Naval Underwater Systems Center Research Articles

Nonlinear acoustics and the Acoustical Society of America

The modern era of nonlinear underwater acoustics had its roots in a remarkable session at the 57th ASA meeting at Providence RI in June, 1960, chaired by Westervelt, of Brown University, who also presented his remarkable new theory of the parametric acoustic array. This conceptual “device” enables highly directive low frequency sound to be created from the nonlinear interaction of two high frequency radiations of high directivity, which was confirmed in a model- tank study paper in this session by Brown Univ. Professor Robert Beyer and student Bellin. JASA has been the major worldwide forum for publications in nonlinear underwater acoustics, ever since, with much of the U.S. work done at the Navy Underwater Sound Laboratory and its successor, the Naval Underwater Systems Center, as well as the Applied Research Laboratories of the University of Texas at Austin. Topics have included parametric arrays, the nonlinear generation of harmonic radiations and transients, acoustic saturation, nonlinear transmitting and receiving sonar and imaging, and many practical applications to underwater sound and acoustical oceanography. Current and/or developing applications include underwater communications, backscattering measurements, penetration of narrow beams into sediments, sub-bottom profiling, and fish school quantification and classification. These and other topics are reviewed and recent implementations are described. [Work supported by ARL:UT Austin.]

Parametric acoustic array development at the U.S. Navy’s New London, Connecticut laboratory.

A brief history of the development of parametric acoustic sources at the U.S. Navy Underwater Sound Laboratory (USNUSL), and its successor, the Naval Underwater Systems Center is presented. Inspired by Robert Mellen, the Parametric Sonar Group was formed to explore the practical implications of Westervelt’s idea for underwater acoustics. Spanning more than two decades, this research pursued various potential applications exploiting the unique characteristics of parametric sources, including echo‐ranging in reverberant environments, communications involving voice, data, music, and video signals, target‐strength measurements, bottom bathymetry, high‐resolution sub‐bottom profiling, and measurements of scattering and reflection from surfaces. Parametric source design procedures were developed, and guidelines were established for diagnosing and avoiding undesirable effects, such as difference‐frequency instability and spurious nonlinearities, such as direct radiation from the projector, cavitation, and receiver nonlinearity. Theoretical models extended the Westervelt theory to realistic primary fields. For planar projector arrays, parametric source design curves, valid for levels in the primary far field, enabled designers to predict performance without resorting to computer calculations. To obtain source‐levels and beam‐widths within the primary near field, where the secondary signal is generated, a computer program, called CONVOL5 in its present configuration, can be used to obtain more detailed performance predictions.

An autonomous moored ocean profiler

An unconventional set of environmental and acoustic data, measured from an autonomous moored ocean profiler, is presented. The profiler is a programmable robotic underwater winch and data acquisition system that cycles vertically through the water column. The system profiles at pre‐determined time intervals, surfaces to transmit data via RF links, and can be deployed for up to 180 days. Built by WETLabs Incorporated (Western Environmental Technology Laboratories) for the Naval Underwater Systems Center (NUWC), the system is outfitted with three environmental sensors and two acoustic vector sensors. The environmental sensors include; a Nortek Vector velocimeter which samples current components and characterizes surface wave velocities, a Seabird FastCAT Conductivity, Temperature, Depth (CTD) sensor; and a Wetlabs Fluorometer‐Turbidity optical sensor that measures both chlorophyll‐a and turbidity. The Wilcoxon acoustic vector sensors measure acoustic pressure and the three components of acoustic particle acceleration. Wilcoxon Research (a subsidiary of Meggitt Corporation) and Applied Physical Sciences (APS) have developed underwater acoustic vector sensors for many applications. The quality and sensitivity of these vector sensors has steadily improved. A review of early (pre‐2002) vector sensor development efforts is discussed.

Adaptive beamforming at very low frequencies in spatially coherent, cluttered noise environments with low signal-to-noise ratio and finite-averaging times

Realistic simulations with spatially coherent noise have been run in order to compare the performance of adaptive beamforming (ABF), inverse beamforming (IBF), and conventional beamforming (CBF) for the case of finite-averaging times, where the actual spatial coherence of the acoustic field, or covariance matrix, is not known a priori, but must be estimated. These estimation errors cause large errors in the ABF estimate of the directionality of the acoustic field, partly because ABF is a highly nonlinear algorithm. In addition, it is shown that ABF is fundamentally limited in its suppression capability at very low frequency (VLF), based on the sidelobe level of the conventional beampattern in the direction of the noise interferer [G. L. Mohnkern, "Effects of Errors and Limitations on Interference Suppression," NOSC Technical Document 1478, Naval Ocean Systems Center (1989)]. The simulations include a low-level plane wave signal of interest, a stronger noise plane wave interferer, and spatially random background noise. Both IBF and ABF performed significantly better than CBF, and IBF's performance was slightly better than ABF's performance. The performances of IBF and the ABF algorithm, the minimum variance distortionless response (MVDR) [A. H. Nuttall and D. W. Hyde, "Unified Approach to Optimum and Suboptimum Processing for Arrays," USL Report Number 992, Naval Underwater Systems Center, New London, CT (22 April 1969)] were recently compared independently [J. S. D. Solomon, A. J. Knight, and M. V. Greening, "Sonar Array Signal Processing for Sparse Linear Arrays," Defense Science and Technology Organization (DSTO) Technical Report (June 1999)] using measured data, with the result that IBF outperformed MVDR. This result is significant because MVDR requires orders of magnitude more processing power than IBF or CBF.

Low-frequency volume scatter and accompanying bioacoustic measurements in the Gulf of Alaska

Volume scattering from 200 to 1500 Hz was measured during the Gulf of Alaska surface scatter and air/sea interaction experiment occurring in February 1992. Scattering strength as a function of frequency and depth was measured and layer strength and column strength were calculated using a vertically bistatic measurement technique developed by Stockhausen and Figoli [SACLANT ASW Research Center Technical Report No. 225, 15 May 1973]. These measurements were accompanied by concurrent measurements of size/depth distributions of the fish population present using a dual beam echosounder system. Fish distributions were used to predict layer and column strength by employing the NUWC Interval Column Strength Model developed by Saenger etal. [Naval Underwater Systems Center Technical Report No. 9001 (31 December 1991)]. Comparisons of the measured and predicted results show that low-frequency scattering resonances may be related to biologics.

Approximation Methods in Discrete Spatial Density Analysis for Finite Populations

The author's three-parameter square-root model for the measurement of discrete spatial density in human populations was previously derived under the assumption that exact coordinate locations of the density points were available. The model, called the population density index (PDI) model, has been expanded to include a set of routines for calculating two-dimensional spatial density measures based upon in situ geometric approximations of the interobject Euclidean distance measure for any finite sample size. The derivation and specification of the algorithm for the abbreviated calculation routines are presented and exemplified. The author has been able to apply the methods of the PDI model to submarine environments at the U.S. Naval Underwater Systems Center, resulting in several U.S. Patent applications.

The automated production control documentation system

A prototype software system was developed for the U.S. Naval Underwater Systems Center(NUSC) as a demonstration of the Cleanroom Software Engineering methodology. The Cleanroom method is a team approach to the incremental development of software under statistical quality control. Cleanroom's formal methods of Box Structure specification and design, functional verification, and statistical testing were used by a four-person team to develop the Automated Production Control Documentation(APCODOC) system, a relational database application. As is typical in Cleanroom developments, correctness of design and code were ensured through team reviews. Eighteen errors were found during functional verification of the design, and nineteen errors were found during walkthrough of the 1820 lines of FOXBASE code. The software was not executed by developers prior to independent testing (i.e., there was no debugging). There were no errors in compilation, no failures during statistical certification testing, and the software was certified at the target levels of reliability and confidence. Team members attribute the ultimate error-free compilation and failure-free execution of the software to the rigor of the methodology and the intellectual control afforded by the team approach.

Numerical Modeling and Solution of Galvanic Corrosion Systems: Part I. Governing Differential Equation and Electrodic Boundary Conditions

Abstract This is the first in a pair of papers describing the development of the computational corrosion analysis accomplished at the Naval Underwater Systems Center and the University of Connectic...

Measurement and modeling of acoustic waves in the 50- to 600-Hz range at the Hudson Canyon site

Measurements of the shallow-water propagation of acoustic waves on the New Jersey continental shelf were conducted by the Naval Underwater Systems Center, September 1988. On the same site, accurate measurements of geoacoustic properties were obtained by Yamamoto et al. (1988) using the bottom shear modulus profiler (BSMP) method invented by T. Yamamoto. The bottom properties extracted by the BSMP inversion method were introduced to SAFARI computer code for modeling of normal-mode acoustic propagation by the author. Favorable agreement has been found between model calculations and results of the acoustic propagation experiment conducted by NUSC. Comparison has revealed findings about the contributions of the compressional and shear wave characteristics of the seabed to the acoustic waveguide. The compressional wave profile has been found to contribute to the characteristics of the acoustic waveguide modal structure, while the shear wave profile has been found to contribute only to the attenuation of the acoustic wave propagation. [This work sponsored by the Office of Naval Research.]

A Proposed Model for the Measurement of Population Density

A mathematical model is proposed to measure population density using a formula called the population density index ( PDI). The population density index model includes a measure of interperson distance and is scaled for geometric area. The population density model measures population density with greater precision and flexibility than the conventional population density model. The population density index model is designed for small-scale projects involving as few as two and as many as one hundred density points. The derivation of the model is presented, along with an example of its use in a research project at the Naval Underwater Systems Center.

A Crowding Index for Finite Populations

The classical definition of population density used in social science disciplines as a measure of density or physical crowding has severe shortcomings since actual spatial orientation is disregarded. A formula is proposed to measure physical crowding or population density which corrects the deficiency of the conventional formulation. As a generalization of the Euclidean distance formula, the proposed index measures relative population density as a function of spatial orientation and size of geometric area. Three mathematical properties of the index stated as conjectures have been supported by Monte Carlo simulations. The formula is evaluated and justified on three key scientific criteria: parsimony, mathematical soundness and empirical verifiability. Crowding is an obvious problem in the small compartmentalized workspaces of U.S. Navy nuclear submarines. The measurement of physical crowding by use of the proposed formula in Concepts of Operations Experiments conducted at the Newport Laboratory of the Naval Underwater Systems Center is reported and discussed.

A PROPOSED MODEL FOR THE MEASUREMENT OF POPULATION DENSITY

A mathematical model is proposed to measure population density using a formula called the population density index (PDI). The population density index model includes a measure of interperson distance and is scaled for geometric area. The population density model measures population density with greater precision and flexibility than the conventional population density model. The population density index model is designed for small-scale projects involving as few as two and as many as one hundred density points. The derivation of the model is presented, along with an example of its use in a research project at the Naval Underwater Systems Center.

A CROWDING INDEX FOR FINITE POPULATIONS

The classical definition of population density used in social science disciplines as a measure of density or physical crowding has severe shortcomings since actual spatial orientation is disregarded. A formula is proposed to measure physical crowding or population density which corrects the deficiency of the conventional formulation. As a generalization of the Euclidean distance formula, the proposed index measures relative population density as a function of spatial orientation and size of geometric area. Three mathematical properties of the index stated as conjectures have been supported by Monte Carlo simulations. The formula is evaluated and justified on three key scientific criteria: parsimony, mathematical soundness and empirical verifiability. Crowding is an obvious problem in the small compartmentalized workspaces of U.S. Navy nuclear submarines. The measurement of physical crowding by use of the proposed formula in Concepts of Operations Experiments conducted at the Newport Laboratory of the Naval Underwater Systems Center is reported and discussed.

Human Factors Engineering Methodologies in Submarine Combat Systems Concept of Operations Experiments

Concept of Operations Experiments (COOPEXs) are conducted at the Naval Underwater Systems Center to evaluate submarine combat system operability through structured walkthroughs of submarine missions in a full-scale replica of the combat system environment. Data were collected from one COOPEX for the purpose of piloting human factors engineering methodologies. Partial results based on a different COOPEX scenario are reported and compared. The data reduction and analysis procedures of digraph analysis, Q-analysis, multidimensional scaling and crew density were applied to assess combat system information flow and configuration effectiveness. Results revealed the potential for significantly enhancing submarine combat system performance when applied to larger, more complex data sets. Plans for subsequent research are discussed.

Modeling of fluid‐injection effects on flow noise

Based on Naval Underwater Systems Center [communications with E. Payne of NUSC] and Soviet [Sov. Phys. Acoust. 30(5), 394–397 (1984)] water‐tunnel data, the Corcos wall‐pressure model was modified to include fluid‐injection effects. Boundary‐layer parameters were used to model the wall‐pressure frequency spectral density and the longitudinal cross‐spectral density. Using predictions from a Martin Marietta boundary‐layer code, favorable comparisons were made to the NUSC measured boundary‐layer profiles and wall‐pressure frequency spectra. Excellent agreement was obtained for both the effect of injection rate and the reduced effectiveness of fluid injection with distance from the injection source. Calculated wavenumber spectra showed that at low frequencies (less than about 200 Hz) spectral levels increased with injection, while at higher frequencies spectral levels decreased. The predicted convective peaks shifted to higher wavenumbers due to the decrease in convective velocity with increasing injection ra...

The effects of boundary surface inhomogeneities on acoustic scattering. I. Theory

Analytical methods of Marsh [J. Acoust. Soc. Am. 33, 330–333 (1961)] and Kuo [J. Acoust. Soc. Am. 36, 2135–2142 (1964)] are applied to high-frequency acoustic wave scattering from an ocean bottom of roughness amplitude typically quite small in comparison with the acoustic wavelength of interest. The bottom surface variation in acoustic velocity is considered negligible but the bottom surface variation in density is considered appreciable and included in the model. The analytical result indicates the possibility of a new scattering effect in grazing incident directions due to correlated roughness and density variations. When there exists an identifiable dominant roughness wavenumber, the theory predicts discrete backscattering. This phenomenon was observed in an experiment reported by Roderick and Dullea (TD 7181, Naval Underwater Systems Center, 1984). When the dominant roughness wavenumber is zero, the result is that of Rayleigh’s flat boundary. When the dominant roughness wavenumber is low compared to acoustic wavenumber, the result is that of the Kirchhoff approximation.

Design model of large, uniform, conformal arrays of bender bar and flextensional transducers

The single element design technology of flextensional and bender bar transducers is several decades old but use of either type of transducer in conformal arrays presents newer and more formidable design problems. When the array is very large the effects of edge diffraction on the outer elements can be ignored to generate a zeroth ordered waveguide design model to estimate radiation loading at any steering angle. Highly eccentric shelled flextensionals and bender bar transducers are then included in one common format. Since both types are largely flexural, they are resonant at frequencies where the interelement spacing is much smaller than a wavelength in water and only the low‐frequency inertial and plane‐wave volume flow components of loading need be determined. Several array geometries have been studied and the reactive loadings calculated. This paper shows both the theoretical and numerical results of various mass loadings as functions of array and element geometry. [Research supported by the Naval Underwater Systems Center, New London; the Naval Ocean Systems Center, San Diego; the Electric Boat Division of General Dynamics.]

An improved formula for wavefront curvature ranging based on measuring the normal curvature of wavefronts

The conventional formula for wave‐front curvature ranging degrades as the source moves away from broadside. This is because it is known [G. C. Carter, J. Acoust. Soc. Am. 65, 528–530 (1979)] that the conventional formula is equivalent to predicting range by triangulation, and this produces poor predictions in the presence of the refraction that is encountered off broadside. An improved formula that partially corrects for refraction is presented. It calculates the so‐called normal curvature of the wave front—the curvature where the wave front intersects the plane containing both the line through the array of receivers and the line perpendicular to the wave front. This normal radius of curvature is an improved approximation for the range when the source moves away from broadside. The improved and the conventional formulas are compared in examples. [Work supported by the Naval Underwater Systems Center, and the Naval Air Development Command.]

Function theoretic methods for acoustic wave propagation in the ocean

In this approach to modeling the sound propagation in the ocean, function theoretic methods are used in partnership with numerical methods. The problem of computing a sound field in the ocean is greatly simplified by using a two‐pronged approach involving (1) function theoretic methods that analytically incorporate the major features of the ocean and its bounding surfaces, including the radiation condition and the average index of refraction, and (2) numerical methods to model the effects of the secondary but detailed features of the ocean and its boundaries. For example, to model a sound field in a uniform ocean with perfectly reflecting boundaries over a long distance is a difficult numerical problem but a trivial analytical problem. In our two‐pronged approach, numerical techniques are used only to compute the changes that are observed as a result of perturbing the ocean from its analytical idealization. [This work was supported by Code 10 and Code 3332 of the Naval Underwater Systems Center.]

Low-frequency ocean surface noise sources

The interaction of the wind with the ocean surface has long been recognized as the major source of ocean ambient noise. High-frequency noise data 1200 to 2 kHz) has consistently been found to have strong wind-dependent characteristics associated with spray, splashes, bubbles, and rain. Recently, wave-wave interaction has been shown to be a source of infrasonic (0.2 to 2 Hz) noise and ocean bottom microseisms. Generally, the low-frequency noise (2 to 20 Hz) is associated with noise from distant ships. However, narrow-hand (as opposed to 1/3-octave) measurements show in addition to the noise from ships a wind-dependent characteristic. Furthermore, mid-ocean basin vertical directionality measurements show noise intensity near the horizontal with a broad frequency characteristic in diverse geographic locations. These results suggest a wind-generated noise due to a mechanism such as wave-wave interaction, wind turbulence, or the interaction of surface waves with turbulence is coupled into the mid-basin sound channel by either a shallowing sound channel such as found at high latitudes or a down-slope conversion process due to the basin boundaries and sea mounts. Theoretical expressions are derived from first principles following the approaches of Yen and Pertone [Naval Underwater Systems Center TR5833 (1979)] and Huon Li [Naval Ocean R&D Activity, TN89 (1981)] yielding the frequency-dependent radiation characteristics for wave-wave interaction, wind turbulence, and wave-turbulence interaction. These results show that wave-turbulence interaction is a possible source of wind-driven noise in the 10- to 200-Hz regions. Other possible mechanisms such as nonlinear capillary wave interactions are discussed and compared to this wave-turbulence mechanism.