Index of content:
Volume 75, Issue 1, January 1984

Smoothed boundary conditions, coherent low‐frequency scatter, and boundary modes
View Description Hide DescriptionLow‐frequency coherent scatter from a rough surface may be conveniently investigated using a linear boundary condition applied to a smoothed surface, of the form ∂φ_{ s }/∂z=ηφ, where φ, φ_{ s } are solutions of the wave equation representing, respectively, the total and scattered field potentials. The validity of the theories discussed here is restricted to k h≲1, where k is the wavenumber and h the mean spacing between roughness elements. The constant η is a function of frequency, angle of incidence, and type of roughness; in the general case of scatterers distributed isotropically over an interface between two fluids it is sensitive to eight physical parameters. Methods of calculating η for various types of rough boundary are discussed, and comparisons are made—notably between the boss and the stochastic perturbation models. Also examined are interesting implications of the smoothed boundary conditions; e.g., the b o u n d a r y w a v e which is a true propagating mode corresponding to energy trapped in the vicinity of a rough surface, and which is only generated by a source near this surface (it thus differs fundamentally from the evanescent modes of a diffraction grating which may be excited by plane waves and are therefore not true boundary modes). For source and receiver near the boundary, and for negligible incoherent scatter, the farfield amplitude of the boundary wave may exceed that of the direct (normal) acoustic arrival—a fact which has been verified experimentally in model work. Incoherent scatter introduces an attenuation factor exp(−δr), where r is the source–receiver distance and δ is proportional to the sixth power of the frequency.

Matrix viscosity and cavity‐size distribution effects on the dynamic effective properties of perforated elastomers
View Description Hide DescriptionThe study presented here introduces a novel methodology to predict the (frequency‐dependent) effective material parameters characterizing the dynamic behavior of viscoelastic substances containing many randomly located air‐filled perforations. These composite materials have uses as underwater sound absorbers. The methodology described here is an extension of our earlier work which pertains to the case of gas‐filled perforations in nonabsorbing matrices. [G. Gaunaurd and H. Überall, J. Acoust. Soc. Am. 7 1, 282–295 (1982)]. That prior work was extended here to the case of absorbing matrices containing ensembles of cavities of various sizes following several arbitrary size‐distribution functions. The method accounts for the effect of resonances, for arbitrary levels of viscosity, for arbitrary cavity‐size distributions, and it is fundamental insofar as it generates direct predictions accounting for all these effects starting straight from the basic principles of Continuum Mechanics. Computer codes to implement the model predictions were generated, and a large number of pertinent plots of the frequency dependence (at fixed concentrations) or of the concentration dependence (at fixed frequencies) of the various effective moduli and other material descriptors have been computed and displayed in many graphs. Under various conditions the present results reduce to many of the earlier results available in the literature which serve as checkpoints. The various plots generated here pertain to various chosen cavity‐size distribution functions and to various selected levels of (dilatational and shear) absorption in the matrix. The generation and display of graphs such as these permit the present analysis of these matrix‐viscosity and size‐distribution effects mentioned in the title.

The transition matrix for acoustic and elastic wave scattering in prolate spheroidal coordinates
View Description Hide DescriptionA spheroidal‐coordinate‐based transition matrix is derived for acoustic and elastic wave scattering. The formalism is based on Betti’s third identity and an appropriately chosen set of vector spheroidal basis functions. Transition matrices are obtained for the scattering from an elastic inclusion in an elastic medium and in an inviscid fluid.

Geometrical theory of diffraction by an open rectangular box
View Description Hide DescriptionPredictions based on the geometrical theory of diffraction for sound radiation from a source within an open rigid rectangular box are compared with a set of experimental and numerical results obtained by Furue, Terai, and Matsu’ura (9th International Congress of Acoustics, Madrid, Spain, July 1977). The comparison with the experimental results shows a substantial verification of the theory.

Diffraction of waves and singular stresses in a soft ferromagnetic elastic solid with two coplanar Griffith cracks
View Description Hide DescriptionMagnetoelastodynamic stress intensity factors are computed for diffraction of normally incident longitudinal waves by two coplanar Griffith cracks in a soft ferromagneticelastic solid. The solid is permeated by a uniform magnetostatic field normal to the crack surface. The problem is formulated by means of integral transforms, and reduced to the solution of a singular integral equation of the first kind. Numerical calculations are carried out and stress intensity factors are obtained for several values of frequency, magnetic field, and geometrical parameter.

Acoustical wave propagation in cylindrical ducts: Transmission line parameter approximations for isothermal and nonisothermal boundary conditions
View Description Hide DescriptionApproximate expressions are given for the characteristic impedance and propagation wavenumber for linear acoustic transmission through a gas enclosed in a rigid cylindrical duct. These expressions are most complicated in the transition zone where the thermoviscous boundary layers are on the order of the tube radius. The approximations are accurate to within 1% for all frequencies and tube diameters except within the transition zone where the approximations are accurate to within 10%. A simple modification of the transmission line parameters is presented for the case where the tube walls are nonisothermal.

A temperature correlation for the radiation resistance of a thick‐walled circular duct exhausting a hot gas
View Description Hide DescriptionIt is often useful to know the radiation impedance of an unflanged but thick‐walled circular duct exhausting a hot gas into relatively cold surroundings. The reactive component is shown to be insensitive to temperature, but the resistive component is shown to be temperature dependent. A temperature correlation is developed permitting prediction of the radiation resistance from a knowledge of the temperature difference between the ambient air and the gas flowing from the duct, and a physical basis for this correlation is presented.

Frequency domain method for the prediction of the ultrasonic field patterns of pulsed, focused radiators
View Description Hide DescriptionA theoretical model is presented which can be used to calculate the pressure field patterns of pulsed, focused ultrasonic radiators in attenuating and nonattenuating media. Pressure pulses are calculated by superimposing continuous wave solutions at discrete frequencies. Due to the speed of the method, time signals can be calculated at many positions in the transducer beam in a reasonable amount of time. To test the model, theoretical predictions for the pressure signals are compared to hydrophone measurements for a conventional diagnostic transducer. In addition, signal envelopes are studied in order to determine the effects of attenuation and dispersion on the imaging characteristics of a focused radiator. This work may have significant application to the design of transducers for specific imaging purposes or to the analysis of the imaging process.

An analytical model for noise generated by axial oscillations of unbaffled cylindrical elements
View Description Hide DescriptionA simple method to predict the noisegenerated by cylindrical‐shaped machine elements in axial vibration is presented. An approximation of the Helmholtz integral equation valid when the receiver–source distance is much greater than either the cylinder’s diameter or length is used to determine the acoustic pressuregenerated by axial oscillations of cylinders at any aspect ratio or frequency. The results are used in developing free‐field and reverberent field design contours. Experimental evidence points to the validity of the prediction model. Included are two design problems and solutions that show the method can be used to reduce noisegenerated by cylindrical shaped bodies.

The acoustic radiation force on a heated (or cooled) rigid sphere—Theory
View Description Hide DescriptionA finite amplitude soundwave can exert a radiation force on an object due to second‐order effect of the wave field [L. V. King, Proc. R. Soc. London, Ser. A 1 4 7, 212–240 (1934)]. In this work we study the radiation force on a rigid small sphere (i.e., in the long wavelength limit), which has a temperature different from that of the environment. This investigation assumes no thermally induced convection and is relevant to material processing in the absence of gravity. Both isotropic and nonisotropic temperature profiles are considered. In this calculation the acoustic effect and heat transfer process are essentially decoupled because of the long wavelength limit. The heat transfer information required for determining the force is contained in the parameters which are integrals over the temperature distribution.

Acoustic streaming in a waveguide with slowly varying height
View Description Hide DescriptionAn analysis of acoustic streaming in a two‐dimensional waveguide having slowly varying height is presented. Special attention is paid to waveguides with cross sections that are small compared to the acoustic and/or wall wavelengths. It is shown that the dynamic behavior of the enclosed fluid can be parameterized by the values of three small parameters, ε, 1/S, and 1/R, where ε is the ratio of the typical duct height H _{0} to the wall wavelength L _{0}, 1/S is the ratio of the typical oscillatory particle displacement U _{0}/ω to the typical duct height H _{0} and 1/R is the ratio of the oscillatory boundary layer thickness l _{ν} to the typical duct height H _{0}. An analytical solution describing the streaming flow in the duct is given in terms of a regular perturbationsequence in ε. It is shown that the oscillatory pressure must satisfy the lossy Webster horn equation to O(ε^{2}) if the no slip boundary condition is to be satisfied. Outside the boundary layer it is shown that the time averaged slip velocity is the sum of two terms. The first term is proportional to the product of the incident and reflected wave amplitudes. The second term is proportional to the difference between the incident and reflected acoustic intensity of the wave. For small values of 1/S, 1/R, and ε the streaming solution given is shown to be valid until εR/S ^{2} becomes of O(1).

Acoustic streaming due to an oscillatory source near a plate
View Description Hide DescriptionHigh‐frequency oscillations of a source cause an oscillatory flow near a flat plate. In addition, a nonlinear steady flow is also generated by viscous interactions. The problem is solved by matched asymptotic expansions. It is shown that a strong steady toroidal recirculation cell exist around the unsteady source.

Sound‐speed profile sensitivity of deep‐ocean multipath receptions
View Description Hide DescriptionThe sensitivity of oceanic sound transmissions to the choice of a sound‐speed profile is analyzed using ray theory. The profile may be any one from a collection of depth‐dependent, single‐minimum profiles which can be used to model a deep‐ocean sound channel. Several configurations are considered with fixed source and receiver, separated by less than about 50 km, so that different types of ray propagation can occur. Given a specified profile, procedures are prescribed for constructing a simpler profile, for which all important acoustic quantities are either identical or negligibly different. The construction methods have physical interpretations and identify the critical aspects of profile data which influence transmissions. The ray geometries associated with the two profiles are shown to be very close. Useful formulas are presented which demonstrate that per‐ray phases and amplitudes corresponding to the simpler profile approximate accurately those of the specified profile. The total‐field phase and amplitude differences associated with the two profiles are discussed briefly. Thus, when our procedure is applied, propagation results are not sensitive to the type of profile selected.

The coherent Green’s function for acoustic propagation in a random ocean
View Description Hide DescriptionWe have derived an algorithm for calculating the coherent Green’s function of an acoustic wave propagating in an ocean possessing index‐of‐refraction fluctuations. This function is related to the so‐called strength parameter which can be used to characterize the statistics obeyed by the acoustic field. Since we are interested in a wave solution we do not make the geometric optics approximation. Consequently, it is necessary to generalize the usual form of the Markov approximation. This is done in analogy with Dashen’s investigations. Our analysis accounts for the ocean boundaries and the depth dependence of the mean index of refraction. It is, however, restricted to convergence zone propagation. The phenomenological model of internal waves introduced by Garrett and Munk is used to describe the random fluctuations in the index of refraction. The analysis is based on the use of a Feynman path integral. The path integral formalism is particulary well suited to the approximations we consider. The algorithm consists of solving the parabolic equation using the split‐step Fourier algorithm technique with an effective index of refraction term. The presence of the internal wave fluctuations are reflected in this term through an imaginary piece which attenuates the coherent Green’s function.

Acoustic studies of broadband scattering from a model rough surface
View Description Hide DescriptionExperimental measurements of the normal incidence underwater acoustic backscatter from a modelrough surface having Gaussian statistics with a rms height 0.22 cm and a correlation length 1.9 cm are presented. Scattering measurements were obtained over the frequency range 20–1200 kHz for a variety of transmitter and receiver distances from the model surface. A novel feature of the experiment was the use of a parametric array as the wideband, highly directional acoustic source. An important aspect of the study is the use of a Fresnel phase approximation in the development of the theoretical expressions; this approach allows an understanding of the range dependence of the scattering coefficients. Theoretical and experimental values of the normal incidence scattering coefficients show good agreement over the range of frequencies and transmitter/receiver distances employed.

The spatial coherence of sound scattered from a wind‐driven surface: Comparison between experiment, Eckart theory, and the facet‐ensemble method
View Description Hide DescriptionClay and Medwin [J. Acoust. Soc. Am. 4 7, 1419–1429 (1970)] performed an experiment in which they measured the spatial coherence of signals scattered from a wind‐driven surface in a water tank. The coherence values were obtained by cross‐correlating signals received at two hydrophones and were presented as a function of receiver separation. In this paper, a comparison is provided between these measured values and values predicted using (1) a technique based on Eckart theory [C. S. Clay, J. Geophys. Res. 7 1, 2037–2046 (1966)] and (2) the facet‐ ensemble method [W. A. Kinney e t a l., J. Acoust. Soc. Am. 7 3, 183–194 (1983)]. The former technique is presented by way of a review and provides an approximate single‐valued estimate of coherence independent of receiver separation. The facet‐ensemble method, on the other hand, provides precise estimates that are fully dependent on geometry. Agreement between the method and the experiment is good.

Underwater sound generation by breaking wind waves
View Description Hide DescriptionThe problem of identifying the source of wind‐generated underwater sound is reviewed. Amalgamated observations of the ambient noise reveal a similarity structure, both in the acoustical spectrum and wind dependency, which allows for a considerable simplification of the problem. Mechanisms of sound generation are discussed with particular reference to oscillating bubbles. Air entrainment by breaking waves and the probabilistic distribution of bubbles are discussed. A model for underwater noise generation by bubbles oscillating in a breaking wave is proposed. It is argued that the most intense sound is associated with bubbles the radius of which is comparable to the Kolmogorov scale length. A slight three‐eighths wind dependency is predicted for the frequency of the maximum intensity. Several arguments, one based on the number density of bubbles in a breaking wave, another based on the areal coverage of whitecaps, lead to the deduction that the sound intensity from a field of breaking waves varies as friction velocity to the three‐halves power. Agreement in structure and order of magnitude is demonstrated.

Response of elastic cylinders to convective flow noise I. Homogeneous, layered cylinders
View Description Hide DescriptionOne of the noise mechanisms experienced by passive towed sonar arrays is that of convective flownoise due to boundary layer turbulence generated as the array moves through the water at a fixed tow speed. The purpose of the present work is to arrive at quantitative predictions of the effects of convective flownoise using relatively simple model calculations. Line arrays are modeled as homogeneous, layered cylinders while turbulenteddies are modeled as random pressure fluctuations traveling at the convective speed of the eddies (about 80%) of the tow speed. The qualitative difference between solid and liquid fills is explained with this analysis. Solid‐filled arrays are more susceptible to convective flownoise than are liquid‐filled arrays because the noise‐carrying shear waves are highly attenuated in the liquid. The detailed analysis is presented both for homogeneous cylinders and for cylinders with multiple homogeneous layers. Examples are presented to illustrate the analysis and the numerical methods employed in the calculations.

Measurements on the origin of the wind‐dependent ambient noise variability in shallow water
View Description Hide DescriptionContributions of environmental quantities related to the noise source field and the propagation path are derived from the comparison of measurements of the wind‐dependent noise by omnidirectional receivers at a fixed North Sea station with shipborne measurements in the Baltic Sea. The influence of propagation loss on the wind‐dependent shallow water noise appears to be only marginal, even at extremely different sea areas. The quantity governing the noise spectrum level under uncontaminated conditions is the wind speed at the sea surface for which the second power law relation has been verified between 50 Hz and 20 kHz and above a ‘‘threshold’’ wind speed of ≊5 kts. Neither the characteristic height of the sea waves nor the wind turbulence at the reference height are relevant to the noise production, but both may indicate wind profile changes which originate an essential portion of the noise variability for a given wind speed. Further deviations from the second power law are attributed to a bubble layer effect under storm conditions reducing or enhancing the high frequency noise level thus yielding a spread of the average spectrum level of more than 20 dB.

Theoretical prediction of a backscattering maximum at Rayleigh angle incidence for a smooth liquid–solid interface
View Description Hide DescriptionA numerical integration method for the description of acoustic bounded beams is used to calculate possible backscattering strength from a smooth liquid–solid interface. It is shown that the backscattering strength is maximum for Rayleigh angle incidence. The influence of beam shape and beamwidth on the backscattering strength near the maximum is demonstrated.