PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

SonicBAT: Some highlights and subsequent developments
Victor W. SPARROW1; Trevor A. STOUT1; Kevin A. BRADLEY2; Christopher M. HOBBS2
1

Pennsylvania State University, United States
2

KBR, United States

ABSTRACTThe Sonic Booms in Atmospheric Turbulence (SonicBAT) project concluded in 2018. The overall goal of
SonicBAT was to develop tools to predict the influence of atmospheric turbulence on shaped sonic booms
for newly proposed low-boom supersonic passenger aircraft. There was a substantial experimental
component to obtain statistically-useful datasets of recorded sonic booms in both dry and humid
environments. The project was carried out by a large team, and the authors of this paper are a small subset of
the individuals involved. The purpose of this presentation is to highlight some of the main findings ofSonicBAT and to provide pointers to the primary technical report and other publications that are now
becoming available, both from SonicBAT and from subsequent findings. Overall, SonicBAT was successful
in developing multiple ways of predicting the influence of atmospheric turbulence on the propagation ofarbitrarily shaped sonic boom waveforms as they propagate through the earth’s planetary boundary layer.
The influence of turbulence is profound for N-wave sonic booms but is reduced for low-boom sonic boom
signatures.
Keywords: Sonic Boom, Turbulence, Aircraft

1. INTRODUCTION
During the 1960’s and early 1970’s there were a number of theories attempting to explain why
sonic boom signatures became distorted during their passage to the ground. It was observed that the
distortion of the spiking and rounding of N-wave sonic booms would occur most times of the day withthe exception of early in the morning, sometimes (1). A theory of Pierce and Maglieri (2) was
eventually accepted and built upon by others, identifying that atmospheric turbulence in the planetary
boundary layer was responsible for distorting the N-wave sonic booms. However, in those earlyyears, it was not possible to recreate the sonic boom distortion with a fidelity such that one could
know the statistical occurrence of the spiking and rounding. It was also not possible to know whether
non-N-wave signatures would be similarly distorted, and this point was concerning to both NASA andairframers interested in developing low-boom supersonic aircraft that might be quiet enough to be
acceptable to the public.
The SonicBAT project, standing for SONIC Booms in Atmospheric Turbulence, began as aproposal from Wyle Laboratories, Inc. (now KBR) and The Pennsylvania State University (Penn State)
to NASA through their NASA Research Announcements (NRA) solicitation in 2014. Penn State andWyle had been talking with NASA for several years prior to 2014 to request that a large-scale studyof atmospheric turbulence effects on sonic booms be initiated. As the joint proposal was selected forfunding, the size of the effort became clear: there would be multiple prediction models investigatedand validating those models would require field measurement campaigns in widely varying
atmospheric conditions. It would also require NASA to deploy aircraft and sonic boom measurement
equipment at remote locations and make direct measurements of atmospheric turbulence and othermeteorological parameters almost simultaneously with making microphone measurements. The
other project partners grew to include Boeing, Eagle Aeronautics, Lockheed Martin, Gulfstream
1

1592

vws1@psu.edu

Aerospace Corporation, Technical & Business Systems, and the Laboratory of Fluid Mechanics andAcoustics at Ecole Centrale de Lyon. This paper will focus primarily on the work of Penn State andWyle working with NASA. The project was technically challenging and stretched everyone involved.
Other than the most recent developments, most of the material regarding SonicBAT will beavailable later in 2019 in a NASA Contractor Report (CR), and that report will give much greater
detail and specificity in the descriptions (3). The remainder of this summary paper is arranged asfollows: The next section briefly describes the field measurements of conventional N-wave sonicbooms used for validating the prediction methods described in Section 3. Section 4 describes theprimary results coming out of the SonicBAT. Section 5 extends those results beyond SonicBAT to
the work reported by Stout in his Ph.D. thesis (4). Section 6 provides additional links to the literature
coming out of SonicBAT in the near future for those wanting to know more, and Section 7 concludes
this paper.

2. FIELD MEASUREMENTS
2.1 Overall Considerations
A distinguishing feature of the SonicBAT field measurements was the effort undertaken to carefully
characterize the atmosphere and atmospheric turbulence at the same time the microphone recordings
were acquired. To the authors’ knowledge, this is the first time sonic boom tests were conductedwith such elaborate measurements of the atmosphere. And as will be explained, those measurements
were critical for the success of SonicBAT.
In the original planning for SonicBAT it was well understood that the developed prediction models
would need to work well anywhere in the continental U.S., if one wanted to consider overland civil
supersonic flight. Both dry and humid conditions would need to be included, as it was understood in
the 1990s that humid conditions would lead to louder sonic booms, due to decreases in the sonic boom
rise time. After a detailed survey of possible locations, the dry conditions at NASA’s Armstrong
Flight Research Center and the humid conditions at NASA’s Kennedy Space Center were selected forthe field tests. Hence one test was for low-humidity extreme and the other for high.
Another important aspect of the field measurements was the attempt to minimize, for most of theaircraft flight passes, any variation in course, altitude or Mach number between the flights. In
SonicBAT the emphasis was on obtaining a large body of sonic boom measurements where the primary
influence on the microphone recordings was from variations in the atmosphere. The philosophy was
to keep all other flight parameters as unchanged as possible, so the statistical variations in received
levels would be due to the atmosphere, not to other changes in experimental conditions. Since future
civilian supersonic aircraft are envisioned to fly overland at Mach numbers on the order of 1.6, thetests were conducted at the highest Mach numbers possible given the aircraft available and theprevailing atmospheric conditions. At the two measurement sites the test Mach numbers were usuallyaround M=1.39 at NASA’s Armstrong Flight Research Center and around M=1.35 at NASA’s Kennedy
Space Center. The aircraft used for both tests was a McDonnell Douglas F/A-18 Hornet (F-18). The
F-18 altitude was between 10.4 to 10.5 km (34,000 to 35,000 feet) msl for both tests.
An additional notable aspect of SonicBAT is that most of the data analysis in the project employedmodern loudness metrics, such as Steven’s Mark VII Perceived Level (PL). This is important because
subjective tests have shown that human hearing does not correlate loudness with maximum pressurevery well (5), and in the older sonic boom literature only maximum pressure values are reported. PL
is a much better metric for assessing loudness of sonic booms.
2.2 Aircraft Deployed and Meteorological Measurements
For the flight tests NASA utilized F-18 jet aircraft to create the sonic booms, and they also flew a
TG-14 motorized sailplane with a microphone probe mounted under and forward of the wingtip. The
TG-14 was flown on a trajectory so that it would be in between the supersonic F-18 and the groundmicrophone array, and it would be well-positioned to capture the sonic boom signature before it
entered the planetary boundary layer. The TG-14 pilot was instructed to fly just above the boundary
layer, staying out of the rough air created by the boundary layer cap. To deploy these aircraft assets,
including the pilots, aircraft, fuel, maintenance crew, ground control engineers, and other required
staffing and supplies was an enormous undertaking by NASA.
In addition to the usual weather balloon launches to get atmospheric profiles, NASA obtained andbrought to each of the field tests ultrasonic anemometers and a mini-SODAR. The purpose of the1593

ultrasonic anemometers was to directly characterize the structure parameters of the turbulence, andthey were very effective for this purpose. In addition, a measurement of the atmosphere with a miniSODAR at each site allowed for a better picture of the atmosphere above the microphone arrays,
giving information such as the 3-D winds and the height of the atmospheric boundary layer,
confirming the data from the weather balloons. For the more humid atmosphere at Kennedy Space
Center, a humidity flux sensor was also acquired and utilized. This allowed for an adjustment to thedry structure parameter values due to the humidity that were not necessary in the dry desert
environment at Armstrong Flight Research Center.
2.3 Measurements at NASA’s Armstrong Flight Research Center
NASA’s Armstrong Flight Research Center (AFRC) is the base for NASA’s aircraft research, and
it is located in the Mojave Desert, within the boundaries of Edwards Air Force Base, north of Palmdale,CA, itself north of Los Angeles, CA. Supersonic flights for SonicBAT were conducted during July
2016, and most of the days were cloudless. There were three microphone arrays. The details of theother arrays are available in the Contractor Report, but the primary array was linear, with 16
microphones spaced approximately every 30.5 m (100 ft), along the flight direction. All microphones
were ½” diameter infrasonic devices placed on groundboards. All data were acquired using 24-bit
A/D at 51200 samples/s. The TG-14 data were acquired at the higher sample rate of 65,535 samples/s.
The TG-14 was in proper position for 60 of the 69 supersonic flight passes made by the F-18. It wasdetermined that 96 percent of the 2059 signatures recorded across all microphone arrays were affectedby atmospheric turbulence.
2.4 Measurements at NASA’s Kennedy Space CenterNASA AFRC deployed their assets to NASA’s Kennedy Space Center (KSC) during August 2017.
KSC is located adjacent to the Atlantic Ocean on Florida’s East coast. A primary consideration wasto eliminate, as much as possible, any impact of supersonic testing activities on the residents of nearby
Titusville, FL affectionately known to the planning and measurement team as the “wall of humanity.”
There was much effort placed into reducing to near zero any members of the public hearing sonicbooms, and this was primarily accomplished through careful flight planning by NASA.
The majority of the instrumentation at KSC was very similar to the instrumentation used in the
AFRC tests, with the addition at KSC of the humidity flux sensor mentioned in Section 2.2. One
major difference at KSC, however, was that the weather conditions included clouds and occasionalrain showers and thunderstorms. This required multiple postponements and some cancellation ofplanned flights. Further the ground microphone team needed to run and cover up microphones toprotect them from rain on multiple occasions on very short notice. Some microphones weresusceptible to fine sand being blown into their active areas, making them inoperable. For the KSC
test the TG-14 was in proper position for 35 of 56 passes of the F-18 aircraft. Approximately 1883
signatures were obtained, and 95% of those were affected by turbulence. As predicted, the morehumid environment of KSC led to shorter rise times and many “crackier” booms heard by the fieldtechnicians. However, some booms were substantially softened, and these may be booms that had
passed through thick cloud layers. Another difference from AFRC is that there was often a sea breeze
occurring at KSC, affecting the atmospheric boundary layer, and this is described more in theContractor Report.

3. PREDICTION OF SONIC BOOM PROPAGATION THROUGH TURBULENCE
There were two prediction models developed under the auspices of SonicBAT. The first was
TURBO, a classically-based model developed by John Morgenstern of Lockheed Martin. Becauseof space limitations, that model will not be covered here. One can find a complete description in the
SonicBAT Contractor Report, available later in 2019.
3.1 Two-dimensional Simulations
The second prediction model will be described briefly here, as the present authors are more familiar
with it. The numerical model used was the Khokhlov-Zobolotskaya-Kuznetzov (KZK) equation, andprior to SonicBAT it had shown good potential for modeling sonic booms and similar types of waves
propagating through atmospheric turbulence, see Averiyanov 2011 (6). Due to space limitations thedetails of the KZK implementation will not be provided here. The propagation would occur throughinhomogeneous temperature fluctuations (scalar turbulence) and inhomogeneous wind fluctuations

1594

(vector turbulence). The Random Fourier Modes approach of Blanc-Benon (7) was utilized for
implementing the turbulent distributions in the atmosphere, and the turbulence model of Wilson (8),repeated in Ostashev and Wilson (9), provided the structure of the turbulence as a function of height
above the ground. The actual turbulence and other atmospheric measurements from the field tests
were used to provide inputs to the numerical model. All the details of the KZK numerical model andthe inputs are provided in the Ph.D. dissertation of Trevor Stout (4), and the appendices of that
dissertation include the actual model source code in C++. Support for running the KZKFourier code,
as it is called, was provided by NASA on their Pleiades High Performance Cluster. The sampling
rate used was usually 200 kHz, although that sampling rate was reduced to 51.2 kHz when examining
shaped waveforms without short rise times.
All of the KZKFourier results reported in the SonicBAT Contractor Report were two-dimensional,
meaning the 3rd transverse dimension parallel to the ground was assumed constant. This restriction
was due to the very high computational cost of fully three-dimensional simulations which will be
described in Section 5.3 below.

4. PRINCIPAL RESULTS OF SONICBAT
4.1 Large High-Quality Database of Sonic Booms and Atmospheric Turbulence
Since no databases of sonic booms with coordinated turbulence and atmospheric measurements
were available previously, this is an important product of the SonicBAT program. The major
limitation to this database is that it is exclusively for conventional N-wave signatures.
4.2 New Prediction Models
Both the KZKFourier and TURBO models are available to NASA and its designates, andmodifications of the approaches will allow for further developments going forward. As alreadymentioned, the KZKFourier prediction model is included in Trevor Stout’s Ph.D. dissertation. Thisshould supply ample opportunity for new understanding.
4.3 Validation between prediction and measurement of N-wave booms
One of the first tasks after the KZKFourier model was working and the near simultaneous
measurement of sonic booms in atmospheric turbulence were processed was to see how closely thestatistical distribution of PLs compared between model and measurement. The Contractor Report
and Trevor Stout’s Ph.D. dissertation have more details. There is excellent agreement between thehistograms between calculation and measurement when comparing the PL values received on the
ground, relative to a nominal (no turbulence) signature. This figure will be available soon in a peerreviewed journal article, and the comparison will be shown at the ICA2019 meeting.
4.4 PCBoom Improvements, including New Finite Impulse Response Filters for PCBoom
SonicBAT also required new features be added to the sonic boom prediction program PCBoom.
One of these developments is that PCBoom will now allow one to use NASA’s sBoom program topropagate the signature to the ground instead of using PCBoom’s built in FOBoom module based on
the Anderson Algorithm. sBoom instead uses a time-domain Burgers Equation solver.
Further, PCBoom’s WCON module was updated to handle high-resolution signatures with a userdefined sampling rate. In addition, program flow was updated to allow Burgers-evolved signatures(from the PCBurg module) to interface properly and be used with the turbulence models.
Locey and Sparrow (10) had introduced the concept of using a finite impulse response (FIR) filter
to model sonic boom propagating through turbulence in 2007. The concept was to use measurementsfrom a sailplane and ground measurements to show exactly how the sonic boom was affected byturbulence. Using the KZKFourier prediction model developed in SonicBAT, a much larger set of
FIR filters were developed for use in predicting the effects of turbulence on sonic boom waveforms.
These new KZKFourier-developed FIR filters have been incorporated into PCBoom in the WCON
module. Hence the new capability allows anyone using the modified version of PCBoom to apply
the influence of turbulence to any signature in PCBoom. The filters incorporated will provide a mean
Perceived Level signature, and signatures with plus or minus one standard deviation from the mean.
Hence, one can see the range of turbulence effects and both the spiking and rounding (for N-waves).
The turbulence effects can be seen on the standard metrics of SELA, SELB, SELC, SELE, PL, andNASA’s ISBAP (indoor sonic boom annoyance predictor), as well as maximum overpressure.

1595

4.5 New Understanding of Turbulence Effects on Shaped Boom Waveforms
Once the validation was complete, showing good statistical agreement between predicted andmeasured sonic boom loudness results for N-waves, the effort switched to the original question: Are
shaped sonic booms less prone to spiking and rounding than conventional N-waves? In SonicBAT
the team members of Boeing, Lockheed-Martin, and NASA all provided shaped signatures for low
boom concept aircraft which were used as inputs to the KZKFourier prediction program. In summary
the results show that there are definitely fewer high-PL or high-ISBAP events for the shaped waves
when compared to N-waves, and this was true for all the shaped signatures considered. Thus, thestudy corroborates the previous analysis using NASA shaped sonic boom demonstrator (SSBD)
aircraft, see Morgenstern et al. 2005 (11) and Plotkin et al. 2005 (12), that the benefits of boom
shaping loudness reduction persist even in the presence of turbulence. SSBD only had front-shock
shaping, and SonicBAT has extended the result to fully-shaped supersonic aircraft. Additional
simulations showed that this shaping benefit would exist over a wide range of atmospheric conditions.

5. RESULTS SUBSEQUENT TO SONICBAT
Much of the research formally supported through SonicBAT concluded in the Spring of 2018, but
subsequent follow-on studies in the Ph.D. Dissertation of Trevor Stout and journal articles continued
for almost a full year later. Some of the primary new findings are now summarized.
5.1 Effect of Nonlinearity for N-wave and Shaped Signatures
One assumption in the FIR filter approach taken in Section 4.4 is that the propagation effects ofnonlinearity are negligible over the propagation distance through the boundary layer. To investigate
this, a study was undertaken by T. Stout in his Ph.D. dissertation, which was later reported upon at
the 21st International Symposium on Nonlinear Acoustics in Santa Fe, NM, USA, July 9-13, 2018 (13).
Simulations of both N-waves and shaped waves were run with and without the nonlinear terms of the
KZK equation included. The results show that for N-waves the effects of nonlinearity can beimportant, but for waves having longer rise times the effects of nonlinearity can be neglected; thus,
for smooth sonic boom waves it may not be necessary to explicitly include nonlinearity. The study
comparing propagation with and without nonlinearity also showed the criticality of including
nonlinearity for prediction comparisons with the SonicBAT experimental data, all N-waves.
5.2 Efficient time-domain spline interpolation
To ensure a large number of 2-D simulations could complete in a reasonable time, and to makeattempting 3-D simulations tractable in any sense, it was necessary to identify the fastest algorithm tointegrate the KZK equation for nonlinearity, temperature fluctuation, and advection. A study
published in September 2018 JASA Express Letters has shown that using an exact time-domain
solution implemented using natural splines preserving C2 continuity are best and can give a 50%
speedup or more over other choices (14). This cut the computation time for the “production runs” inSonicBAT significantly.
5.3 Three-dimensional Simulations
Having derived a fast method to solve the KZK equation, 3-D simulations became more tractable.
While the calculations and results for the two-dimensional simulation are all along a line parallel tothe ground, the three-dimensional simulations are in a plane aligned with that same line and theperpendicular to that line. The calculation rectangular array is perpendicular to sound rays heading
down to the ground. For simplicity, it is assumed that the sound rays are straight, so the 3-D
calculation domain is a rectangular prism. When comparing 2-D to 3-D simulations the sampling
rate was held at 51.2 kHz for all calculations. The 2-D domain was 1000 m in length and the 3-D
domain was 400 m by 400 m with all grid sizes discretized at 0.5 m. For a 1.76 km propagation
distance, the 2-D simulations each took 13 hours using 3 cores each, and the 3-D simulations took 9days each utilizing 28 cores on a Broadwell node. Therefore the 3-D runs were about 150 times morecomputational expensive than the 2-D runs.

1596

Figure 1: Normalized PL spatial map at bottom of the computational domain near ground for one
realization of a KZKFourier 3-D run (top). Data along y = 100 m (solid) and 350 m (dashed) are alsoplotted (bottom). Red color shows PL increases where energy focused and blue indicates PL decreases
where there was defocusing. Variation in PL is seen across any line across the 2-D spatial map.
5.4 Comparing 2-D and 3-D results
Using the capabilities of NASA Pleiades cluster, a limited number of 3-D simulations were
performed. At the bottom of the computational domain, a plane of microphone measurements can beextracted. This plane is not parallel to the ground, but at an angle perpendicular to the raypaths.
However, this still gives a good indication of how the sounds are distributed on the ground. An
example output of the PL metric is shown in Figure 1, where line slices across the domain show whatlines of microphones would receive on the ground. The white color corresponds to the nominal sonicboom result without turbulence, and deeper red or blue colors show higher or lower deviation in PL
from the nominal, respectively. The results provide a spatial window onto how sonic booms can be
spiked and rounded. A different random number seed for the turbulence would have produced adifferent realization of the spatial map.

1597

In addition, one might wonder whether the statistical occurrence of spiking would change, now
including the third dimension in a 3-D prediction. There is no room in the present ICA 2019 paper
to include all the details, but it was observed, given a very limited number of 3-D runs, that the PL
standard deviation increased by 11% going from 2-D to 3-D. Further for 3-D, the mean values ofturbulized PL decreased, but there was an increase in the number of spiking events. This should be
investigated further in the future with additional 3-D runs with a wider range of turbulence parameters.
These results were first reported in Stout’s Ph.D. dissertation and the 2019 AIAA/CEAS
Aeroacoustics Conference in Delft, The Netherlands, as were the results in the next section (15).
5.5 3-D result implications for microphones arrays at field tests
Having the capability to predict 3-D spatial maps allows one to do a better job in thinking about
how microphones should be arranged on the ground to capture the spiking and rounding of sonic boom
waves. A Monte Carlo experiment was performed where different virtual array types (linear layout,
cross layout, 2-D rectangular grid layout) were used to sample the 3-D spatial maps. The sonic boom
metrics sampled by the different array types were compared with the overall metric distribution to see
how well the arrays could sample the metric’s spatial variation. Separation between adjacentmicrophones was kept to 30.5 m (100 ft) for all arrays, but arrays were tried of different lengths.
Using 1 million array samples of the computational domain, across many array types, it was foundthat the microphone arrays systematically under-predict the PL standard deviation. At the same time
the PL mean is correctly estimated. The cross array had the best precision and accuracy, and the gridarray the worst. It was also found that increasing the effective span of the array lessened the bias in
the sampled PL standard deviation and increased the PL mean precision. Increasing the number ofmicrophones increased the precision of the PL standard deviation. More details are available in the
May 2019 AIAA/CEAS paper (15).

6. LINKS TO THE LITERATURE
The authors are currently involved in getting the SonicBAT results and subsequent findings written
into peer-reviewed journal articles, and at the time of the writing of the current ICA 2019 summary
paper, May 2019, those articles are currently undergoing review by NASA and others (16, 17). Theinterested reader is very welcome to contact the first author (vws1@psu.edu) after the ICA 2019
meeting to request the updated list of references.

7. CONCLUSION AND FUTURE WORKThe SonicBAT project was very successful in advancing our knowledge of how sonic booms areaffected by atmospheric turbulence. One important take-away is that shaped sonic booms really will
spike less frequently than do conventional N-waves. In future efforts many more 3-D simulations
need to be performed with a greater spread of input parameters corresponding to different atmosphericstates. The KZKFourier programs, both 2-D and 3-D, assume that the relative humidity is constantthroughout the computational domain and that geometrical spreading is negligible, and clearly neitherof those are strictly true; hence, including spatially varying relative humidity and geometricalspreading should be implemented. Another point is that the KZKFourier simulations assume an
atmosphere with strong buoyancy forcing as this is inherent in the Wilson model used. In the future,different atmospheric turbulence models could be implemented that correspond to turbulent conditions
on cloudy days or at night. The FIR filters implemented in PCBoom now provide an importantcapability not seen before, and this should be thoroughly exercised for a wide variety of input shapedsonic boom signatures. And with new turbulence models and more 3-D simulations available, theFIR filter coefficients can be updated. Other suggestions for future work are given in T. Stout’s Ph.D.
dissertation.

ACKNOWLEDGEMENTS
Work supported by NASA. The efforts of a large number of NASA employees made this work
possible, and the authors are thankful for NASA’s support throughout the project and in subsequentwork. The authors would also like to thank Philippe Blanc-Benon for his suggestions with thenumerical modeling, John Morgenstern for his overall efforts, the Penn State Graduate Program in
Acoustics (18), and KBR (19). The entire team did a great job. This paper is dedicated to thememory of Kenneth J. Plotkin.

1598

REFERENCES
1. Maglieri DJ, Bobbitt PJ, Plotkin, KJ, Shepherd KP, Coen PG, Richwine DM. Sonic Boom: Six Decadesof Research. 2014. NASA SP-2014-622, Chapter 2.
2. Pierce AD, Maglieri DJ. Effects of atmospheric irregularities on sonic boom propagation. J Acoust
Soc Am. 1972;51(2, Pt. 3):702-721.
3. Bradley K, Hobbs C, Wilmer C, Sparrow V, Stout T, Morgenstern J, Cowart R, Collmar M, Underwood
K, Maglieri D, Shen H, Blanc-Benon P. Sonic booms in atmospheric turbulence (SONICBAT): The
influence of turbulence on shaped sonic booms. NASA Contractor Report, to be released in 2019.
4. Stout T. Simulation of N-wave and shaped supersonic signature turbulent variations. Ph.D.
Dissertation. Graduate Program in Acoustics, The Pennsylvania State University, 2018. Available ashttps://etda.libraries.psu.edu/catalog/15959tqs5346
5. Loubeau A, Naka Y, Cook BG, Sparrow VW, Morgenstern J. A new evaluation of noise metrics forsonic booms using existing data," in Recent Developments in Nonlinear Acoustics: 20th Int. Symp. on
Nonlinear Acoustics, including the 2nd Intl. Sonic Boom Forum, Ecully, France, 2015. AIP Conf. Proc.
Vol. 1685. American Institute of Physics Publishing LLC.
6. Averiyanov M, Blanc-Benon P, Cleveland R, and Khokhlova V. Nonlinear and diffraction effects inpropagation of N-waves in randomly inhomogeneous moving media. J Acoust Soc Am. 2011;129(4):1760-1772.
7. Blanc-Benon P, Lipkens B, Dallois L, Hamilton M, Blackstock D. Propagation of finite amplitude soundthrough turbulence: Modeling with geometrical acoustics and the parabolic approximation. J Acoust
Soc Am. 2002;111(1, Pt. 2):487-498.
8. Wilson DK. A turbulence spectral model for sound propagation in the atmosphere that incorporates shear
and buoyancy forcings. J Acoust Soc Am. 2000;108(5):2021-2038.
9. Ostashev VE, Wilson DK. Acoustics in Moving Inhomogeneous Media. CRC Press; 2016.
10. Locey LL, Sparrow VW. Modeling atmospheric turbulence as a filter for sonic boom propagation. NoiseControl Eng J. 2007;55(6):495-503.
11. Morgenstern J, Arslan A, Lyman V, Vadyak J. F-5 shaped sonic boom demonstrator's persistance ofboom shaping reduction through turbulence. AIAA 2005-12, 43rd AIAA Aerospace Sciences Meeting.
12. Plotkin K, Maglieri D, Sullivan B. Measured effects of turbulence on the loudness and waveforms of
conventional and shaped minimized sonic booms. AIAA 2005-4, 43rd AIAA Aerospace Sciences Meeting.
13. Stout T, Sparrow V. Nonlinear propagation of shaped supersonic signatures through turbulence. Proc
Mtgs Acoust 2018;(34);045011. Proc. of 21st Intl. Symp. on Nonlinear Acoustics.
14. Stout T, Sparrow V. Time-domain spline interpolation in a simulation of N-wave propagation throughturbulence. J Acoust Soc Am. 2018;144(3):EL229-EL235.
15. Stout T, Sparrow V. Three-dimensional simulations of shaped sonic boom signature loudness variations
due to atmospheric turbulence. AIAA-2019-2562, 2019 AIAA/CEAS Aeroacoustics Conf.
16. Stout T, Sparrow V, Blanc-Benon P. Evaluation of numerical predictions of sonic boom level variations
due to atmospheric turbulence. In preparation, please contact vws1@psu.edu.
17. Stout T, Sprrow V. Atmospheric turbulence effects on shaped and unshaped supersonic signatures.
In preparation, please contact vws1@psu.edu.
18. Penn State Acoustics website: https://www.acs.psu.edu/
19. KBR website: https://www.kbr.com/en

1599