Identifying the dynamics underlying the large-scale and fine-scale jetnoise similarity spectra

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1 14th AIAA/CEAS Aeroacoustics Conference (29th AIAA Aeroacoustics Conference) 5-7 May 2008, Vancouver, British Columbia Canada AIAA Identifying the dynamics underlying the large-scale and fine-scale jetnoise similarity spectra F. Kerhervé, A. Guitton, P. Jordan, J. Delville, V. Fortuné, Y. Gervais and C. Tinney This work concerns the development of a diagnostic tool for the analysis of jet noise source mechanisms. The technique comprises three steps: (1) synchronous measurement of pressure and velocity fluctuations (pressure measured in the irrotational near- and farfield regions; velocity measured in the rotational region of the flow); (2) filtering of the near pressure field into radiating and non-radiating components; (3) reconstruction of the velocity fluctuations which are linearly associated with the radiating component of the near pressure field. The technique is here applied to an isothermal, co-axial jet (primary Mach=0.5; secondary Mach=0.25; Re=1,000,000), and we perform a further filtering of the near pressure field so as to extract the space-time structure of the field which radiates to 30 degrees and to 90 degrees (finally, the flow dynamics associated with each of these components is to be estimated). Preliminary results show that: (1) the radiating source activity does not occur in the regions of peak turbulence (in agreement with previous numerical results of Freund 4 ); and, (2) the shape of the radiating sound spectrum looks to be made up of three main components: a coherent low-frequency component associated with the dynamics at the end of the potential core; a coherent high-frequency component associated with the near-nozzle dynamics; and a more broadband high frequency component which may be associated with fine-grained turbulence. The fine-grained component appears to be an order of magnitude less energetic than the two coherent components, and the flatness of the 90 spectrum appears to be a result of a superposition of the highfrequency near-nozzle and the low-frequency potential-core dynamics. I. Introduction The noise radiated by a turbulent jet is generated by the turbulence of the flow. This is probably the last concrete, unambiguous statement that it is possible to make regarding the sources of jet-noise. In effect, because there is no universally-agreed-upon theoretical source description, there is no universally-agreedupon source metric. This places the engineer in a very difficult position when it comes to analysing noisy turbulent jets: how should one attempt to read turbulence data (experimental or numerical) in terms of the sound-producing flow dynamics? It is this difficulty which has motivated the present work: we are developing a diagnostic tool which allows a more pertinent analysis of jetnoise data, be this experimental or numerical. The analysis methodology goes as follows. Pressure and velocity signals are acquired simultaneously. The near pressure field which is sampled on a 45-point axial grid extending from the exit-plane to 10 diameters downstream is decomposed, by means of a frequency-wavenumber filter, into radiating and non-radiating components. By correlating the radiating component of the pressure field with velocity measurements performed at 312 points in the flow, a correlation matrix (dimension 312x45) is obtained which relates the space-time structure of the radiating pressure field to the turbulent velocity fluctuations at each of the in-flow measurement points. Spectral Linear Stochastic Estimation (see 9 for details) can then be used to reconstruct velocity signatures which are linearly associated with this radiating space-time structure. A second objective of the work is to understand the flow dynamics which underlie the polar dependence of jet noise spectra. Attempts to explain this polar dependence abound in the literature: inherently directive convected quadrupoles; randomly-oriented convected quadrupoles; convective-amplification; linear Laboratoire d Etudes Aérodynamiques, CNRS UMR 6609, Université de Poitiers, ENSMA, France. University of Florida, FL , U.S.A. 1 of 11 Copyright 2008 by P Jordan. Published by the American Institute American of Aeronautics Instituteand of Astronautics, AeronauticsInc., andwith Astronautics permission.

2 (a) (b) Figure 1. (a) Coaxial jet nozzle and instrumentation, (b) -top- Longitudinal mean and -bottom- RMS velocity profiles with ( ) location of the near-field microphone array. shear-noise and quadratic self-noise ; mean-flow refraction; coherent structures; superdirective wavepackets; vortex-pairing; non-linear wave interactions; vortex eigenoscillations...the list goes on. More recently, Tam et al 13 have argued that the source mechanisms can be reduced to two distinct components, related to coherent-structures and fine-grained turbulence, and which are believed to dominate radiation to low and high polar angles respectively (angle measured with respect to the downstream flow-axis). This empirical observation is based on two similarity spectra, obtained initially for supersonic flows, but which have been 12, 16 found to fit subsonic jet data quite well, particularly at high subsonic Mach number. We here apply the said diagnostic tool with a view to shedding some light on the flow characteristics responsible for these trends: a wavenumber-frequency bandpass filter is used to isolate components of the near pressure field which radiate to 30 and 90 degrees, and the same analysis methodology is currently being implemented to reconstruct the velocity signatures which are associated with radiation in each of these directions. II. Experimental set-up A. Flow configuration The flow studied is a co-planar coaxial jet. The experiment was performed in an anechoic jetnoise facility at the Centre d Études Aérodynamiques et Thermiques in Poitiers, France. The co-planar nozzle has primary and secondary nozzle diameters of D p = 55mm and D s = 100mm respectively. The Mach number of the primary flow at the exit is 0.5 while the velocity ratio γ, secondary-to-primary, is 0.5. Both flows are at ambient temperature. The boundary-layers are tripped using carborandum located one and half external diameters upstream of the exit plane. B. Measurement setup The pressure field (near- and far-field regions) and the flow field were surveyed, synchronously, using a total of 64 1/4-inch microphones and 3-component Laser Doppler Velocimetry (LDV). The nearfield pressure measurements presented in this paper were performed using a linear array of 45 microphones, which was inclined at 9 in order to follow the spreading jet. This setup is shown in figure 1(a), and figure 1(b) shows the array position relative to the mean and turbulence profiles of the flow. LDV measurements both with and without the nearfield array were performed; the superposition of the red and black profiles in figure 1(b) shows that the array does not disturb the flow. Similar tests for farfield contamination were performed, with and without the nearfield array; the array was not found to modify the shape or level of the farfield spectra over the frequency range considered. Pressure measurements in the acoustic far field were performed using polar a and azimuthal b arcs of microphones. The microphones on both arrays were located 24D s from an origin taken on the jet centera angle measured in a plane containing the flow axis, where 0 corresponds to the downstream flow direction b angle measured in a plane normal to the flow axis 2 of 11

3 (a) (b) Figure 2. (a) Far-field pressure spectra at ( ) 30, ( ) 60 and ( ) 90. (Dashed line) Fine-scale similarity spectrum model of Tam et al. 13 (b) Far-field presure signals at various observation angles from (top) 30 to (bottom) 100. line, one secondary jet diameter from the exit plane. For both surveys, near- and far-field measurements were performed at a sample-rate of 25kHz. Spectral- and correlation-analysis involving the LDV data was implemented using the sample-and-hold reconstruction scheme of Simon & Fitzpatrick. 11 III. Far-Field pressure Far-field spectra at the polar angles 30, 60 and 90 (measured from the jet axis) are presented in figure 2(a). Comparisons with the fine-scale similarity (FSS) spectrum of Tam et al 13 are also shown; good agreement is found. The implication is that in this flow, the source mechanisms are dominated by finegrained turbulence. Sample time-histories of the farfield pressure signals are shown in figure 2(b). While the 30 spectrum fits the FSS shape, it is clear both from the spectrum and the sample time signatures that the sound field radiated to 30 is characterised by quasi-periodic events which look more like the signature of a coherent sound production mechanism. We will investigate this using the analysis tool described in the introduction. The 90 spectrum shows some evidence of interference; this is a result of the proximity of these microphones to the wall of the anechoic chamber. The discrepancy between the measured spectra and the FSS shape at high frequency looks at first like it might be associated with facility noise; however, we will demonstrate that this high-frequency energy is in fact being produced by the jet turbulence. IV. Near-field pressure A. Composition of nearfield Measurements effected in the irrotational nearfield of a subsonic jet are known to provide valuable information regarding the low-order dynamics of the flow. The nearfield is found to be strongly driven by the linear pressure production mechanisms, and it has been demonstrated how the signatures registered in the nearfield can be interpreted in terms of the more coherent quasi-deterministic components of the turbulence. Previous work has also established that, in addition to such hydrodynamic contributions, the nearfield also comprises an acoustic component related to progressive pressure fluctuations destined to reach the farfield. 10 B. Wavy-wall source-mechanism signature It has been shown by Guitton et al 7 that interference between convective-reactive and propagating components of the near pressure field of a wavy-wall source-mechanism will lead to localised cancellation of the pressure fluctuations. Figure 3 shows this phenomenon for a model problem comprising a wavy volume-source in a potential-flow. This interference leads to nulls in the space-frequency coherence patterns measured by a line-array in the nearfield. Such signatures have been found in the nearfield of single-stream jets over an 3 of 11

4 Figure 3. Nearfield of a wavy-volume source. Shown is the acoustic potential, φ, solution of 2 φ = q with q(x, r, θ, t) = exp[ (x x 0) 2 λ 2 (r r 0) 2 x λ 2 ] cos(2π(k xx U ck xt)) cos mθ, where k x and U c are the axial wavenumber and r convection velocity of the wavepacket, λ x and λ y define its axial and radial extent, and m the azimuthal mode number, which is taken here to be 0. Convective (reactive) and propagating components are manifest in the different wavelengths λ propagative and λ reactive. Time-histories from the three coloured dots are shown in the bottom left-hand corner. Interference between the convective (blue) and propagative (pink) components lead to a node where fluctuations are entirely eliminated (black dots). This mechanism is postulated as the cause of the nulls which appear in the nearfield space-frequency coherence (figure4) axial extent of 10D and for Mach and Reynolds numbers as high as 0.6 and , respectively. 5, 6 A more complete presentation of the phenomenon is given in a companion paper. 8 Figure 4 shows space-frequency coherence plots for the co-axial jet studied in this work, at 2D s and 4D s (D s denotes the secondary nozzle exit diamater). The nulls which correspond to the wavy-wall sourcemechanism are observed; moreover, we see two pairs at 2D s (shown by black and red cirlces in figure 4). The black pair correspond to the inner shear-layer (between primary and secondary flows), the red pair to (a) (b) Figure 4. Pressure coherence along the line array as a function of the Strouhal number for reference microphones at (a) x/d s =2and (b) x/d s =4. Solid and dashed lines correspond to equal-energy and anti-phase criteria which when satisfied (where the lines intersect) will lead to interference nodes as shown in figure 3. In figure (a) the black lines show these criteria adapted for the inner shear layer, the red lines are adapted for the outer shear-layer. In figure (b) a the black lines show the criteria adapted for the characteristics of the new mixing-region which exists at x/d s =4(see figure 1(b)) 4 of 11

5 the outer shear-layer (between the secondary flow and the ambient fluid). This result indicates that both shear-layers are generating sound via a linear quasi-irrotational source mechanism. It is remarkable to see that the source signature of the inner shear-layer is present in the near-field. A single pair of nulls is seen at 4D s, at which point the two shear-layers have merged to form a single mixing-zone (see mean and turbulence profiles in figure 1(b)); this indicates that this region of the flow also comprises such a source mechanism. It seems clear that this source mechanism does not amount to sound production by fine-scaled turbulence. C. Acoustic-Hydrodynamic filtering There are two advantages in performing measurements in the near pressure field of a sound-producing jet: (1) the signature of both cause and effect are present; and, (2) a better local understanding can be obtained regarding the acoustic energy which radiates from different regions of the flow. Furthermore, by using a line array which is extended in the axial direction it is possible to identify space-time signatures of both the propagating and non-propagating components. In order to separately study the convective and propagative signatures in the nearfield the line array data is Fourier transformed from (x, t) to (k x,f). Frequency-wavenumber bandpass filtering can then be used to isolate the convective and propagative spectral signatures, and by inverse Fourier transform the corresponding space-time structures can be retrieved. The frequency-wavenumber spectrum, shown in figure 5, comprises three lobes, corresponding to the various mixing-regions and the radiated acoustic field. Energy corresponding to the mixing-regions are concentrated around the lines ω = k x û, where û denotes characteristic subsonic phase-speeds. The red line, ω = k x c o, identifies the demarcation between propagating and non-propagating disturbances; all spectral components below this line are associated with propagating pressure fluctuations. Separation of the pressure into its convective-hydrodynamic and propagating-acoustic components can be achieved by inverse transformation after removal of either the hydrodynamic or the acoustic spectral contents. A sample result is shown in figure 6, where space-time patterns of the measured and filtered components are plotted. The propagating part (figure 6(c)) shows some interesting features: (1) an axially coherent, relatively periodic component; (2) a less coherent, high-frequency component. Figure 5. Contours of the wavenumber-frequency spectrum of the near pressure field (levels in db, with arbirtrary reference of 1 Pa.s.m): The different lines identify signatures propagating at different angles to the line array. The red lines show the demarcation between hydrodynamic and acoustic spectral sectors; the dotted white lines demarcate the spectral sectors corresponding to propagation in the segments 9 < θ < 60 and 60 < θ < of 11

6 (a) (b) (c) (d) Figure 6. Sample space-time plot of nearfield pressure signatures: (a) measurement, (b) convectivehydrodynamic, (c) propagative-acoustic, (d) error resulting from filtering. Colours indicate Pressure level in mpa. V. Relating radiation-signatures to the turbulence A. Spectral Linear Stochastic Estimation We use Spectral Linear Stochastic Estimation to estimate the space-time structure of the flow dynamics which were implicated in the production of the various radiation signatures. For a complete description of this technique the reader can see Ewing & Citriniti, 3 Cater et al. 2 or Tinney et al. 14 ; we here recall the main result. The j-th turbulence velocity component estimate ˆũ j at flow-location x can be written as a linear combination of the pressure fluctuations p i along the line array: ˆũ j(x, ω) = i=m i=1 B ij (x, ω) p i (ω), (1) where M denotes the number of microphones used to perform the estimate and B ij contains the frequencydependent estimation coefficients which relate the velocity fluctuation to each of the microphones on the line array. The estimation coefficients, B ij, are obtained by solving the linear system of equations, where denotes complex conjugate. B. Radiating- source dynamics B ij (x, ω) = [< p i (ω) p k(ω) >] 1 < ũ j (x, ω) p k (ω) > (2) The pressure data is used to reconstruct velocity signals at the 312 measurement points, and a cubic-spline interpolation is then used to increase the grid density to 968 points this interpolation is necessary for the estimation of instantaneous flow topologies, which is the final objective of this work. In figure 7 measured rms levels are compared with levels computed by SLSE using the convective and propagative nearfield footprints. The peak contours of the measured data are superposed on the reconstructed fields in order that differences can be more easily appreciated. These differences illustrate how analysis-metrics based on peak velocity fluctuations are inappropriate. The peak radiating source activity (figure 7(e) & (f)) is both closer to the jet axis, and farther downstream of the end of the potential core than the peak turbulence levels (figure 8); and two other hot-spots are identified which were not obvious from the LDV measurements, one in the inner shear-layer at x/d s 1.5, and the other in the intermediate mixing region at x/d s 4, where the two initial shear-layers come together it is at these points, incidently, that the wavy-wall signatures are most distinct (see figure 4). The difference between the peak radiating source activity and the peak turbulence activity is reminiscent of that identified by Freund 4 (using data obtained by Direct Numerical 6 of 11

7 (a) (b) (c) (d) (e) (f) Figure 7. Turbulence rms levels (top row), compared with non-radiating and radiating source rms levels (middle and bottom rows respectively). Left column: u ; right column: v. The black contours correspond to the measured field; these are superposed on all fields so as to highlight differences between turbulence and source activity. (i) (a) (b) (c) (d) (e) Figure 8. Solid lines: longitudinal fluctuations; dashed lines: radial fluctuations; Black: measurement; blue: radiating source fluctuations; red: non-radiating source fluctuations. Sub-figures (a)-(e) correspond to the hot-spots identified by the red squares in figure 7(e) and (f); subfigure(i) shows a point closer to the jet exit, in the inner shear-layer. 7 of 11

8 Simulation of a low Reynolds number jet) between the radiating components of the Lighthill source term on one hand, and the turbulence and total-source levels on the other (see figure 11 in the said paper). Figure 8 shows the measured u and v power spectral densities at the said hot-spots, compared with those of the radiating and non-radiating source activity. The spectral slope of the radiating source dynamics follows the measured spectral slope more closely than does the non-radiating signature. This is indicative of the fact that the non-radiating hydrodynamic pressure disturbances remain trapped in the flow; their domain of influence is proportional to the turbulence scales which produced them, and so higher-frequency, small-scale non-radiating dynamics do not register in the nearfield. On the other hand, propagating disturbances generated by all scales register on the line array, and so a fuller radiating source -spectrum results. Another point worth noting is that the peak which is manifest in the radial velocity fluctuations of both the inner and outer initial shear-layers (this is the signature of coherent Kelvin-Helmholtz dynamics, which are closely associated with the wavy-volume source discussed earlier) shows up in the radial component of the radiating source spectrum (figure 8(i), (a) and (b)), indicating that these near-nozzle coherent dynamics are important in the generation of propagating pressure fluctuations. In figure 8(i), (a) and (b) this additional hump in the radiating source spectrum leads to a spectral shape which looks more broadband; it seems clear however that this shape has little to do with fine-grained turbulence, being associated rather with high-frequency, coherent Kelvin-Helmholtz dynamics in the near-nozzle region. Can the flatness of the 90 farfield spectrum be explained in the same way? This question is addressed in the next section. VI. Radiation as a function of emission angle A second filtering operation can now be performed with a view to isolating the space-time structure of the pressure field radiating in different directions. In figure 5 lines were included which demarcate the frequency-wavenumber content of the pressure field radiating in two polar sectors. Using bandpass filters to isolate these regions of the spectrum, the space-time character of the field radiating in each of the 60-degree segments can be retrieved by inverse Fourier transform. The nearfield spectra for different emission angles are shown in figure 10, as a function of axial position on the line array. The acoustic farfield spectra are also shown in figure 10 for comparison. The spectraltruncation of the data is due to the combined effect of the limited spatial discretisation (which leads to a coarse wavenumber grid) and the k ω demarcations which isolate the spectral sectors of interest. This effect can be seen in figure 9: for radiation in the sector centered on 30 we do not have any data below St Ds 1.3, while for the sector centered on 90 there is no data below St Ds 0.8 (see zoom in subfigures (b) and (c)); when considering the entire acoustic portion of the spectrum we are limited to frequencies in the range St Ds > 0.5. Extrapolation schemes are currently being evaluated to overcome this limitation; however, this is proving to be quite delicate, as a very small amount of hydrodynamic energy suffices to completely contaminate the acoustic spectral regime, and extrapolations applied without care lead to the entrainment of hydrodynamic energy into the acoustic part of the spectrum. We here see the limitation of the experiment. For numerical applications this issue will be less restrictive; and of course, larger jets and smaller microphones can also help alleviate the difficulty. The most interesting observation which can be made from figure 10 is that the spectra for radiation in (a) (b) (c) Figure 9. (a) Frequency-wavenumber spectrum; (b) spectral content associated with radiation in sector 60 < θ< 120; (c) spectral content associated with radiation in sector 0 < θ < 60 8 of 11

9 (a) x/ds=0.62 (b) x/ds=1 (c) x/ds=3 (d) x/ds=4 (g) x/ds=6 (h) x/ds=8 Figure 10. Near-field pressure spectra filtered to extract the spectral character of radiation in two 60 sectors; black: measurement; red: total acoustic signature; green: radiation in sector 60 < θ < 120; blue: radiation in sector 0 < θ < 60. the sectors centered on 30 and 90 have very similar shapes up to a Strouhal number of about St Ds 4 (this shape, indicated by the dotted line CSS PC, has a steep slope characteristic of the LSS shape). Above this frequency the spectral shape of the field radiated in the 90 sector differs considerably from the 30 shape. For positions downstream of x/d s = 3, this additional high-frequency energy may be related to fine-grained sound emission (indicated by the curve F SS G ); however, as we have already seen, the more pronounced peak in the near-nozzle region has been associated with the coherent flow dynamics of the inner 9 of 11

10 shear-layer (compare with figure 8(i) and (a)) c. Furthermore, the high-frequency level in the near-nozzle region is of the order of 72dB (see black dashed line in figure 10(a)), compared with levels of the order of 60dB at locations downstream of x/d s > 3: the high-frequency contribution from the coherent near-nozzle flow dynamics are thus an order of magnitude greater than the fine-grained turbulence contribution, if we can interpret the downstream sideline radiation signatures in this way. This preliminary analysis can be summed up by three spectral shapes indicated by the dashed lines in figure 10, and which we have denoted CSS PC, CSS NN and F SS G, where CSS and F SS stand for Coherent-Structure-Spectrum and F ine-scale-spectrum, respectively, and the subscripts PC, NN and G stand for P otential-core, N ear-n ozzle and Global. The next phase of this work will involve reconstructing the velocity fields (rms distributions, spectra and instantaneous topologies) associated with these different radiation signatures. It should thus be possible to strengthen the arguments presented above regarding the flow dynamics associated with the polar dependence of jet noise spectra. VII. Conclusion An analysis tool for understanding the flow dynamics implicated in the generation of jet noise has been presented. The technique is based on synchronous measurement of pressure (in the irrotational nearfield) and velocity (in the rotational region). Nearfield pressure signatures are decomposed into propagating and non-propagating components, the former being further split as a function of emission angle. Each of the signatures is then used to filter the velocity measurements (using Spectral Linear Stochastic Estimation) in order to identify the associated flow dynamics. Results are presented for a co-axial jet. The preliminary analysis presented in this paper leads to the following observations. The regions of peak radiating source activity do not coincide with the regions of maximum turbulent kinetic energy (this result is in agreement with that of Freund 4 ). Four regions of elevated, radiating source -activity are identified: two associated with the inner and outer initial shear-layers; a third associated with the region downstream of the secondary annular potential-flow region; and a fourth downstream of the end of the primary potential core. Analysis of the radiating-source activity and the space-time structure of the sound field radiating in sectors centered on 30 and 90 shows that the radiated field comprises three dominant components: one associated with coherent flow-dynamics in the near-nozzle region, one associated with the dynamics downstream of the end of the potential core, and a third which may be associated with fine-grained turbulence; the latter appears to be an order of magnitude weaker than the coherent source components. Acknowledgments The experiments described in this paper were partially funded by the EU program CoJeN (AST3-CT ). The authors also gratefully acknowledge the Agence Nationale de la Recherche (ANR-05- BLAN program) for financial support. References 1 Adrian RJ (1977), On the role of conditional averages in turbulence theory, 4th Biennal Symp Turbulence Liquids 2 Cater,J., Mathews,M., Gallagher,M. & Fitzpatrick,J.A. (2004) Source Identification Models for Turbulent Boundary Layer Excitation Proc. Int. Conf on Flow Induced Vibrations (eds. De Langre & Axisa), pp , Ewing D, Citriniti J (1999), Examination of a LSE/POD complementary technique using single and multi-time information in the axisymmetric shear layer, Sorensen, Hopfinger, Aubry (eds), Proc. IUTAM Symp on Simulation and Identification of Organised Structures in flows, Denmark, May 1997, pp Freund JB (2001), Noise sources in a low-reynolds-number turbulent jet at Mach 0.9, J. Fluid Mech., Vol. 438, pp Guitton A, Jordan P, Delville J (2007), Interpreting pressure interference-patterns in the entrainment region of a subsonic jet, West-East High Speed Flow Field Conf., 6 Guitton A, Jordan P, Laurendeau E, Delville J (2007), Velocity dependence of the near pressure field of subsonic jets: understanding the associated source mechanisms, AIAA Paper c The reason that the high-frequency peaks in figure 10(a) and (b) do not coincide more exactly with those in figure 8(a) and (b) is because the latter are estimated using the entire line array, whereas the former signatures are observed more locally. The estimation technique is currently being re-applied using different sub-sets of the line array microphone-ensemble, in order to more precisely identify the flow dynamics involved, for example, in these near-nozzle radiation patterns. 10 of 11

11 7 Guitton G, Jordan P, Delville J, (2008), The source mechanism associated with coherent structures in subsonic jets, In review for Int. Jnl. Aeroacoustics 8 Guitton A, Kerhervé F, Jordan P, Delville D (2008) AIAA th AIAA/CEAS Aeroacoustics conference, Vancouver, Canada. 9 Tinney C, Coiffet F, Delville J, Glauser M, Jordan P, Hall A (2006) Spectral Linear Stochastic Estimation, Exp in Fluids, Vol 41(5): Tinney C, Jordan P (2008), The near-field pressure surrounding co-axial subsonic jets, J. Fluid Mechanics, In press for JFM 11 Simon L, Fitzpatrick J (2004), An improved sample-and-hold reconstruction procedure for estimation of power spectra from LDA data, Exp in Fluids, Vol. 37, pp Tam CKW, Zaman KBMQ (2000), Subsonic jet noise from non-axisymmetric and tabbed nozzles, AIAA Journal, Vol. 38, pp Tam CKW, Golebiowski M, Seiner M (1996), On the two components of turbulent mixing noise from supersonic jets, AIAA Paper Tinney CE, Coiffet F, Delville J, Hall MA, Jordan P, Glauser MN (2007), On spectral linear stochastic estimation, Exp. in FLuids, Vol. 41(5), pp Tinney CE, Jordan P, Hall AM, Delville J, Glauser MN (2007), A time-resolved estimate of the turbulence and sound source mechanisms in a subsonic jet flow, J. Of Turbulence, Vol. 8(7), pp Viswanathan K (2007), Investigation of the sources of jet noise, AIAA Paper of 11