The final report for progress during the period from 15 Nov. 1988 to 14 Nov. 1991 is presented. Research on methods for analysis of sound propagation through the atmosphere and on results obtained from application of our methods are summarized. Ten written documents of NASA research are listed, and these include publications, manuscripts accepted, submitted, or in preparation for publication, and reports. Twelve presentations of results, either at scientific conferences or at research or technical organizations, since the start of the grant period are indicated. Names of organizations to which software produced under the grant was distributed are provided, and the current arrangement whereby the software is being distributed to the scientific community is also described. Finally, the names of seven graduate students who worked on NASA research and received Rensselaer degrees during the grant period, along with their current employers are given

Jacobson, M. J.

Robertson, J. S.

Siegmann, W. L.

English

NASA Technical Reports Server

(_IASA-C_-I93082) RESEARCH SUMMARY
Fin_1 R_-_port, 15 Nov. 1988 - 14
Nov. 1991 (Rensselaer Polytechnic
Inst. ) 12 p
N93-27127
Uncl as
G3/71 01647?9
Final Report
Grant Number NAG-I-929
15 November 1988 - 14 November 1991
by
W. L. Siegmann, J. S. Robertson
and
M. J. Jacobson
Department of Mathematical Sciences
Rensselaer Polytechnic Institute
Troy, New York 12180-3590
R.P.I. Math. Scis. Rep. No. 204
May 14, 1993
This work was supported by
Applied Acoustics Branch
Langley Research Center
National Aeronautics and Space Administration
Grant Number NAG-I-929
https://ntrs.nasa.gov/search.jsp?R=19930017938 2020-03-17T05:56:54+00:00Z
ABSTRACT
This is the Final Report for N.A.S.A. Grant Number NAG-I-929. It
summarizes research results and lists publications and reports, presentations,
software distribution, and students who performed N.A.S.A. research.
-2-
INTRODUCTION
This Final Report summarizes progress under National Aeronautics and Space
Administration Grant Number NAG-1-929, which provided support for the period from
15 November 1988 to 14 November 1991.
Section I summarizes our research on methods for analysis of sound propagation
through the atmosphere and on results obtained from application of our methods. Section
II lists ten written documents of N.A.S.A. research, and these include publications,
manuscripts accepted, submitted, or in preparation for publication, and reports. Section
III indicates twelve presentations of results, either at scientific conferences or at research
or technical organizations, since the start of the Grant period. Section IV provides names
of organizations to which software produced under the Grant has been distributed, and
also describes the current arrangement whereby the software is being distributed to the
scientific community. Finally, Section V gives the names of seven graduate students
who worked on N.A.S.A. research and received Rensselaer degrees during the Grant
period, along with their current employers.
-3-
I. RESEARCH SUMMARY
There is a significant level of interest in the analytical and numerical modeling of
lower frequency atmospheric acoustic propagation. The parabolic approximation
method, often more accurate than ray models for frequencies of interest, can be applied to
acoustic propagation in the atmosphere. In Reference 1 we discuss appropriate physical
and asymptotic conditions under which this model is valid. Modifications of an existing
implicit finite difference implementation for computing solutions to the parabolic
approximation are discussed. In addition, we present calculations of acoustic intensity
levels in a windy atmosphere and contrast the results with those of ray theory.
The effects of a ridge on a low frequency acoustic propagation in quiescent and
windy atmospheres are investigated using a parabolic approximation. 2 A logarithmic
wind speed profile, commonly employed to model atmospheric wind currents, is
modified and used to model two-dimensional atmospheric flow over a triangularly shaped
hill. The parabolic equation is solved using an implicit finite difference algorithm.
Several examples are examined to determine the combined effects of source-ridge
distance, ridge dimensions, wind speed profile, and cw source frequency on the received
acoustic field.
Many mechanisms can be responsible for fluctuations of sound intensity and
phase through the atmosphere over the Earth's surface. The effect of wind gusts on
received intensity at short range is examined. 3 Using a parabolic approximation, relative
intensity for a continuous wave omnidirectional source is calculated using the effective
sound speed profiles obtained from meteorological data. Two characteristic scale
thicknesses are used to model the wind gust profiles. The thinner layer thickness can
result in temporal intensity fluctuations as high as 10 dB at a range of 100 m. It is
emphasized that these fluctuations are refractive and deterministic. In an actual
experiment, these fluctuations would be detected along with additional variations caused
by wind noise turbulent scattering.
There is substantial interest in the analytical and numerical modeling of low
frequency, long range atmospheric acoustic propagation. Ray based models, because of
their frequency limitations, do not always give an adequate prediction of quantities such
as sound pressure or intensity levels. However, the parabolic approximation method,
widely used in ocean acoustics and often more accurate than ray models for frequencies
of interest, can be applied to this type of acoustic propagation in the atmosphere.
Modifications of an existing implicit finite difference implementation for computing
solutions to the parabolic approximation are discussed. 4 A locally reacting ground
-4-
surfaceis usedwith a oneparameterimpedancemodel,while a non-reflectingboundary
condition is used to handle the upper boundary. Relative sound pressure level
calculationsareperformedfor a numberof flow resistivity valuesin both homogeneous
andnonhomogeneousatmospheres.Comparisonsto experimentaldataaremadewhich
suggesthis modelingapproachcanbeuseful in the studyof thesetypesof propagation
problems.
Long range,low frequencysoundpropagationovervarying terrainconditionsis
animportantproblemwith manyapplications.The modelingof cw acousticsignalsare
considered5asthey propagateovervariableimpedancetopography. We usethe NASA
Implicit Finite Difference(NIFD) implementationof theparabolicapproximationsound
propagationmodel that incorporatesvariableimpedancegroundsurfaces.The accuracy
of this numerical model is demonstratedwith a pair of benchmarkproblems. An
applicationof the resultsis usedto predictexcessattenuationof pure tonesignalswhose
propagationpath includesportions of a flat lake surface. Both quiescentand windy
atmospheresare treated. For long ranges, multiple impedanceboundarieshave a
significant effect on soundattenuationat higher frequenciesin both the no wind and
receiverdownwardcases.
A parabolicequation(PE)methodfor predictingcoherent,low frequencyacoustic
propagation through small-scale atmospheric turbulence is presented.6 Frequency
constraintson theapplicabilityof stochasticparabolicapproximationsareavoidedby f'trst
averagingthestochasticHelmholtzequationandthenapplyingaparabolicapproximation
to theresultingdeterministicequation.Turbulenceeffectsare incorporatedby meansof
spatially varying effectivewavenumbers. Comparisonof exactsolutionsin thecaseof
infinite spacepropagationdemonstratesthe advantagesandlimitationsof this approach.
A uniform asymptotic expression for the effective wave number profile in the case of
isotropic turbulence is used to develop a half space PE formulation that is valid in the
limit of low frequency, small-scale inhomogeneity. For anisotropic turbulence that is
correlated more strongly in range than height, a modified mean value theorem for the
two-dimensional Helmholtz operator is used to find the effective wave number.
Numerical examples demonstrate that excess attenuation due to the imaginary component
of the effective wave number is the primary effect of weak turbulence on coherent, low
frequency propagation.
The effects of a large ridge on low frequency acoustic propagation through an
ideally moving atmosphere are investigated 7 using a narrow-angle, two-dimensional
parabolic approximation. The winds in this investigation are associated with an ideal
two-dimensional fluid flow. The ridge is taken to be triangularly shaped with a
-5-
horizontal earth-air interface on both sides. Consequently,a Schwarz-Christoffel
transformationis usedto translatetheflow into oneovera horizontalboundary. For the
acousticsproblem,theparabolicequationwith a rigid earth-airboundaryis solvedusing
an implicit finite differencealgorithm. Severalexamplesareexaminedto determinewhat
effectsthis methodof modelingthewind hasonsoundpressurelevels.
Low frequency,long rangesoundpropagationfrom sourcesat low to medium
altitude inevitably involves interaction with the topography and the acoustical
characteristicsof the ground surface. Improvementof propagationpredictions from
parabolic approximation methods therefore requires accurate treatment of acoustic
interactionswith the ground. In order to handleimpedanceboundary conditions in
connection with finite difference implementationsof parabolic approximations,new
procedureswhich are more accuratethanexisting onesaredeveloped.8 The caseof
horizontal boundaries is treated first, and then extensionsare provided for bottom
topographywhich is modeledby piecewiselinear slopes.The methodsareemployedin
the NASA Implicit Finite Difference (NIFD) implementation. Benchmarktestsare
included to documentthe accuracyof the boundarycondition treatments. Numerical
illustrationsovermodelbottomtopographyarealsoprovided,with comparisonsto results
from earlieralgorithms.
Using the parabolicapproximation,effectsof multiples ridgeson low frequency
long rangepropagationin an atmospherewith winds are investigated9 The ridgesare
perfectlyreflectingperturbationsalongthegroundboundary,andtheyareexaminedwith
different heights,sizes,andlocations. The windy atmosphereis comprisedof a typical
logarithmicvelocity profile andisboundedaboveby anartificial absorbinglayer beneath
a pressurereleasesurface. Excessattenuationlevelswithin theatmosphericwaveguide
aredeterminedby solving anappropriateparabolicequationusing the NASA Implicit
Finite Difference (NIFD) algorithm. Numericalresultsarecomparedto determinethe
effects of variations in the number of ridges, ridge separation, and ridge dimensions.
Also discussed are the effects of wind profile and frequency variations.
Acoustic propagation calculations performed to full wave methods typically
produce a large amount of numerical data. This data represents the relative intensity or
excess attenuation of the acoustic field at each range and height/depth location of interest.
Efficient display of this information is essential for developing useful interpretations of
results and for determination of the mechanisms that influence the propagation. The
DISSPLA library of Fortran subroutines is used to develop a collection of subprograms
for presenting acoustic propagation results. 10 Two-dimensional graphs of intensity
versus range or height, three-dimensional plots of intensity versus both range and height,
-6-
contourplotsof intensity in arange-heightplane,andcontourshadeplotsareamongthe
main types of displays for which subprogramsare provided. The subprogramsare
designedfor portability to systemsfor which the DISSPLA library is available. Local
systemruncommandsareprovided.
-7-
II. PUBLICATIONS AND REPORTS
°
.
o
.
°
.
.
°
*
10
J. S. Robertson, M. J. Jacobson, and W. L. Siegmann, "Mathematical Modeling of
Sound Propagation in the Atmosphere using the Parabolic Approximation," Trans.
Sixth Army Conference on Applied Math. and Computing, Army Res. Office (Res.
Triangle Park, NC), Report 89-1, 125-131 (1989).
J. S. Robertson, M. J. Jacobson, W. L. Siegmann, and D. P. Santandrea, "Acoustical
Effects of a Large Ridge on Low-Frequency Sound Propagation in Stationary and
Moving Atmospheres," Applied Acoustics 31,265-280 (1990).
J. S. Robertson, "Numerical Simulation of Intensity Fluctuations Caused by Wind
Gusts," J. Acoust. Soc. Am. 87, 1353-1355 (1990).
J. S. Robertson, W. L. Siegmann, and M. J. Jacobson, "Low-Frequency Sound
Propagation Modeling over a Locally Reacting Boundary with the Parabolic
Approximation," manuscript accepted for publication, J. Acoust. Soc. Am.
P.J. Schlatter, J. S. Robertson, W. L. Siegmann, and M. J. Jacobson, "Low-
Frequency Long-Range Sound Propagation over Impedance Discontinuities with
the Parabolic Approximation," manuscript accepted for publication, J. Acoust Soc.
Am.
I. W. Schurman, W. L. Siegmann, M. J. Jacobson, and J. S. Robertson, "Parabolic
Approximations for Coherent Low Frequency Acoustic Propagation through
Atmospheric Turbulence," manuscript submitted for publication, J. Acoust. Soc.
Am.
M. J. Jaye, M. J. Jacobson, J. S. Robertson, and W. L. Siegmann, "Influence of an
Ideal Wind Profile of Sound Propagation over a Ridge," draft manuscript
completed, in preparation for submission.
T. M. Kastner, J. S. Robertson, W. L. Siegmann, and M. J. Jacobson, "An Improved
Implicit Finite Difference, Locally Reacting Ground Surface Model for the
Parabolic Approximation," draft manuscript completed, in preparation for
submission.
D. P. Santandrea, M. J. Jacobson, J. S. Robertson, and W. L. Siegmann, "Acoustical
Effects of Multiple Ridges on Low-Frequency Propagation in a Moving
Atmosphere," draft manuscript completed.
M. L. Linnington, W. L. Siegmann, J. S. Robertson, and M. J. Jacobson, Graphical
Display of Underwater and Atmospheric Acoustic Propagation Results, "RPI
Mathematical Sciences Report 185, June 1990.
-8-
III. PRESENTATIONS
°
.
°
°
.
°
°
o
o
10.
11.
12.
J. S. Robertson, "Analytical and Numerical Modeling of Atmospheric Propagation
using the Parabolic Approximation," NASA Langley Research Center, June 1989.
J. S. Robertson, "The Parabolic Approximation in Atmospheric Acoustics: Target
Acquisition Ramifications," Northrup Corporation, Anaherm, CA, July 1989.
J. S. Robertson, "The Parabolic Approximation in Atmospheric Acoustics," JASON
Summer Study Institute, LaJolla, CA, July 1989.
J. S. Robertson, M. J. Jacobson, and W. L. Siegmann, "Low-Frequency Long-Range
Sound Propagation Modeling over a Locally-Reacting Boundary with the Parabolic
Approximation," 118th Meeting of the Acoustical Society of America, St. Louis,
MO, December 1989.
J. S. Robertson and W. L. Siegmann, "Long-Range Sound Propagation over
Variable Impedance Boundaries," NASA Langley Research Center, Hampton, VA,
January 1990.
J. S. Robertson, M. J. Jacobson, and W. L. Siegmann, "Mathematical Modeling of
Long-Range Sound Propagation in the Atmosphere using the Parabolic
Approximation," U. S. Army CECOM Test Integration Working Group, Fort
Monmouth, NJ, March 1990.
J. S. Robertson, "Applications of Computational Acoustics to Problems Arising
from Passive Detection of Rotary Wing Aircraft," Naval Postgraduate School,
Monterey, CA, April 1990.
J. S. Robertson, P. J. Schlatter, W. L. Siegmann, and M. J. Jacobson," Numerical
Modeling of Long-Range Sound Propagation over Variable Impedance
Boundaries," Fourth International Long-Range Sound Propagation Symposium,
NASA Langley Research Center, Hampton, VA, May 1990.
J. S. Robertson, "Application of Computational Acoustics to Problems Arising from
Passive Detection of Rotary Wing Aircraft," The Open University, Milton Keynes,
England, September 1990.
M. J. Jaye, M. J. Jacobson, J. S. Robertson, and W. L. Siegmann, "The Influence of
an Ideal Wind Profile on Sound Propagation over a Ridge," 121st Meeting of the
Acoustical Society of America, Baltimore, MD, May 1991.
P. J. Schlatter, J. S. Robertson, and W. L. Siegmann, "Low-Frequency Long-Range
Sound Propagation over Impedance Discontinuities with the Parabolic
Approximation," 121st Meeting of the Acoustical Society of America, Baltimore,
MD, May 1991.
I. W. Schurman, W. L. Siegmann, M. J. Jacobson and J. S. Robertson, "Parabolic
Approximations for Coherent Low-Frequency Acoustic Propagation through
Atmospheric Turbulence," 123rd Meeting of the Acoustical Society of America,
Salt Lake City, UT, May 1992.
-9-
IV. SOFTWARE DISTRIBUTION
1. NASA Langley Research Center, Hampton, VA.
2. U.S. Army Atmospheric Sciences Laboratory, White Sands Missile Range, NM.
3. Georgia Institute of Technology Research Institute, Atlanta, GA.
4. Illinois Institute of Technology Research Institute, Chicago, IL.
5. U.S. Army Laboratory Command, Adelphi, MD.
6. U.S. Army Construction Engineering Research Laboratory, Champaign, IL.
7. Sanders Associates, Nashua, NH.
8. U.S. Army Communications-Electronics Command, Ft. Monmouth, NJ.
9. COLSA Incorporated, Huntsville, AL.
Electronic Distribution
A file transfer protocol (tip) server has been established for distributing computer
codes and related matter to acousticians with access to Internet. The server, which is
accessible from sites all over North America as well as Europe and Austrialia, has files
containing the source code to the NASA Implicit Finite Difference (nifd) model. These
are available via anonymous ftp from euler.math.usma.edu. The Internet Protocol (IP)
address is 129.29.79.198 and the files are located in the/ftp/acoustics directory. These
files will be updated periodically as refinements are made.
In addition, acousticians wishing to share their codes with the acoustics
community may submit them directly to euler.math.usma.edu. They may be placed in
the/ftp/incoming directory. Questions regarding submission procedures should be
directed to robertson@euler.math.usma.edu.
Recent retrievals of NIFD
Date Originating machine Who
May 2 93 22:56 ckwang.gatech.edu
May 4 93 23:24 almaak.usc.edu
May 5 93 13:08 nimue.hood.edu
Apr 18 93 19.33 mesu7.ust.hk
Apr. 21 93 08:25 mines.u-nancy.fr
Mar 30 93 05:35 137.195.28.5
Apr 2 93 15:57 skule.ecf.toronto.edu
Mar 18 93 11:56 titan.yorku.ca
leem@ckw ang.gatecvh.edu
asdf@
mayfield@ nimue.hood.edu
ckleung@hkumea.hku.hk
smerzouk@ mines.u-nancy.fr
andrerw@uk.ac.hw.phy
lindsas@ecf.utoronto.ca
fs300021
- 10-
V. GRADUATE STUDENTS PERFORMING NASA RESEARCH
l°
°
°
,
o
,
.
Daniel P. Santandrea, Master of Science in Applied Mathematics, May 1989
[Currently at General Electric Corporation, Syracuse, NY].
Philip J. Schlatter, Master of Science in Applied Mathematics, May 1990 [Currently
at United States Military Academy, West Point, NY].
Michael J. Jaye, Master of Science in Applied Mathematics, May 1990 [Currently
at United States Military Academy, West Point, NY].
Michael L. Linnington, Master of Science in Applied Mathematics, May 1990
[Currently at United States Military Academy, West Point, NY].
Thomas M. Kastner, Master of Science in Applied Mathematics, May 1991
[Currently at United States Military Academy, West Point, NY].
Curtis W. Clark, Master of Science in Applied Mathematics, May 1991 [Currently
at Loral Corporation, Lexington, MA].
Iman W. Schurman, Doctor of Philosophy in Applied Mathematics, July 1991
[Currently at The Johns Hopkins University Applied Physics Laboratory, Laurel,
MD].
-11-


Research summary

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server