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Field measurements of sonic boom penetration into the ocean
R. A. Sohn
Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543
F. Vernon, J. A. Hildebrand, and S. C. Webb
Scripps Institution of Oceanography, La Jolla, California 92093-0205
共Received 21 October 1999; accepted for publication 3 March 2000兲
Six sonic booms, generated by F-4 aircraft under steady flight at a range of altitudes 共610–6100 m兲
and Mach numbers 共1.07–1.26兲, were measured just above the air/sea interface, and at five depths
in the water column. The measurements were made with a vertical hydrophone array suspended
from a small spar buoy at the sea surface, and telemetered to a nearby research vessel. The sonic
boom pressure amplitude decays exponentially with depth, and the signal fades into the ambient
noise field by 30–50 m, depending on the strength of the boom at the sea surface. Low-frequency
components of the boom waveform penetrate significantly deeper than high frequencies.
Frequencies greater than 20 Hz are difficult to observe at depths greater than about 10 m.
Underwater sonic boom pressure measurements exhibit excellent agreement with predictions from
analytical theory, despite the assumption of a flat air/sea interface. Significant scattering of the sonic
boom signal by the rough ocean surface is not detected. Real ocean conditions appear to exert a
negligible effect on the penetration of sonic booms into the ocean unless steady vehicle speeds
exceed Mach 3, when the boom incidence angle is sufficient to cause scattering on realistic open
ocean surfaces. © 2000 Acoustical Society of America. 关S0001-4966共00兲03106-4兴
PACS numbers: 43.28.Mw, 43.30.Nb, 43.30.Hw 关DLB兴
INTRODUCTION
Objects traveling faster than the speed of sound generate
shock waves that result in impulsive acoustic signatures
known as sonic booms. The typical acoustic signature of a
sonic boom is the ‘‘N-wave’’ 关Fig. 1共a兲兴, which is character-
ized by sharp pressure jumps at the front and back of the
waveform, with a slow pressure drop in between. It has been
recognized from the early days of supersonic flight that sonic
booms generate undesirable environmental impacts over
populated areas,
1
primarily because of startle response to the
shock wave pressure rise, and low-frequency building re-
sponse 共i.e., vibration, rattle兲.
The undesirable acoustic qualities of sonic booms led to
legislation in the U.S. 共and most countries internationally兲
forbidding supersonic flight and the generation of sonic
booms over land, except in designated military corridors. As
a result, most sonic booms are currently generated over the
ocean. Sources of sonic booms over water include the Con-
corde, which flies routinely between Paris and New York,
and rocket launches associated with satellite deployments.
The restriction of supersonic flight to air spaces over
water has refocused sonic boom environmental impact re-
search to the marine habitat, and to marine mammals, in
particular. While the characteristics of sonic booms in air are
well understood and supported by a vast body of research
共e.g., Carlson and Maglieri,
2
Darden
3
兲, data constraining the
penetration of sonic booms into the ocean, and the charac-
teristics of boom pressure signatures underwater, are scarce.
The original theory for the propagation of sonic booms
across the air/sea interface was developed by Sawyers,
4
and
by Cook.
5
For level flight, booms generated by objects trav-
eling at speeds less than that of sound in water 共1500 m/s, or
Mach ⬃4.4兲 create an evanescent wavefield in the water
column, decaying exponentially with depth. The decay is
wavelength dependent, with short wavelengths 共high fre-
quencies兲 attenuating faster than long wavelengths 共low fre-
quencies兲.
The Sawyers and Cook theories were validated with
laboratory experiments involving spherical blasts
6
and small,
high-speed projectiles.
7
Early attempts to validate the theory
with field experiments, however, were unsuccessful. Young
8
and Urick
9
attempted to quantify the penetration of sonic
booms in the ocean 共in separate experiments兲 by measuring
boom pressure signatures immediately above, and at several
depths below, the air/sea interface. Underwater sonic boom
pressure measurements from these experiments exhibit dif-
ferent decay rates with respect to depth, and neither matches
the analytical theory or laboratory data. Urick’s results devi-
ated enough to cause him to question the validity of the
evanescent wave theory for sonic booms in water.
Disagreement between the field data and the analytical
theory introduced some uncertainty regarding the validity of
the theory and its underlying assumptions in real world as
opposed to laboratory conditions. In particular, the theories
of Sawyers
4
and Cook
5
both assume a perfectly flat ocean
surface, but the ocean surface is continually perturbed by
ocean waves. The possible effects of a realistic ocean rough-
ness on the penetration of booms into the water was recently
investigated using numerical methods by Rochat and
Sparrow,
10
and Cheng and Lee,
11
with each arriving at dif-
ferent conclusions. Rochat and Sparrow concluded that
roughness has a negligible effect, with underwater pressure
level variations from a flat interface of 1 decibel or less. In
contrast, Cheng and Lee concluded that the sea surface
roughness exerts a first-order effect on boom penetration,
particularly at large depths and low frequencies. At issue is
the magnitude of the scattered component of sonic boom
3073 3073J. Acoust. Soc. Am. 107 (6), June 2000 0001-4966/2000/107(6)/3073/11/$17.00 © 2000 Acoustical Society of America
energy in the water column, and its proportion to the evanes-
cent signal.
The lack of consistency between the numerical
studies,
10,11
and disagreement between the analytic theory
4,5
with the field experiments,
8,9
underscores the need for reli-
able measurements of sonic booms underwater to serve as a
benchmark for the validation of theoretical models, and to
provide a foundation for environmental impact assessments.
The early data of Young and Urick suffer from the techno-
logic limitations of their day. Specifically, the data acquisi-
tion systems employed in the experiments did not have
adequate low-frequency response, and the pressure measure-
ments are likely contaminated by the interaction of the sonic
boom with the mechanical systems used to suspend the hy-
drophones in the water column. A sonic boom measured by
Urick
9
is shown in Fig. 2. The pressure signatures bear little
resemblance to an N-wave, primarily because the measure-
ment system lacked the low-frequency response to measure
the slow pressure decay between the fore and aft shocks. In
addition, the ringing observed in the water column measure-
ment indicates that the data are contaminated by mechanical
interactions with the suspension system.
Instrumentation has improved dramatically since the ex-
periments of Young and Urick, and modern systems are ca-
pable of making high-fidelity measurements of sonic booms
underwater. For example, a Concorde boom was serendipi-
tously recorded in 1996 by a hydrophone array off Nova
Scotia,
12
and the underwater boom waveform contains the
low-frequency components missing in the Young and Urick
measurements. However, correlation of this measurement
with theoretical results is difficult because the boom wave-
form was not measured in air, and because the underwater
waveform is curiously complicated by ringing that may have
resulted from the excitation of a low-frequency seismic
mode in the shallow seabed.
In this paper we present the results of a field study that
provides the first simultaneous, high-fidelity measurements
of sonic booms in the air and ocean. We take advantage of
modern instrumentation systems to extend the frequency
range of the measurements down to a few Hz, and use data
telemetry from a small spar buoy to avoid contaminating the
incoming sonic boom as it crosses the air/sea interface. We
measured six sonic booms at five depths in the water 共down
to 112 m兲, and just above the air/sea interface. We find that
the pressure signatures we measured are in excellent agree-
ment with the analytical theory of Cook
5
共as implemented by
Sparrow and Ferguson
13
兲 down to ⬃40–50 m, where the
signal is lost in the ambient field.
FIELD PROGRAM
The field experiment was conducted on May 11–12,
1999 in the East Cortez Basin 共32.2 °N, 118.7 °W兲, approxi-
mately 140 km W-SW of San Diego, CA. The location pro-
vided deep water 共1600 m兲 within a military air space. Sur-
FIG. 1. Characteristics of a typical ‘‘N-wave’’ sonic boom measured on the
ground. 共a兲 Simple N-wave time series. The straight-line approximation is
parameterized by a ‘‘rise time’’ 共t兲 which is the time from the onset of the
boom to maximum pressure, and the total duration 共D兲 of the waveform.
Rise times typically range from 2–20 ms, and durations are typically 100–
400 ms. 共b兲 Theoretical energy spectrum of an N-wave boom with a rise
time of 8 ms and a duration of 350 ms.
FIG. 2. Sonic boom measured by Urick 共Ref. 7兲 in the air and in the water
at a depth of ⬃15 m. The effective pass-band of these measurements is
75–150 Hz.
3074 3074J. Acoust. Soc. Am., Vol. 107, No. 6, June 2000 Sohn
et al.
: Sonic boom penetration into the ocean
face support for the experiment was provided by the R/V
N
EW HORIZON. Flight support was provided by the Naval
Air Station at Pt. Mugu, CA.
During the course of the experiment, the sea-state and
weather were essentially constant. The NOAA environmen-
tal buoy near Catalina Island 共33.75 °N, 119.08 °W兲 reported
a significant wave height and period of 1.2 m and 8 s, re-
spectively, an air temperature of 14°C, and an average wind
speed of 2 m/s. Wind and swell estimates made on station
aboard the R/V N
EW HORIZON were somewhat greater, with
prevailing winds of 4.5–9 m/s 共10–20 kts兲 and a swell of
2–3 m at a predominant period of 8–10 s.
The conditions during the experiment fall into the Beau-
fort Force 4–5 category. Wind and waves generally grew
during the day. By afternoon scattered white caps were
present, but breaking waves were not observed.
Instrumentation
The instrument package consisted of a 115-m vertical
hydrophone array suspended from a small spar buoy 共6.5-m
tall, 0.4-m diameter兲 at the sea surface 共Fig. 3兲. The vertical
array contained nine hydrophone elements 共Benthos/
Aquadyne AQ-1 cartridges兲, with one phone mounted in air
on top of the buoy 共⬃2 m above the water兲, and eight phones
at 15-m intervals in the water column. The shallowest and
deepest phones were located at 7 and 112 m depth, respec-
tively. The hydrophones’ signals were sampled at 500 Hz
and analog bandpass filtered. The in-air hydrophone pro-
vided a flat response from 1–60 Hz, a 10-dB/decade roll-off
between 60 and 150 Hz, and a ⬃50 dB/decade roll-off above
150 Hz. The water hydrophones had a flat response from
3–200 Hz, with a steep roll-off 共⬃70 dB/decade兲 above 200
Hz.
Annular vibration isolators with a nominal resonant fre-
quency of ⬃1 Hz were utilized to decouple the vibration of
the suspension line from the hydrophone elements 共see Fig.
3, inset兲. A 20-kg weight was attached to the bottom of the
hydrophone array with a length of shock cord to maintain a
vertical profile in the water column, and to move the reso-
nant frequency of the suspension system 共⬃0.1 Hz兲 outside
the frequency range of the measurements. A GPS receiver
was mounted on top of the buoy to provide position updates
once a minute, with a nominal error of 100 m.
The hydrophone data were digitized at the buoy, and
then telemetered in real-time to a receiving station aboard the
R/V N
EW HORIZON. A buoy telemetry system was employed
to avoid contaminating the sonic boom as it crossed the air/
sea interface. During the supersonic passes the R/V N
EW
HORIZON stood off several kilometers from the buoy with the
engines idling and the propellers de-clutched. The bandwidth
of the telemetry system permitted the digitization of six data
channels 共out of nine hydrophone stations兲 at a 500-Hz
sample rate. Different channel configurations were employed
for the first and second day of the experiment 共see Results,
below兲.
Measurements of the in-air sonic booms generated dur-
ing the experiment were also made by personnel from NASA
Dryden using the SABER system.
14
These measurements are
not reported here, but provided redundancy should the in-air
sensor on the data buoy have failed. The SABER measure-
ments 共with a sampling rate of 10 kHz兲 were also used to
examine the high-frequency characteristics of the booms en-
tering the water column.
Flight plan
Six supersonic passes were made with U.S. Navy F-4
aircraft over the two days of the experiment. The overflight
altitude was varied from 610–6100 m 共2000–20 000 ft兲 to
provide a range of boom pressures 共96–530 Pa, or 2–11 psf兲
at the air/sea interface. Aircraft speeds ranged from Mach
1.07–1.26, corresponding to the aircraft’s best speed at each
altitude.
After transiting from Pt. Mugu to the experimental site,
the aircraft established radio contact with the R/V N
EW
HORIZON and were given an updated target position. Once a
FIG. 3. Schematic illustration of instrumentation em-
ployed in this experiment. Details of the near surface
package and the suspension system are shown in inset.
3075 3075J. Acoust. Soc. Am., Vol. 107, No. 6, June 2000 Sohn
et al.
: Sonic boom penetration into the ocean
supersonic run was underway, the test pilots noted the speed,
altitude, and heading of the aircraft, along with a single po-
sition 共latitude/longitude兲 at the beginning of the run. The
aircraft position and magnetic heading 共accurate to within 3
deg兲 at the beginning of the run were used to estimate a flight
track for each supersonic pass.
Since the aircraft did not have GPS data loggers, it is
impossible to know the exact lateral distance between the
flight track and the data buoy. Based on straight-line flight
track estimates, all of the tracks pass over the buoy within
the tolerance of the estimates, except for one 共Pass 2兲. The
straight-line estimate for Pass 2 runs ⬃1 km west of the
buoy. This is significant given that the horizontal error is
only slightly less than the aircraft altitude 共1.5 km兲. How-
ever, no aircraft had an automatic heading-hold system, and
therefore the actual flight tracks 共for all the supersonic runs兲
may have varied from the straight-line estimates.
Results
Time series and spectral plots of each sonic boom mea-
sured during the experiment 共Pass 1–6兲 are shown in Figs.
4–9. Data from six hydrophones were recorded during each
run. Measurements made during the first day of the experi-
ment 共Pass 3, 5, 6; Figs. 6, 8, 9兲 recorded hydrophone data
in-air, and at 7, 22, 37, 82, and 112 m beneath the sea sur-
face. Measurements made during the second day of the ex-
periment 共Pass 1, 2, 4; Figs. 4, 5, 7兲 recorded data in-air, and
at 7, 22, 37, 52, and 67 m beneath the sea surface. The shift
toward shallower depths on the second day was made after it
FIG. 4. Pressure measurements and
theoretical predictions from Pass 1,
Mach 1.07 at 610-m altitude. Time se-
ries 共left side兲 and amplitude spectra
共right side兲 are shown for each mea-
surement. Sensor depth is shown on
the far left side. For time series plots,
data are shown as a solid line and the-
oretical predictions 共based on in-air
measurement at top兲 are shown as a
dashed line. For spectral plots, boom
amplitude spectra are shown as a solid
line and ambient noise spectra are
shown as a dashed line. Note that the
pressure scale 共y-axis兲 used for the
time series plots varies with depth.
3076 3076J. Acoust. Soc. Am., Vol. 107, No. 6, June 2000 Sohn
et al.
: Sonic boom penetration into the ocean
was realized that the booms were failing to generate detect-
able signals near the bottom of the hydrophone array.
The time series data for the in-water measurements are
compared with the linear, analytical theory of Sparrow and
Ferguson,
13
which is based on the work of Cook.
5
The
method assumes a flat air/sea interface, and no interaction
with the seafloor 共deep water兲, but allows for arbitrary boom
wave shapes. To generate the theoretical pressure signatures
in the water column, the spectrum of the in-air pressure sig-
nature was calculated, weighted by an exponential decay
with respect to wavelength and depth, and then transformed
back into the time domain. A Blackman window was applied
to the in-air data segment before calculating the fast Fourier
transform 共FFT兲 to reduce Gibbs phenomenon associated
with truncating an infinite series. The theoretical waveforms
shown in Figs. 4–9 were bandpass filtered 共3–200 Hz兲 to
mimic the analog circuitry of the in-water hydrophones. This
filtering slightly distorts the theoretical wave shapes, but is
required to provide an equal comparison to the measure-
ments.
The amplitude spectrum of the boom waveform and the
ambient noise field at each hydrophone channel are shown
on the right side of Figs. 4–9. The amplitude spectrum of the
ambient noise field represents the FFT of a randomly se-
lected segment of data immediately preceding the boom ar-
rival. A Gaussian window was applied to both the boom
pressure signature and the ambient noise segment prior to
estimation of the amplitude spectrum.
Discussion
The primary experimental objective of this work was to
make high-fidelity measurements of sonic booms at the air/
sea interface and at several depths in the water column. We
FIG. 5. Pressure measurements and
theoretical predictions from Pass 2,
Mach 1.15 at 1525-m altitude. Plots as
in Fig. 4.
3077 3077J. Acoust. Soc. Am., Vol. 107, No. 6, June 2000 Sohn
et al.
: Sonic boom penetration into the ocean
begin the discussion by assessing the extent to which this
objective was met. We then compare our measurements to
theoretical predictions, and discuss the implications of the
similarities/differences for the validation of the theory under
real ocean conditions. We conclude with a brief review of
some remaining issues and unanswered questions regarding
the penetration of sonic booms into the ocean.
Fidelity of sonic boom pressure measurements
We begin by examining the fidelity of the in-air mea-
surement, which is important considering that it is used as a
source function for the theoretical predictions of boom pres-
sures underwater. All of the in-air pressure signatures in this
experiment are characterized by fairly simple N-waves, and
the amplitude spectra of the in-air signals have the expected
shape, with two separate corner frequencies corresponding to
the boom duration and rise time 关compare top right panels of
Figs. 4–9 with Fig. 1共b兲兴. The low-pass filter applied to the
in-air pressure data 共60 Hz corner frequency兲 removes any
contributions from reflected phases at the microphone. It ap-
pears that our in-air measurements adequately characterize
the sonic boom impinging the air/sea interface above the
vertical hydrophone array, especially at low frequencies,
which are of primary importance to this study.
Several of the supersonic passes made during the experi-
ment were at fairly low altitudes, and under these conditions
individual shocks from the various aerodynamic features
共e.g., nose, wings, cockpit兲 would not be expected to have
coalesced into single bow and tail shocks 共e.g., Hayes
15
兲.
Uncoalesced shocks create extra spikes in the acoustic sig-
nature. These extra spikes generate relatively high-frequency
pressure perturbations that are removed by the low-pass fil-
ters, and in these cases we expect that the simple N-waves
FIG. 6. Pressure measurements and
theoretical predictions from Pass 3,
Mach 1.17 at 2135-m altitude. Plots as
in Fig. 4.
3078 3078J. Acoust. Soc. Am., Vol. 107, No. 6, June 2000 Sohn
et al.
: Sonic boom penetration into the ocean
rendered by the in-air sensor do not perfectly represent the
actual booms at the sea surface. Indeed, the SABER mea-
surements made aboard the R/V N
EW HORIZON for the low-
altitude passes contain spikes embedded in the N-wave sig-
nature 共although these measurements also contain spikes
from reflections off the ship’s superstructure兲. It will be seen
in the following section that the failure to capture high-
frequency spikes in the in-air measurement is not a signifi-
cant shortcoming since these features are almost immediately
removed from the evanescent wavefield beneath the sea sur-
face.
The principle concern for the underwater boom mea-
surements is to keep noise levels on the individual sensors as
close to ambient as possible. Achieving low noise levels on a
hydrophone array suspended at shallow depths is difficult
because the hydrophones are mechanically linked to the mo-
tion of the surface wavefield. The suspension system de-
couples the hydrophones from the jerking of the array by
motions of the buoy and from strum 共e.g., Sotirin and
Hildebrand
16
兲 induced by current flowing past the array.
Inspection of the ambient noise pressure spectra in Figs.
4–9 indicates that our attempts to minimize noise levels on
the hydrophone array using vibration isolators and shock
cord 共Fig. 3兲 were fairly successful. The pressure variance of
the ambient field on individual hydrophone elements was
typically less than 100 Pa
2
in the relevant band from 3–200
Hz. This corresponds to a dynamic head of less than 1 mm of
water, root-mean-square 共rms兲. Ambient noise pressure vari-
ance on the deepest phones is especially small, with typical
values of 2–5 Pa
2
. In practical terms this resulted in excel-
lent signal-to-noise levels for boom measurements down to
about 40–50-m depth. At this depth the amplitude of the
FIG. 7. Pressure measurements and
theoretical predictions from Pass 4,
Mach 1.13 at 2865-m altitude. Plots as
in Fig. 4.
3079 3079J. Acoust. Soc. Am., Vol. 107, No. 6, June 2000 Sohn
et al.
: Sonic boom penetration into the ocean
boom pressure signal is equal to or less than the ambient
levels on the hydrophone array.
Additionally, the underwater boom signatures do not
contain any ringing as do those measured by Urick
9
or De-
sharnais and Chapman.
12
Nor does the acoustic field contain
any measurable perturbation from the surface buoy. This
demonstrates that by using a small diameter spar buoy as a
surface mooring for the data acquisition system we avoided
contaminating the boom waveform with mechanical cou-
pling down the suspension line. By conducting the experi-
ment in deep water, we also appear to have avoided interac-
tion with the seabed.
We conclude that the pressure measurements made dur-
ing the course of this experiment provide accurate renderings
of the sonic boom wavefields generated at the instrument
array, especially at low frequencies.
Agreement between data and theory
The agreement between our data and the analytical
method of Sparrow and Ferguson,
13
which is based on the
theory of Cook,
5
can be observed by comparing the solid and
dashed lines in the time series plots of Figs. 4–9. Data and
theory are in agreement at all depths and for all booms
within the limitations of the signal-to-noise ratio. The signal
is above the noise to depths of 37 m for all booms, and to
greater depths for lower altitude flights with stronger booms.
Examination of spectral attenuation provides additional
insight into the agreement between our data and linear
theory. The evanescent decay of a sonic boom underwater
4,5
scales as e
⫺ k
0
z
, where k
0
is the wavelength in air divided
by Mach number, z is depth, and
⫽
冑
1⫺ M
2
/W
2
, where M
is Mach number and W is the ratio of sound speed in air to
FIG. 8. Pressure measurements and
theoretical predictions from Pass 5,
Mach 1.21 at 4570-m altitude. Plots as
in Fig. 4.
3080 3080J. Acoust. Soc. Am., Vol. 107, No. 6, June 2000 Sohn
et al.
: Sonic boom penetration into the ocean
water. The correlation between this theoretical expression
and our Pass 1 measurements 共strongest boom兲 is shown in
Fig. 10. The data follow the theoretical decay curves until
they approach the noise floor, at which point ambient noise
overwhelms the signal.
The agreement between the predicted waveform and the
signal measured at the deeper hydrophones precludes the ex-
istence of a scattered component of the sonic boom signal
propagating as an acoustic wave in the water with an ampli-
tude greater than 4 Pa peak to peak. The largest sonic boom
measured in air had a peak-to-peak amplitude of 800 Pa,
demonstrating that the scattered component in the water was
no more than 0.5% of the incident boom amplitude.
In order for an airborne acoustic wave to enter the ocean
it must have a grazing angle of at least 77° 共from the hori-
zontal兲. The grazing angles of booms generated during this
experiment 共i.e., Mach cone angle兲 range from ⬃20–30°.
This means that, in the high-frequency approximation, ocean
waves had to be 50–60° steep to generate a meaningful scat-
tered component and cause significant deviations from a flat
interface assumption. However, waves in the open ocean
break if their steepness exceeds ⬃8° 共Stokes
17
兲. Indeed, ob-
servations of wave steepness in the open ocean from a vari-
ety of sea states give values of 0.5–6° 共Khandekar
18
兲.
Given the low supersonic speeds, and hence low grazing
angles of the booms generated during our experiment, our
failure to measure a significant scattered component of the
boom signal underwater is not surprising. Indeed, we only
expect a significant scattered component if the boom inci-
dence angle is within a few degrees of 77, or just below the
angle required for acoustic transmission. If we allow for a
maximum wave steepness of 6°, then we expect a detectable
scattered component at incidence angles of 71°, correspond-
ing to a vehicle speed of Mach ⬃3.
FIG. 9. Pressure measurements and
theoretical predictions from Pass 6,
Mach 1.26 at 6100-m altitude. Plots as
in Fig. 4.
3081 3081J. Acoust. Soc. Am., Vol. 107, No. 6, June 2000 Sohn
et al.
: Sonic boom penetration into the ocean
Thus the scattered boom signal is expected to be negli-
gible until vehicle speeds reach Mach ⬃3. At Mach ⬃3 very
rough sea states have the potential to scatter significant
amounts of boom energy into the water column. Between
Mach 3 and Mach 4.4 the magnitude of the scattered signal
will increase with vehicle speed and sea state. Above Mach
4.4 standard acoustic transmission theory applies.
Remaining issues
The results of this experiment demonstrate that the pen-
etration of sonic booms into deep water from level aircraft
flight at velocities significantly less than 1500 m/s 共Mach
⬃4.4, the speed of sound in water兲 can be accurately pre-
dicted with analytical theory. We found that the presence of
a ‘‘real’’ surface wavefield at the air/sea interface did not
cause any observable differences between the data and the
theory. Thus there is now uniform agreement between the
original theories of Sawyers
4
and Cook,
5
laboratory tests,
6,7
the numerical method of Rochat and Sparrow,
10
and the field
results of our experiment. As a result we consider the first-
order physics of the penetration of sonic booms across the
air/sea interface to be well understood and validated.
There are three special cases of sonic boom penetration
into the ocean that were not addressed in this experiment:
penetration into shallow water, penetration from booms
propagating at speeds greater than Mach ⬃3, and penetration
from booms generated during unsteady flight 共maneuvers兲.
Penetration of booms into shallow water is a phenomenon
that will almost certainly require experimental data owing to
the difficulties associated with incorporating a realistic seaf-
loor into numerical computations.
19
In addition, a single ex-
periment may not suffice in this regard since the shallow-
water problem may be site-specific owing to the diversity of
seabed compositions found offshore the United States 共and
globally兲. For example, the continental margins of the east-
ern U.S. have a different composition, and hence different
geoacoustic characteristics, than the continental slope of the
western coast.
As discussed above, significant amounts of scattered en-
ergy from booms are expected if vehicle speeds exceed
Mach 3, and if they exceed Mach 4.4 then sonic boom pen-
etration into the water is governed by standard plane wave
transmission theory. These high speed scenarios are associ-
ated with much more efficient boom penetration into the wa-
ter, and may generate underwater pressure levels substan-
tially larger than those measured in this experiment.
However, few vehicles in existence today travel faster than
Mach 3, and those that do tend to do so at very high altitudes
共e.g., space shuttle reentries兲. Consequently, these types of
booms are both rare and of low amplitude. Therefore, it is
not clear whether or not this particular scenario warrants a
concerted experimental program.
Flight maneuvers have the potential to modify the pen-
etration of sonic booms into the ocean by changing the angle
of incidence of the booms at the air/sea interface. In this case
maneuvers are broadly interpreted to include any unsteady
flight operations, including climb, descent, and acceleration.
We are concerned not so much with classic focusing
effects,
20
but rather with phase matching of the acoustic sig-
nal at the air/sea interface. Under the proper conditions, an
object traveling at relatively low supersonic speeds 共a 29°
dive at Mach 1.5, for example兲 can generate a boom pressure
field that phase matches along the horizontal air/sea inter-
face. This is physically equivalent to the conditions resulting
from steady flight at speeds greater than Mach 4.4 as de-
scribed in the previous paragraph. A survey of the potential
for routine rocket launches and aircraft operations to maneu-
ver and generate phase-matched booms over the ocean is
beyond the scope of this work. However, if the flight track
parameters for a given mission are known, the phase velocity
of the boom pressure field at the air/sea interface can be
FIG. 10. Evanescent attenuation of sonic booms under-
water. Pressure data from the top three hydrophones
from Pass 1 共Fig. 4兲 are compared with linear theory
共Refs. 4 and 5兲. Mean spectral noise levels at 22-m
depth are shown for comparison. Attenuation is refer-
enced to the spectral levels of the in-air measurement,
such that the noise floor would move up on this plot for
the smaller booms of Passes 2–6.
3082 3082J. Acoust. Soc. Am., Vol. 107, No. 6, June 2000 Sohn
et al.
: Sonic boom penetration into the ocean
easily checked. A field experiment to measure the penetra-
tion of phase-matched booms from maneuvering objects
would be significantly more complicated than that conducted
in this work, but might be warranted, for example, if routine
rocket launches generate phase-matched booms.
CONCLUSIONS
We measured six sonic booms from Navy F-4 aircraft
under steady flight with sensors located just above the air/sea
interface and at five depths in the upper 115 m of the water
column. Boom pressures exhibit a frequency-dependent de-
cay with depth, with low frequencies penetrating signifi-
cantly farther than high frequencies. All of the boom pres-
sure signals measured in this experiment decay to ambient
levels in all frequency bands by 40–50 m. Boom waveforms
measured at individual depths in the water column exhibit
excellent agreement with analytical theory that assumes a flat
air/sea interface. At supersonic speeds significantly less than
Mach 3, we conclude that the ocean wavefield does not sig-
nificantly affect boom penetration into the ocean, and that
analytical theory 共e.g., Sawyers,
4
Cook,
5
Sparrow and Fergu-
son
13
兲 is a valid tool to estimate underwater sonic boom
pressures. In particular, these theories can be confidently
used to estimate potential environmental impacts of sonic
booms underwater.
ACKNOWLEDGMENTS
We thank Jacques Lemire and Glenn Offield for superb
engineering support during the instrumentation development
and field experiment, Bill Gaines for facilitating the experi-
mental logistics and clearances, Jo Griffith for graphics, and
the test pilots at the Naval Air Station Pt. Mugu for their
flight support during the experiment. We thank Vic Sparrow
for helpful discussions, and two anonymous reviewers for
suggestions that have improved the manuscript. This work
was funded by the NASA Langley Research Center 共Tech-
nical Monitor, Dr. Kevin Shepherd兲.
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