Broadband Shock-associated Noise Research Articles

Statistical sources for broadband shock-associated noise using the Navier-Stokes equations.

A decomposition of the Navier-Stokes equations is used to identify the equivalent source term for broadband shock-associated noise (BBSAN). An analytical closed-form model to predict BBSAN is developed using an acoustic analogy based on the Navier-Stokes equations. The field-variables are decomposed into the base flow, aerodynamic fluctuations, and acoustic fluctuations. The spectral densities of fluctuating acoustic quantities are obtained by convolving the vector Green's function with the source terms involving the two-point cross-correlation of the aerodynamic quantities. The scaling of the source term with the off-design parameter β=(|Mj 2-Md 2|)1/2 is compared with experimental results. The base flow is obtained using a Reynolds-averaged Navier-Stokes solution, while the fluctuating statistical quantities are obtained using theoretical and experimental results. This paper identifies the equivalent source of BBSAN based on the scaling analysis and the physical mechanism of shock-associated noise. The identified source term resides within the Navier-Stokes equations without further rearrangement and correlates very highly with BBSAN. Predictions for BBSAN are made at multiple observer angles and nozzle pressure ratios using the identified source term, and these predictions compare favorably with the experimental results. Finally, identification of the source locations in the jet exhaust responsible for BBSAN at different Strouhal numbers is performed.

Effect of fluid injection on turbulence and noise reduction of a supersonic jet.

Supersonic jets, such as the ones used in high-performance military aircraft, have both downstream and upstream noise components due to the large-scale turbulent structures and the presence of shock cells in the jet plume. The fluid insert technology is a noise reduction method that has been shown to effectively reduce both these noise components. This paper analyses the unsteady flow changes associated with different fluid insert configurations with a goal of helping to understand the detailed noise reduction mechanisms. Using direct cross-correlations of the near-field data with the far-field microphone signals, it is found that even the use of a single injector as a fluid insert helps break up the large-scale structures of the flow. However, a more azimuthally distributed blowing is required to reduce the upstream broadband shock-associated noise (BBSAN). Addition of upstream injectors at each azimuthal location further enhances the BBSAN reduction. Decomposition of the jet flow-field into hydrodynamic and acoustic modes shows that fluid insert nozzles reduce the amplitude and convection speed of the coherent acoustic mode in the plane of highest noise reduction. This article is part of the theme issue 'Frontiers of aeroacoustics research: theory, computation and experiment'.

Reducing noise from twin supersonic jets using very-low-frequency control

The intense jet noise radiated by closely spaced, twin supersonic hot jets leads to sound-induced structural vibration, fatigue and personnel related operational difficulties. Experimental, theoretical, and computational investigations into the physics and control of jet noise have identified several important sound sources, including wavepackets, screech, Mach wave radiation, and broadband shock associated noise (BBSAN). Reducing the loudest sources of jet noise, without sacrificing propulsive performance, has relied on intuition, parametric survey, or optimal control techniques. With the aim of developing a more general and robust method of jet noise reduction (JNR), we present a physics-based approach that leverages very-low-frequency jet dynamics in order to achieve JNR whilst preserving propulsive performance. Our approach formulates the control problem using the very-low-frequency global modes of the compressible Navier-Stokes operator linearized about the jet mean flow to disrupt the nonmodal transient growth processes. The presentation will showcase uncontrolled and controlled single and twin supersonic hot jets issuing from biconical nozzles, with conditions and geometries motivated by tactical Naval aircraft. The predictions utilize fully resolved numerical simulations whose data inform the control development and which evaluate its performance on the jet exhaust and on its radiated noise.

Analysis of turbulence in convergent-divergent nozzles with fluid insert noise reduction technology

The noise generated by tactical fighter aircraft engines is harmful to personnel working in the vicinity of the aircraft and can cause annoyance to communities in the vicinity of air bases. The primary noise sources in supersonic jets are related to the supersonic convection of large-scale turbulent structures, which generate intense noise in the jet downstream direction, and the interaction of the turbulence with the jet’s shock cell structure that results in broadband shock-associated noise, which radiates predominantly in the sideline and upstream directions. The use of fluid inserts in the divergent section of variable area exhaust nozzles has been shown experimentally, at small and moderate scale, to reduce noise radiation from both noise sources. To understand the fluid insert noise reduction mechanisms, a Large Eddy Simulation database is developed and analyzed. The focus is on differences between turbulence properties in a baseline and a fluid insert nozzle. The flow database is analyzed using Spectral Proper Orthogonal Decomposition and Doak’s Momentum Potential Theory. The latter theory permits the decomposition of the flow into hydrodynamic, thermal and acoustic components. The changes in the acoustic component are related to the observed changes in the radiated noise.

Antisymmetric Oscillation Modes in Rectangular Screeching Jets

In this paper, the origin and the properties of the oscillation modes in screeching non-ideally expanded rectangular jets are investigated using compressible implicit LES of rectangular supersonic jets. At the exit of a converging diverging rectangular nozzle of aspect ratio 2 and of design Mach number 1.5, the jets are under- and over-expanded. Seven simulations with four different temperature ratios ranging from 1 to 3 and two different nozzle pressure ratios are performed. The geometry of the nozzle and the exit conditions are chosen such that to match the experimental study conducted at the University of Cincinnati. First, the over-expanded jets are studied. It is shown that the total number of shock cells decreases with increased temperature ratio. However, the temperature does not influence the size of the first shock cell and the linear decrease of the shock cell size in the downstream direction. The spreading of the jet is observed to be higher along the minor axis plane than along the major axis plane. The intensity of the screech noise increases with the temperature ratio in the present study although the opposite is observed in the experiments. Moreover, for jet temperature ratios of 2.5 and 3, the strong flapping motion of the jet along the minor axis plane due to the screech feedback mechanism yields to an antisymmetric organization of the Mach wave radiation. Thereafter, the near- and far-field acoustic are studied. In the near-field, screech tones are captured, whose frequencies are consistent with both experimental data and theoretical models. In the far-field, four acoustic components typical of non-ideally expanded supersonic jets are observed, namely the screech noise, the broadband shock-associated noise, the mixing noise and the Mach wave noise. Their directivities and frequencies are in agreement with experimental results and models. The mechanism of the screech noise generation is studied by using a Fourier decomposition of the pressure field. For the four over-expanded jets, a flapping motion along the diagonal or along the minor axis plane of the jet is noted. Finally, the hypothesis that the acoustic waves completing the feedback loop in these jets are linked to the upstream-propagating acoustic wave modes of the equivalent ideally expanded jets is tested. Using a jet vortex sheet model to describe the dispersion relations of these modes, it is found that this hypothesis allows us to explain the antisymmetric jet oscillation observed at the screech frequencies. Based on frequency-wavenumber decomposition of the pressure fluctuations in the jets, it is shown that at the screech frequencies, acoustic waves propagating in the upstream direction at the ambient speed of sound exist also in the jet flow, additionally to the acoustic waves propagating outside of the jet. These acoustic waves belong to the neutral acoustic wave modes of the equivalent ideally expanded jet. These results support the idea that a vortex sheet model of the corresponding 2-D planar ideally expanded jet is capable of predicting the wave modes of a non-ideally expanded rectangular supersonic jet. They also suggest that these waves are involved in the feedback part of the screech mechanism; explaining why, for the simulated screeching rectangular jets, the associated oscillation mode is antisymmetric.

Scaled Demonstration of Fluid Insert Noise Reduction for Tactical Fighter Aircraft Engines

This paper summarizes a university-industry cooperative project to develop a new method of noise reduction applicable to tactical fighter aircraft engines. There is an acute need for reduction of the noise produced during takeoff in aircraft carriers. This paper describes the fluid insert noise reduction technology, also referred to as “distributed blowing.” The method involves injection of air through the divergent wall of a converging–diverging nozzle to generate fluid inserts. Substantial noise reductions in small-scale experiments have been achieved for mixing noise in the maximum noise emission direction and in broadband shock-associated noise. This paper describes the extension of the methodology to moderate-scale experiments conducted in industry. Changes to the original small-scale design for use in the industry-scale model experiments are described. The experiments were conducted in the GE Aviation Cell 41 Laboratory, and noise reductions were achieved that were very similar to those obtained in the small-scale experiments. Changes to the operating parameters produced noise reductions that in some cases exceeded comparable small-scale results. Scaling the moderate-scale experiments to a full-scale aircraft produces reductions in the A-weighted spectral peak that exceed 7 dB in the direction of maximum noise emission.

Three-Way Spectral Decompositions of High-Performance Military Aircraft Noise

High-performance military aircraft noise contains large- and fine-scale turbulent mixing noise and broadband shock-associated noise. A three-way spectral decomposition quantifies the contribution from each noise type in the sound of a tied-down F-35B aircraft on a linear ground-based array spanning 35–152 deg. This large spatial aperture allows for detailed investigation into the spatial variation in broadband shock-associated noise and fine- and large-scale turbulent mixing noise. The spectral models used in the decomposition capture the main features of the measured spectra with three exceptions: 1) that the F-35B engine noise contains multiple spectral peaks in the maximum radiation region, 2) that the nonlinear propagation increases the high-frequency spectral levels, and 3) that the low-frequency levels in the maximum radiation region are less than those predicted by the large-scale similarity spectrum. The F-35B broadband shock-associated noise has the same characteristic shape and variation in peak frequency as overexpanded, laboratory-scale jets. However, the peak level and width exhibit different trends than laboratory-scale broadband shock-associated noise and those recently reported for the F/A-18E aircraft. The strengths and limitations of current models to represent the spatial variation in the spectral content of F-35B noise can guide research efforts to more fully understand the sound radiation.

Large-Eddy Simulations Analysis of Supersonic Heated Jets with Fluid Injection for Noise Reduction

The present work uses large-eddy simulations to analyze the effectiveness of a noise reduction strategy on a military-style nozzle based on the GE F400-series engines. The nozzle has a design Mach number of 1.65 and is operated in supersonic overexpanded jet conditions. The characteristics of unheated and heated jets are presented and compared. The noise reduction strategy developed at the Pennsylvania State University is based on injectors blowing air into the diverging section of the nozzle to emulate the effect of interior corrugation. The injection can be activated during takeoff and turned off during other phases of flight so that performance is not adversely affected. The injectors have the potential to break down the shock cells into smaller and weaker structures, affecting the mechanisms that generate broadband shock-associated noise and to weaken the larger-scale turbulent structures. The overall sound pressure levels are reduced along most of the observer angles on a plane in between two injector lines. A maximum noise reduction of about 3 dB is obtained along the direction of maximum sound propagation.

Azimuthal mode analysis of broadband shock-associated noise in an under-expanded axisymmetric jet

Broadband shock-associated noise (BBSAN) is a high frequency noise generated in imperfectly expanded jets from the interaction of turbulent structures and shock-cells. This paper presents an azimuthal mode analysis of BBSAN in the jet, near-field and far-field from an unstructured large-eddy simulation of a non-screeching supersonic under-expanded jet. The studied supersonic jet is issued from a round convergent nozzle with a perfectly expanded Mach number of 1.15 and Reynolds number based on the nozzle diameter of 1.25 × 106. Aerodynamic and far-field acoustic numerical results are validated against experiments. Pressure fluctuations represented in the frequency-wavenumber domain follow the neutral waves from a vortex-sheet model of an ideally expanded jet. The far-field pressure field is decomposed in azimuthal modes based on Fourier coefficients, showing three different regions: broadband behaviour of the mixing noise for downstream angles below 50° with the first modes containing most of the energy, BBSAN with similar amplitudes for the first 4 azimuthal modes at central angles between 50° and 130°, and distinct modes at upstream angles above 130°. A decomposition in negative/positive phase-velocity waves of the jet and near-field pressure field allows the identification of these characteristic modes. The complexity of the flow is illustrated with the analysis of the root-mean-square and spectral contents of the first 4 azimuthal modes. The modes exhibit peaks at different shock-cells and radial positions as well as depicting particular radiation patterns that depend on both the mode and frequency.

Impact of coherence decay on wavepacket models for broadband shock-associated noise in supersonic jets

Motivated by the success of wavepackets in modelling the noise from subsonic and perfectly expanded supersonic jets, we apply the wavepacket model to imperfectly expanded supersonic jets. Recent studies with subsonic jets have demonstrated the importance of capturing the ‘jitter’ of wavepackets in order to correctly predict the intensity of far-field sound. Wavepacket jitter may be statistically represented using a two-point coherence function; accurate prediction of noise requires identification of this coherence function. Following the analysis of Cavalieri & Agarwal (J. Fluid Mech., vol. 748, 2014. pp. 399–415), we extend their methodology to model the acoustic sources of broadband shock-associated noise in imperfectly expanded supersonic jets using cross-spectral densities of the turbulent and shock-cell quantities. The aim is to determine the relationship between wavepacket coherence-decay and far-field broadband shock-associated noise, using the model as a vehicle to explore the flow mechanisms at work. Unlike the subsonic case where inclusion of coherence decay amplifies the sound pressure level over the whole acoustic spectrum, we find that it does not play such a critical role in determining the peak sound amplitude for shock-cell noise. When higher-order shock-cell modes are used to reconstruct the acoustic spectrum at higher frequencies, however, the inclusion of a jittering wavepacket is necessary. These results suggest that the requirement for coherence decay identified in prior broadband shock-associated noise (BBSAN) models is in reality the statistical signature of jittering wavepackets. The results from this modelling approach suggest that nonlinear jittering effects of wavepackets need to be included in dynamic models for broadband shock-associated noise.

Equivalent Shock-Associated Noise Source Reconstruction of Screeching Underexpanded Unheated Round Jets

This paper investigates the broadband shock-associated noise (BBSAN) radiated from supersonic jets at the root source level. The sources are modeled according to an acoustic analogy. The acoustic-analogy model is informed by high-spatial-resolution two-dimensional two-component particle image velocimetry (PIV) data and solutions to the Reynolds-averaged Navier–Stokes (RANS) equations for the reconstruction of the equivalent BBSAN sources. The measurements are of screeching underexpanded jets issuing from a purely converging nozzle at ideally expanded Mach numbers of 1.45 and 1.59. The jet conditions are simulated using a RANS solver with a shear-stress-transport turbulence model. The RANS scales are modeled using formulations of a two-timescale model based on the turbulence dissipation and large-eddy-convection time. The large-eddy-convection-based scale is recommended as a replacement for the standard turbulence-dissipation scale in low-order BBSAN models. The equivalent BBSAN sources are reconstructed from the PIV measurements and RANS solutions at the peak Strouhal number. The equivalent BBSAN sources extracted from the PIV and RANS data are shown to have a favorable agreement.

Broadband shock-associated noise from a high-performance military aircraft.

Broadband shock-associated noise (BBSAN) is a prominent noise component from nonideally expanded jets in the forward and sideline directions. BBSAN from laboratory-scale jets has been studied extensively, and spatial trends in BBSAN spectral peak characteristics-frequency, level, and width-have been established. These laboratory-scale trends are compared to those for BBSAN from a tied-down F-35B operated at four engine conditions. While the peak frequency varies as expected, both spatially and across engine condition, the peak level and width do not, pointing to the need for additional research into BBSAN for high-performance military aircraft.

Localization of directional noise sources from high-performance military aircraft through subarray beamforming analysis

High-performance military aircraft noise is created by multiple sound generation mechanisms that need to be understood to guide noise reduction efforts and for adequate sound field predictions. Phased-array methods can be used to produce frequency-dependent equivalent acoustic source models. The Hybrid (beamforming) method [Padois et al., J. Sound Vib. 333 (2014)] is applied to an acoustical measurement along a 71-microphone ground-based array, spanning 32 m, placed in the vicinity of a high-performance military aircraft as the engine was operated at different powers. Application of the Hybrid method to the full-array creates an overall equivalent source model that is sufficient for predicting overall field radiation but fails to separate the different noise sources. Applying the Hybrid method to subarrays separates broadband shock-associated noise from the main radiation lobes of turbulent mixing noise. Results show that the subarray-based equivalent source distributions for the different types of noise originate from overlapping source locations. Further analysis of the subarray-based equivalent noise sources using coherence and directionality from the unwrapped phase of the cross-spectral source reconstructions identifies overlapping, frequency-dependent source regions with characteristics unique to broadband shock-associated noise and turbulent mixing noise. [Work supported by an Air Force Research Laboratory SBIR.]

Effects of passive grids on pipe and orifice jet noise

The present study investigates the effect of passive grids on the acoustic characteristics of pipe and orifice jets for different Nozzle Pressure Ratios (NPRs). A detailed blow-down and directivity studies have been carried out for various emission angles. To understand the distribution of acoustic radiations with frequency, the spectral analysis is performed. Additionally, the acoustic power is estimated in order to signify the effects of grids. The presence of grids influences the noise level depending on the operating ranges of NPRs. At low NPRs, the grids enhance the overall sound pressure level; mainly due to the turbulent mixing noise. Whereas, at high NPRs, a considerable noise reduction is observed. However, grids assist to shift the noise level from low frequency to high frequency for all ranges of NPR. The eddy fragmentation by the grids at low NPR results in shifting the low frequency noise to a high frequency. In general, at high NPRs the shock associated noise [screech and broadband shock associated noise (BSAN)] is dominant over the turbulent mixing noise. The presence of grids successfully eliminate the dominant tones (screech) by disrupting the feedback loop and attenuate the BSAN by converting strong shock cells into weaker multiple shock-lets.

High order harmonics anomaly of jet screech

Imperfectly expanded supersonic jets under strong screech could generate both fundamental screech tones and multiple tones at the harmonics of the fundamental frequency. The paper compares the fundamental frequency of jets from both AR = 3 (Aspect Ratio) and AR = 4 rectangular nozzles, and conducts analysis of harmonics on Sound Pressure Level (SPL) spectrums of jet noise. The research suggests that the fundamental frequency of the first two- or three-order harmonics increases when the Nozzle Pressure Ratio (NPR) decreases, whereas the highest order harmonic decreases when the NPR decreases. Besides, the paper also observes the differences between the highest order harmonics and other harmonics that have never been reported before. Further analysis on flow field schlieren of AR = 3 nozzle indicates that the highest order harmonic is the outcome of interaction between second shock-cell and nonlinear instable wave. The revolution of these high order harmonics can provide guidance for the prevention of small-scale structure fatigue damage. Moreover, the distribution test of the noises is also carried out to verify the high order harmonics anomaly, and indicate that the jet noise spreads mainly towards downstream while screech towards upstream. In addition, the broadband shock-associated noise spreads vertical to the jet flow and exhibits the feature of directivity.

Evaluating the effectiveness of subarrays in beamforming computations of complex jet noise source environments

Conventional acoustic beamforming methods, while powerful for localizing acoustic sources, require an uncorrelated monopole assumption, depend on the input array location, and are unreliable in a complex source environment, such as jet engine noise. The complexities arise from the large, partially correlated, extended source region, the multiple types of noise sources, such as directional and omnidirectional, and partially correlated sources that violate the integral uncorrelated monopole assumption of beamforming. The complexity of these sources requires advanced beamforming methods. The aim of this research is to determine what advanced beamforming methods tell us about complex, full-scale jet noise sources. To learn about these sources, an array spanning the entire length of a jet from an F-35 aircraft is split into multiple subarrays. Application of the beamforming algorithm to a subarray in the maximum sound region localizes the directional sources present in jet noise; a subarray to the side of the engine characterizes more omnidirectional sources; and a subarray farther forward yields the approximate origin of broadband shock-associated noise. Using these advanced beamforming methods, combined with the subarray processing, opens new insights in this complex environment. [Work supported by the Air Force Research Laboratory; data courtesy of F-35 JPO.]Conventional acoustic beamforming methods, while powerful for localizing acoustic sources, require an uncorrelated monopole assumption, depend on the input array location, and are unreliable in a complex source environment, such as jet engine noise. The complexities arise from the large, partially correlated, extended source region, the multiple types of noise sources, such as directional and omnidirectional, and partially correlated sources that violate the integral uncorrelated monopole assumption of beamforming. The complexity of these sources requires advanced beamforming methods. The aim of this research is to determine what advanced beamforming methods tell us about complex, full-scale jet noise sources. To learn about these sources, an array spanning the entire length of a jet from an F-35 aircraft is split into multiple subarrays. Application of the beamforming algorithm to a subarray in the maximum sound region localizes the directional sources present in jet noise; a subarray to the side of the ...

Identification of temporal and spatial signatures of broadband shock-associated noise

Broadband shock-associated noise (BBSAN) is a particular high-frequency noise that is generated in imperfectly expanded jets. BBSAN results from the interaction of turbulent structures and the series of expansion and compression waves which appears downstream of the convergent nozzle exit of moderately under-expanded jets. This paper focuses on the impact of the pressure waves generated by BBSAN from a large eddy simulation of a non-screeching supersonic round jet in the near-field. The flow is under-expanded and is characterized by a high Reynolds number $$\mathrm{Re}_\mathrm{j} = 1.25\times 10^6$$ and a transonic Mach number $$M_\mathrm{j}=1.15$$ . It is shown that BBSAN propagates upstream outside the jet and enters the supersonic region leaving a characteristic pattern in the physical plane. This pattern, also called signature, travels upstream through the shock-cell system with a group velocity between the acoustic speed $$U_{\mathrm{c}}-a_\infty $$ and the sound speed $$a_\infty $$ in the frequency–wavenumber domain $$(U_\mathrm{c}$$ is the convective jet velocity). To investigate these characteristic patterns, the pressure signals in the jet and the near-field are decomposed into waves traveling downstream ( $$p^+$$ ) and waves traveling upstream ( $$p^-$$ ). A novel study based on a wavelet technique is finally applied on such signals in order to extract the BBSAN signatures generated by the most energetic events of the supersonic jet.

Numerical study of the flow and the near acoustic fields of an underexpanded round free jet generating two screech tones

The flow and near acoustic fields of a supersonic round free jet are explored using a compressible large eddy simulation. At the exit of a straight pipe nozzle, the jet is underexpanded, and is characterized by a Nozzle Pressure Ratio of 4.03 and a Temperature Ratio of 1. It has a fully expanded Mach number of 1.56, an exit Mach number of 1, and a Reynolds number of 6×104. Flow snapshots, mean flow fields and convection velocity in the jet shear layers are consistent with experimental data and theoretical results. Furthermore, two screech tones are found to emerge in the pressure spectrum calculated close to the nozzle. Using a Fourier decomposition of the pressure fields, the two screech tones are found to be associated with anticlockwise helical oscillation modes. Besides, the frequencies of the screech tones and the associated oscillation modes both agree with theoretical predictions and measurements. Moreover, pressure fields filtered at the screech frequencies reveal the presence of hydrodynamic-acoustic standing waves. In those waves, the regions of highest amplitude in the jet are located in the fifth and the sixth cells of the shock cell structure. The two screech tones therefore seem to be linked to two different loops established between the nozzle and the fifth and sixth shock cells, respectively. In the pressure fields, three other acoustic components, namely the low-frequency mixing noise, the high-frequency mixing noise and the broadband shock-associated noise, are noted. The directivity and frequency of the mixing noise are in line with numerical and experimental studies. A production mechanism of the mixing noise consisting of sudden intrusions of turbulent structures into the potential core is discussed. Then, the broadband shock-associated noise is studied. This noise component is due to the interactions between the turbulent structure in the shear layers and the shocks in the jet. By analyzing the near pressure fields, this noise component is found to be produced mainly in the sixth shock cell. Finally, using the size of this shock cell in the classical theoretical model of this noise component, a good agreement is found with the simulation results.

Characterization of broadband shock-associated noise from high-performance military aircraft

For nonideally expanded jets, broadband shock-associated noise (BBSAN) is a feature in the sideline and forward directions. While BBSAN has been studied fairly extensively for laboratory-scale jets, its presence and characteristics in full-scale, tactical aircraft noise need to be evaluated. Noise measurements on a tied-down F-35 provide the opportunity to characterize full-scale BBSAN using a linear ground array that spanned a large angular aperture: 35–152 degrees relative to the front of the aircraft. The main questions are whether the full-scale BBSAN shares the same characteristics as those observed in laboratory-scale BBSAN and if current models capture the features of full-scale BBSAN. The variation in the spectral shape, peak frequency, and peak level of full-scale BBSAN across angle for different engine powers is explored and compared to prior laboratory studies. Comparisons are also made with models for BBSAN based on stochastic theory ([Tam et al., J. Sound Vib. 140, 55–71 (1990)]) and the simplified model used in Kuo et al. [AIAA Paper 2011–1032 (2011)] for lab-scale BBSAN. Frequency-dependent convective speed estimates obtained from the current BBSAN models are compared to estimates based on directivity. [Work supported by the Office of Naval Research and the F-35 JPO.]

Spectral decomposition of turbulent mixing and broadband shock-associated noise from a high-performance military aircraft

Sound from high-performance military aircraft originates primarily from the turbulent mixing noise, but at smaller inlet angles, broadband shock-associated noise (BBSAN) is present. The similarity spectra of the two components of turbulent mixing noise developed by Tam et al. [AIAA Paper 96–1716 (1996)] represent noise associated with fine and large-scale turbulent structures and provide reasonable fits for ideally expanded, supersonic jet noise. For non-ideally expanded jet flow, BBSAN contributions to the spectral shape need to be included in spectral decompositions in the sideline and forward directions. A model proposed by Tam et al. [J. Sound Vib. 140, 55–71 (1990)] and later simplified by Kuo et al. [AIAA Paper 2011–1032 (2011)] provides a spectral function that models the BBSAN spectral shape. The ability of the BBSAN and similarity spectra shapes to account for the measured spectra is evaluated for ground-based microphones that covered a spatial aperture from 35 to 152 degrees. Spectral decompositions at low and high engine powers are compared. Using turbulent mixing noise similarity spectra decomposition in conjunction with BBSAN empirical fits, a better equivalent source model can be developed. [Work supported by the Office of Naval Research and the F-35 JPO. Distribution A: Approved for public release; distribution unlimited.]