Richard S. Keiffer

A model for variations in the range and depth dependence of the sound speed and attenuation induced by bubble clouds under wind-driven sea surfaces

When modeling sound propagation through the uppermost layers of the ocean, the presence of bubble clouds cannot be ignored. Their existence can convert a range-independent sound propagation problem into a range-dependent one. Measurements show that strong changes in sound speed and attenuation are produced by the presence of swarms of microbubbles which can be depicted as patchy clouds superimposed on a very weak background layer. While models suitable for use in acoustic calculations are available for the homogeneous bubble layer (which results from long time averages of the total bubble population), no similar parameterizations are available for the more realistic inhomogeneous bubble layer. Based on available information and within the framework of a classification scheme for bubble plumes proposed by Monahan, a model for the range and depth dependence of the bubbly environment is developed to fill this void. This model, which generates a possible realization of the bubbly environment, is then used to calculate the frequency-dependent change in the sound speed and attenuation induced by the presence of the bubble plumes. Time evolution is not addressed in this work.

The impact of the background bubble layer on reverberation‐derived scattering strengths in the low to moderate frequency range

The impact that a near‐surface, range‐independent background or persistent bubble layer may have on the derivation of sea surface backscattering strengths from reverberation measurements is examined. A simple ray model is proposed to account for the refractive and attenuating effects of the bubble layer and is used to calculate the modified insonification of the air–sea interface. This simple approach is validated against a highly accurate numerical solution. Scattering at the interface is handled via first order small perturbation theory. The combined propagation/scattering model is exercised in the low‐ to moderate‐frequency range in order to examine bubble‐induced modifications to sea surface backscatter calculations. Results indicate that the refractive effects due to the background bubble layer significantly enhance scattering levels as a function of wind speed. Furthermore, reasonable variations in the background bubble spectrum are shown to yield scattering levels that compare quite well with explo...

A time domain rough surface scattering model based on wedge diffraction: Application to low-frequency backscattering from two-dimensional sea surfaces

A time domain method for calculating the acoustic impulse response of impenetrable, rough, two-dimensional (2D) surfaces is presented. The method is based on an extension of the wedge assemblage (WA) method to 2D surfaces and objects. Like the WA method for one-dimensional (1D) surfaces, the approach for 2D surfaces uses Biots and Tolstoys exact solution for the impulse response of an infinite impenetrable wedge [J. Acoust. Soc. Am. 29, 381-391 (1957)] as its fundamental building block. The validity of the WA method for backscattering from 2D sea surfaces is assessed through comparisons with calculations based on Milders operator expansion (OE) method [J. Acoust. Soc. Am. 89, 529-541 (1991)]. Average intensities for backscattering from 2D fully developed seas (20 m/s wind speed) were computed by the WA and OE methods using 50 surface realizations and compared at 11 frequencies between 100 and 200 Hz. A single, moderately low grazing angle of incidence (20 degrees) and several scattered grazing angles (90 degrees, 45 degrees, 20 degrees , and 10 ) were considered. Excellent overall agreement between the two models was obtained. The utility of the WA method as a tool to describe the physics of the scattering process is also discussed.

An evaluation of the Kirchhoff approximation in predicting the axial impulse response of hard and soft disks

To test the ability of the Kirchhoff approximation for estimating the various components in the near‐field impulse response of a circular disk, the predictions from a time domain formulation of the Helmholtz–Kirchhoff solution [Trorey, Geophys. 35, 762–864 (1970)] are benchmarked against results obtained via the Fourier synthesis of highly accurate frequency domain solutions [Kristensson and Waterman, J. Acoust. Soc. Am. 72, 1612–1625 (1982)]. In these numerical experiments, a collocated point source and receiver lie on the symmetry axis of an acoustically hard (rigid) or soft (pressure release) disk. A time‐domain analysis is carried out in order to unambiguously evaluate the Kirchhoff approximation for different components of the scattered field. It is found that, while Helmholtz–Kirchhoff predicts the correct reflected component, it fails to accurately predict the strength of the diffracted component. The magnitude of the error depends on whether the disk is soft or hard and on the source/receiver heig...

Coupling scattering from the sea surface to a one‐way marching propagation model via conformal mapping: Validation

Propagation models in underwater acoustics usually incorporate sea surface scattering effects in an ad hoc manner which in most cases requires making severe approximations. In particular, to include in a coherent manner in a marching acoustic propagation model the scattering that occurs at a rough sea surface poses a serious problem. Dozier [J. Acoust. Soc. Am. 75, 1415–1432 (1984)] introduced a rigorous approach in the framework of the split‐step parabolic equation model, which used a sequence of conformal mappings to flatten segments of the sea surface locally. Each conformal mapping preserved the elliptic form of the wave equation. In each transformed space the parabolic approximation is made and the solution advanced one range step. The method has the attractive feature of handling surface roughness within a propagation model in a mathematically consistent manner, including refraction and multiple surface interactions when and where they occur. In this work the technique developed by Dozier is impleme...

The impulse response of an aperture: Numerical calculations within the framework of the wedge assemblage method

A numerical calculation technique applicable to arbitrary aperture shapes on which Dirichlet (soft) or Neumann (hard) boundary conditions exist is described. The method is based on a generalization of the wedge assemblage (WA) method to fully two‐dimensional surfaces and yields the impulse response directly. Benchmark tests of the technique are conducted for the case of a circular aperture. The results are in near perfect agreement with the reference solution (provided by a T‐matrix code). In addition to a solid validation of the extended WA method, it is shown in this paper that multiple scattering effects can be accurately included. Finally, the physical insight that the WA method offers is demonstrated through its ability to completely and accurately dissect the scattered field into reflected, diffracted, and multiple diffracted components.

On the validity of the wedge assemblage method for pressure‐release sinusoids

In the past, the wedge assemblage (WA) method for calculating the acoustic scattering from rough, long‐crested, or corrugated surfaces has been compared with both experimental data and exact theory with good results. Nevertheless, significant questions about what physics is included in the method and its realm of validity remain unanswered. In this paper, the WA method is applied to scattering from pressure‐release sinusoidal surfaces in order to further explore these topics. Comparisons with accurate benchmark calculations are carried out over a broad range of kh and kΛ (k is the acoustic wave number; h and Λ are the amplitude and wavelength of the sinusoid, respectively) indicate that the primary limitation of the WA method stems from its current failure to include multiple scattering effects. It is also shown that quite good agreement with the benchmark can be achieved by a ‘‘diffraction‐only’’ WA model even when kh≪1 and ‘‘reflection‐like’’ scattering patterns are observed.

Finite-difference time-domain modeling of low to moderate frequency sea-surface reverberation in the presence of a near-surface bubble layer

A finite-difference time-domain (FDTD) solution to the two-dimensional linear acoustic wave equation is utilized in numerical experiments to test the hypothesis that near-surface, bubble-induced refraction can have a significant impact on low to moderate frequency sea-surface reverberation. In order to isolate the effects of bubble-modified propagation on the scattering from the air/sea interface from other possible phenomena such as scattering from bubble clouds, the bubbly environment is assumed to be range independent. Results of the study show that both the strong wind-speed dependence and the enhanced scattering levels of the order found in the reverberation data are obtained when a wind-speed-dependent bubble layer is included in the modeling.

Impulse response of a density contrast wedge: Practical implementation and some aspects of its diffracted component

Abstract Davis and Scharstein have recently derived a complete solution for the impulse response of a density contrast wedge (Davis AMJ, Scharstein RW. J. Acoust. Soc. Am. 1997, 101, 2821–1835). However, the general solution given as a sum of residues, reduces to a closed form only for a discrete set of wedge angles. To circumvent this limitation and make the solution available for arbitrary angles, the explicit form for the residues is provided and the numerical implementation of the solution is discussed. The solution is then applied to the analysis of the diffracted field and physical aspects are analyzed. ©

Modeling the propagation from a horizontally directed high-frequency source in shallow water in the presence of bubble clouds and sea surface roughness

Among the many factors affecting the propagation of sound in shallow water, surface-generated microbubbles have remained virtually unexplored. The collection of microbubbles, bubbles which usually do not result in a uniform layer, presents a complex structure that varies not only in depth but also in range, and can be characterized as a collage of bubble clouds. A numerical procedure is developed in which the bubble clouds are modeled following a classification scheme proposed by Monahan [Natural Physical Sources of Underwater Sound, edited by B. V. R. Kerman (Kluwer Academic, Dordrecht, 1993), pp. 503–517]. An effective complex index of refraction of the bubble mixture is calculated for each point of the resulting range-dependent environment. The combined effect that the sea surface roughness and the bubbly environment have on forward propagation is then modeled through a high fidelity model [Norton et al., J. Acoust. Soc. Am. 97, 2173–2180 (1995)] which combines a finite element Parabolic Equation model...