, based on the high speed schlieren images of a jet flow and the transient ignition process of impinging flames. The SME algorithm is optimized using a graduated non-convexity (GNC) computing scheme, which employs a three stage strategy by linearly combining a convex quadratic function and a slightly non-convex generalized Charbonnier function. The Euler–Lagrange equations have been derived, while the penalty function was separated so that penalty functions can be changed conveniently. Parametric investigations have been conducted to discuss the influence of weight parameters, while the suitable ranges have been obtained after intensive calculations. Comprehensive comparisons have been made between the SME and GNC-SME methods, which indicates that the GNC scheme can preserve the boundary well and avoid local divergence and over-smoothness at the same time. The suitable weight parameter range is also broadened by using the GNC technique. The better robustness of GNC-SME method makes it more adaptive to various applications.

Unsteadiness characterization of shock wave/turbulent boundary layer interaction controlled by high-frequency arc plasma energy deposition

We carried out an experimental study of Mach 2.5 airflow over a semicircular column with 15 kHz arc plasma energy deposition (APED). The APED was pulsed at microsecond time scales, and it rapidly added high-repetition-frequency thermal bubbles that propagated downstream. Time-resolved schlieren imaging with a frame rate of 30 kHz was utilized to record the dynamic flow fields. This study was aimed at investigating the effects of these thermal bubbles on the unsteadiness characterization of a shock wave/turbulent boundary layer interaction (STBLI) by some statistical methods based on the spatial gray value extracted from a sequence of time-resolved schlieren images. The results showed that APED pulsed at 15 kHz was highly effective in weakening both the separation shock and the attached shock continuously and in narrowing the low frequency component of the oscillatory separation shock. A stronger oscillation of the attached shock under APED was found. The thermal bubbles increased the characteristic scales of vortex in the incoming turbulent boundary layer and shear layer, enhancing the fluctuation of the shear layer with large numbers of high-frequency components. The continuous transforming of the enlarged eddies along the shear layer was regarded as the main cause of shock weakening and frequency modulation of the STBLI in this study.

Short-time proper orthogonal decomposition of time-resolved schlieren images for transient jet screech characterization

Short-time Proper Orthogonal Decomposition (POD) is proposed as an image-based technique to study the transient jet screech characteristics of moderately under-expanded supersonic jets emanating from a circular baseline and two bevelled nozzles. Time-resolved schlieren imaging of turbulent flow structures were performed with an ultrahigh-speed schlieren setup. Short-time POD was performed by systematically sampling image-series with a short time delay, performing PODs and applying spectral analyses on the first POD mode coefficients, and plotting the peak frequencies from the resulting PSDs into a peak frequency-occurrence count histogram. The results are in good agreement with the near-field noise spectra and wavelet transform analysis of the microphone measurements, which revealed intermittent jet screech occurrences at St=0.25 for both baseline and 30° bevelled jets, while none was detected for the 60° bevelled jet. In particular, the occurrence counts of the frequency bins is proposed as a suitable parameter to characterize the intermittent nature of jet screech, with the frequency bin revealing the jet screech frequency if present. The present study demonstrates the advantage of short-time POD analysis on time-resolved schlieren images over traditional image-based POD methods, which includes computational gains from parallelization, the ability to handle much larger datasets and revealing insights into a transient flow and noise phenomenon.

Effect of the axial cavity with an opposing high-pressure jet combination in a Mach 6 flow condition

Flow control techniques mitigating the aerothermal heating over bodies are essential for long-duration hypersonic flight. The combination technique of a nose cavity with an opposing jet is exhibited promising effects. There is a lacuna of experimental studies on unsteady aspects of the flow and the heat transfer effects within the cavity. In the current study, we investigated the heat transfer variations and nature of shock around a blunt body with a cylindrical and parabolic cavity geometries combined with opposing jet. Experiments are conducted in the hypersonic shock tunnel for a flow Mach number of 6 for an opposing jet pressure ratio of 18. Time-resolved high-speed schlieren imaging and heat flux measurements over the model surface and within the cavity are carried out. The cavity flow is established by verifying the measured heat flux, pressure, and shock oscillation results. The combination technique shows a significant reduction of heat transfer and flow oscillations in comparison to the nose cavity technique. Notably, the parabolic cavity with the opposing jet showed about a 33% reduction of surface heat flux and a 43% reduction in flow oscillations. The substantial increase of heat flux due to the shock interaction is noted on the nose surface for a cylindrical cavity geometry, and such effect was not prevalent in the case of flow with parabolic cavity geometry.

Elliptic supersonic jet morphology manipulation using sharp-tipped lobes

Elliptic nozzle geometry is attractive for mixing enhancement of supersonic jets. However, jet dynamics, such as flapping, gives rise to high-intensity tonal sound. We experimentally manipulate the supersonic elliptic jet morphology by using two sharp-tipped lobes. The lobes are placed on either end of the minor axis in an elliptic nozzle. The design Mach number and the aspect ratio of the elliptic nozzle and the lobed nozzle are 2.0 and 1.65. The supersonic jet is exhausted into ambient under almost perfectly expanded conditions. Time-resolved schlieren imaging, longitudinal and cross-sectional planar laser Mie scattering imaging, planar Particle Image Velocimetry (PIV), and near-field microphone measurements are performed to assess the fluidic behavior of the two nozzles. Dynamic Mode Decomposition (DMD) and proper orthogonal decomposition analyses are carried out on the schlieren and the Mie scattering images. Mixing characteristics are extracted from the Mie scattering images through the image processing routines. The flapping elliptic jet consists of two dominant DMD modes, while the lobed nozzle has only one dominant mode, and the flapping is suppressed. Microphone measurements show the associated noise reduction. The jet column bifurcates in the lobed nozzle enabling a larger surface contact area with the ambient fluid and higher mixing rates in the near-field of the nozzle exit. The jet width growth rate of the two-lobed nozzle is about twice that of the elliptic jet in the near-field, and there is a 40% reduction in the potential core length. PIV contours substantiate the results.

Onset of Cavity Oscillation From Transverse to Longitudinal Mode in a Supersonic Flow

Abstract Experiments are carried out in supersonic flow past cavities (L/D = 1–3) to comprehend cavity oscillation from transverse to longitudinal mode. To characterize this, time-resolved schlieren images and unsteady pressure measurements are carried out. For L/D = 1, the cavity oscillation is in the transverse direction which is characterized by a single vortex along with low frequency oscillations. In the present studies, for the given length and depth, the L/D = 2 cavity shows both transverse and longitudinal mode of oscillations. This dual nature is ascertained through high-speed schlieren images and large rise in the fluctuating pressure. For L/D = 3, the cavity oscillation is in the longitudinal direction accompanied by low values of fluctuating pressure component and number of discrete modes/tones. Hence, it is believed that the transverse to longitudinal mode of cavity oscillation in the present studies occurs between L/D = 2 and 3. These cavities are driven by a thick shear layer where the vortex convection is found to be nonlinear. The comparison of dominant modes/tones with modified Rossiter and Handa relations indicates the necessity to develop a suitable model for transitional cavities. In-depth analyzes in terms of cross-correlation as well as wavelet transform divulge the basis that generates cavity modes/tones and mode switching phenomena, respectively.

Nonlinear Characteristics of a Rectangular Cavity in Supersonic Flow

Time-resolved schlieren images and unsteady pressure measurements were employed to understand the flowfield characteristics of a rectangular cavity at Mach number 1.8 with a unit Reynolds number of . It was illustrated that the vortex dynamics in the cavity shear layer were found to be nonlinear, where the vortex speed was observed to be varied from to with an average value of . Unsteady pressure measurements inside the cavity revealed six tones, among which the third tone was dominant. The uniqueness of the flow features both outside as well as inside the cavity was studied for one vortex shedding cycle. Analyses using different techniques divulged that the occurrence of the first and second tones was due to wave propagation and vortex shedding, respectively. On the other hand, frequency that corresponds to one time period was correlated to the third tone. Further investigations unveiled that the entrainment of freestream between shear-layer vortices generated type 5 acoustic waves, which were responsible for the production of other cavity tones. The wavelet analyses indicated that the frequencies were amplitude modulated in time, and the wavelet spectra of the second and third tones contain high-energy events along with sporadic distribution of low-energy events without mode switching phenomenon.