19th INTERNATIONAL CONGRESS ON ACOUSTICS
MADRID, 2-7 SEPTEMBER 2007
Acoustic propagation and atmosphere characteristics derived from
infrasonic waves generated by the secondary sonic bang
from the Concorde
PACS: 43.28.Dm
Gainville, Olaf1,2; Blanc, Elisabeth1;
Le Pichon, Alexis1;Piserchia, Pierre-Franck1; Blanc-Benon, Philippe2
1
Laboratoire de Détection et de Géophysique, CEA/DASE, BP12, 91680 Bruyères-le-Châtel,
France; [email protected]; [email protected]
2
Laboratoire de Mécanique des Fluides et d’Acoustique, LMFA UMR CNRS 5509,
École centrale de Lyon, av. Guy de Collongue, 69134 Ecully Cedex, France;
ABSTRACT
Infrasonic signals generated by daily supersonic Concorde flights between North America and
Europe have been recorded by an array of microbarographs in France. These signals are used
to investigate the long range propagation of infrasounds in the atmosphere and the effects of
seasonal atmospheric variability. Measurements are also used to evaluate a three dimensional
ray tracing code. The primary and secondary carpet positions are investigated by solving
temporal ray equations thought realistic atmospheric models. A shooting method is used to
search eigenrays which link the source to receivers. An amplitude equation including
nonlinearity, absorption and relaxation by various chemical species is coupled to the ray solver
to obtain the secondary boom signature at the ground level. Ray tracing code allows a
consistent identification of measured arrivals. A good agreement is found for the amplitude and
for the time duration between predicted and recorded signatures. Statistical analysis of wave
parameters shows seasonal and daily variations associated with changes in the wind structure
of the atmosphere. Variations in the reflection level, travel time, azimuth deviation and
propagation range are explained by the source and propagation models.
INTRODUCTION
In the framework of the Comprehensive Nuclear-Test-Ban Treaty (CTBT), the International
Monitoring System (IMS) develops a sixty barometric stations network. These stations, which
record infrasounds, detect long range explosions, supersonic airplanes, meteors, oceanic
swells, and volcano eruptions. For data analysis, we model the long-range atmospheric
propagation of infrasounds. In this context, we study infrasounds recorded at the Flers station,
France associated with the regular Air France and British Airways flights between North
America (New York) and Europe (London or Paris).
Like any supersonic aircraft, the Concorde generates a system of shock waves. Shock waves
are reflected by the ground and refracted by the atmosphere, and are thus transformed into a
long-duration acoustic signal. Acoustic wave guides may be formed between the ground and
high temperature and wind speed regions in the troposphere, stratosphere, and thermosphere.
The first carpet, associated with the direct downwards propagating acoustic arrival along the
track of the Concorde, was largely study [1]. The second carpet is associated with refraction
from the stratosphere and the thermosphere. Previous works investigated the effects of shock
wave propagation [1-5] on the environment. In New York [6], in Sweden [7], and in France [8],
Concorde flights have been routinely observed with infrasonic arrays. The propagation of
infrasounds emitted by supersonic aircraft in an inhomogeneous media is a three dimensional
phenomenon. Because of computational cost, ray tracing is the only operational method
available to model long range wave propagation for a full three dimensional problem.
After a presentation of the Flers barometric station and of Concorde records, we present our ray
tracing code and atmospheric models used for this study. We discuss a typical feature of
infrasonic Concorde signals recorded in November 1999 with comparisons between
measurements and modeling. Finally, seasonal variations effects on secondary boom recorded
at Flers station are investigated and compared with the model.
INFRASOUNDS RECORDED AT THE FLERS STATION
Infrasonic signals are continuously recorded by a four element array located at Flers, in the
West of France (20.48 °W and 48.76 °N). The Flers array has been set up to characterize
infrasonic sources and to improve atmospheric and propagation models. This array is a
prototype CTBT station. The array, which has an aperture of 3 km, has been operating
continuously since April 1996. The phase parameters are computed by using the Progressive
Multi-Channel Correlation Method (PMCC) used as a real-time detector [9-10], that summarizes
all detected coherent signals. This method, originally designed for seismic arrays, proved to be
very efficient for infrasonic data and is well adapted for analyzing low-amplitude signals waves
within noncoherent noise. This method gives precise trace velocity and azimuth of coherent
waves.
Figure (2) shows a typical detection of the Concorde computed by the PMCC method. This
detection is associated with the regular Air France flight between New York and Paris. This
detection is constituted of successive arrivals with almost the same azimuth. The PMCC method
is also used to analyze systematically arrivals. The year 1999 was analyzed by Le Pichon & al.
[8] and result for the year 2002 are presented in figures (4-5). All the arrivals are detected
automatically by the PMCC method and confirmed by an analyst. Seasonal trends of the
Concorde phase parameters were then obtained.
INFRASOUNDS PROPAGATION MODELING
The long range propagation of infrasounds emitted by the Concorde flight landing in Europe is
modeled using a ray tracing code. This code models the propagation of acoustic waves in a
three dimensional inhomogeneous moving media in the geometrical acoustic limits. Atmosphere
is modeled using realistic winds and temperature profiles.
Ray tracing code
Geometrical acoustics study acoustic wave fronts propagation in the high frequency hypothesis.
In atmospheric propagation, the high frequency hypothesis is based on the assumption that
atmospheric properties (temperature, wind, density) space and time variation scales are much
larger than acoustic wave scales. For a detailed presentation of the geometrical acoustic theory,
we refer the reader to Whitham [11] and Candel [12]. For a detailed presentation of the ray
tracing code, it’s validation and it’s application to the study of a motionless point source, we
refer the reader to Gainville & al. [13].
Our ray tracing code solved ray tracing equations and geodesic elements equations to
computed ray trajectory and amplitude variation using the wave action conservation law. We
use an efficient shooting method to determine all the eigenrays which link the source to the
station. Each eigenray is associated to an arrival at the station. The group velocity of the ray at
the station provides the trace velocity and the azimuth of the wave.
The global pressure signature at the receiver is the sum of eigenray pressure signature
contribution. These pressure signatures are obtained by solving a generalized Burgers equation
along each eigenrays. This generalized Burgers equation take into accounts of nonlinear
effects, thermoviscosity dissipation and molecular relaxation mechanisms. This equation is
solved using a Fourier Galerkin spectral scheme. Specific developments are performed to pass
thought caustics and take into account of ground reflection.
Source model
A supersonic aircraft generates aerodynamic shock waves localized on the Mach cone surface.
This acoustic field can be evaluated from the aircraft section variations using the Whitham
F-function [11,14] or direct numerical resolution of Euler’s equations. Near the source, shock
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19th INTERNATIONAL CONGRESS ON ACOUSTICS – ICA2007MADRID
waves propagation direction is perpendicular to the cone and the acoustic field variations on the
cone are weak. Shock waves are approximated as local plane waves and their long range
propagation is studied in the geometrical acoustic limits. The Mach cone apex is localized at the
aircraft noise. The cone revolution axes is the aircraft speed vector and the semi-angle is α(t) =
arccos(1/M) with M the source Mach number. As the geometrical acoustic model is singular at
the point source, the initial pressure signature is imposed at a short distance of the source
where nonlinear effects are still negligible. The Concorde is assumed as a 60 m length
parabolic body with a radius of 1.5 m. The initial wave front is computed using the Whitham
F-function.
Figure 1.- Wavefront emitted by the Air France Concorde.
Atmospheric models
Sound waves are affected by the temperature, wind velocity, density and molecular composition
of the atmosphere. Wind and temperature profiles used for our simulations are based on
MSISE-90 and HWM-93 empirical models [15]. These models include detailed parameterizations of seasonal changes in the mean state, dominant solar migrating tides, and low-order
stationary planetary waves. These empirical models provide time dependent temperature,
composition and zonal and meridional winds estimates up to elevations of 180 km. To correct
the lake of precision in the troposphere and the stratosphere, these models are linking with
ECMWF near-real time global assimilation of temperature and winds between the ground and
45 km. The main seasonal variation is the reversal of the zonal wind direction around and above
the stratopause (altitude of 40–70 km) which is observed in spring and autumn. We include
molecular composition profiles and absorption relations provided by Sutherland & Bass [16] in
our code to compute the pressure signature evolution along rays.
RESULTS
Infrasonic waves originating from a low-altitude source may be ducted in various regions of the
atmosphere. Phases associated with waves refracted from the troposphere, stratosphere and
thermosphere are referred as Is and It. Is phases are dependent of the season of the year and
are present only in the dominant wind direction. Thermospheric phases are always predicted,
but their amplitudes may be not strong enough to be observable.
Study of the 15 November 1999 detection
The Air France Concorde detection of the 15 November 1999 was presented by
Le Pichon & al. [8] and is now investigated using our nonlinear ray tracing code. At least seven
distinct successive detections are recorded at the Flers station noted (a-g) in figure (2). The
duration of these arrivals are roughly 30 seconds and frequencies are in the range 0.5 Hz to
5 Hz. Whereas the azimuth is approximately constant equal to 287°, the trace velocity increase
globally with the time.
The ray tracing code finds five eigenrays automatically presented in figure (2), over the seven
measured arrivals. The three first (green Is) computed arrivals are stratospheric paths emitted
just before the transonic time where the Concorde keeps the supersonic speed. The next arrival
(red It) is constituted of three thermospheric paths presented on figure (3) which link directly the
source and the receiver. These paths arrive at the same time. The last arrival (blue It) is a
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19th INTERNATIONAL CONGRESS ON ACOUSTICS – ICA2007MADRID
thermospheric path emitted in the bottom direction and reflected by the earth surface.
Thermospheric paths are emitted earlier than stratospheric paths. Other computed
thermospheric paths with arrival times later than presented ones are found but their amplitudes
are too small to be measured. The three stratospheric eigenray arrival times are in agreement
with measured arrivals (b), (c) and (d-e) whereas thermospheric paths are in agreement with
measured arrivals (f) and (g). Measured and computed trace velocities for all these paths are in
agreement. Trace velocity characterized the path kind. However, the first measured arrival (a) is
missing by the ray tracing code. Measured arrivals (d-e-f) show a progressive transition
between stratospheric paths to thermospheric paths. This transition is partly found with the ray
tracing code by the multiple path aspect of the first thermospheric arrival (red It on figure 4).
Measured pressure signature spectra and synthesized pressure signature spectra agreed for
stratospheric arrivals (b) and (c). The signature amplitude is under estimate for thermospheric
arrivals (f) and (g) due to the strong absorption of sound at the refraction altitude (120-140 km).
The energy found by the code for the last stratospheric arrival appears of the order of the sum
of the energies measured for both arrivals (d-e). It appears clearly that the N shape pressure
signature measured for primary carpets [1] is not found for secondary carpets. The measured
pressure signature is not reproduced by our nonlinear ray tracing code model. The pressure
signature may be modified by multipath arrivals and fine structures of the atmosphere such as
gravity waves and turbulence not modeled here.
Figure 2.- Analyzed of the Air France Concorde landing in Paris the 15 November 1999.
The first three graphs are the Flers record PMCC detection of the Concorde. The fourth graph
shows computed pressure signatures using the atmospheric statistical model only (blue) or
linking with ECMWF models (red). The last graph shows trace velocity of each eigenray
computed using the ray tracing code.
Figure 3.- Eigenrays between the Air France Concorde and the Flers station find by the ray
tracing code for the 15 November 1999 flight.
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19th INTERNATIONAL CONGRESS ON ACOUSTICS – ICA2007MADRID
Seasonal variation effects on secondary boom recorded at the Flers station
Statistical observations over one year show that reception azimuths of acoustic waves
originating from Air France (~16h UT) and British Airways (~21h UT) supersonic Concorde
flights are approximately 287° and 300°, respectively. Seasonal azimuth variations are smallest
for the Air France Concorde (~3°) than for the British Airways Concorde (~7°). Detection hours
are well correlated with flight hours and flight days. For studied years, few arrivals (233 arrivals
for 86 detections) were detected from May to September in contrast to the large number of
phases recorded from October to April (578 arrivals for 120 detections). This difference is
associated with an increase of the trace velocity range. The trace velocity is mainly limited to
the ground sound speed in summer and goes up to 480 m/s in winter.
The dominant seasonal variation is the zonal wind component inversion. For the Air France
Concorde, the zonal wind is in the wave propagation direction (with an angle of 15°), so the
influence is mainly on measured arrival kinds and their travel times (figure 4 and 5). For the
British Airways Concorde, the Flers station reception azimuth deviation is more affected by this
zonal wind inversion. The angle between ray trajectories and zonal wind direction is around 30°.
In addition to the difference between the two Concorde wave propagation directions, the flight
hours modify seasonal effects. But, during the year 2002, British Airways flight hour variations
(17h or 21h) show that this effect is secondary. Modeling allows finding the strong daily azimuth
fluctuations measured. Low atmospheric fine structures (under 45 km) are mainly responsible of
these fluctuations. These azimuth fluctuations can be stronger than seasonal azimuth
variations.
Trace velocity which characterized the phase kind is dependant of the season (figure 4). As an
example, a trace velocity of 400 m/s is the characteristic of a stratospheric path in winter and of
a thermospheric path in summer. Moreover, in winter, the daily fluctuation of the trace velocity is
higher than the gap between thermospheric path and stratospheric path. So, as indicated by Le
Pichon & al. [8], the trace velocity is not a clear arrival kind indicator. The necessity of
propagation models and atmospheric models as realistic as possible appears to analyzed
measured arrivals.
Figure 4.- One year modeling of the Air France Concorde flight. First two graphs shows
reception time at the Flers station, Azimuth and trace velocity evolutions for the year 2002.
The last graph links trace velocity with path kinds: stratospheric paths in blue and
thermospheric paths in yellow-red.
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19th INTERNATIONAL CONGRESS ON ACOUSTICS – ICA2007MADRID
Figure 5.- Air France Concorde phase parameters recorded at the Flers station along the year
2002. Reception hour, trace velocity and azimuth are presented.
CONCLUSIONS
The infrasonic signals generated by the Concorde offer a unique opportunity to study acoustic
propagation in the atmosphere. This study provides confirmation that long-range sound
propagation depends strongly on the atmospheric conditions, primarily on the variability of the
meridional and zonal winds. Simulations based on realistic winds and temperature profiles and
the geometrical theory explained most of the daily and seasonal variations of the measured
phase parameters. The 3D eigenrays searching method finds most of measured arrivals at the
station automatically. The energies and the spectrum of computed pressure signatures agree
with measurements. Differences between measured signals and nonlinear computed signatures
may be done by partial reflection and scattering of fine structures of the atmosphere such as
gravity waves and turbulence.
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