Robert A. Zingarelli

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.

A wedge diffraction based scattering model for acoustic scattering from rough littoral seafloors

Models for acoustic scattering from rough surfaces based on Biot and Tolstoys (BT) exact wedge diffraction theory have proven accurate and useful in a number of experimental and numerical studies [1]. Because the BT solution is restricted to impenetrable wedges (acoustically hard or soft boundary conditions), scattering models based on the BT solution have thus far been limited to the rough air/sea interface where the actual boundary conditions are very nearly pressure-release (soft). Recently, important theoretical work [2,3] has extended the exact BT theory to density-contrast but isospeed wedges. This new development makes possible the application of wedge diffraction based scattering models to the roughness at the sea floor where the change in the acoustic impedance at the boundary is dominated by changes in density and only weakly affected by changes in sound speed. However, it is important to confirm that small amounts of sound speed contrast do not perturb the diffraction too much. To contribute to the understanding of how the diffracted wave is affected by sound speed contrast and get some idea as to the practical limitations of wedge-diffraction based scattering models for littoral seafloors, a simple numerical experiment involving a highly accurate Finite-Difference Time-Domain (FDTD) solution to the acoustic wave equation and a wedge-shaped boundary has been explored. This paper presents the results of FDTD experiments designed to quantify any changes in the diffracted field brought about by sound speed contrast. An ad hoc treatment of sound speed contrast is developed based on the requirement that the diffracted wave must smooth out the reflection discontinuity and preserve the continuity of the total field.

A variational data assimilation system for the range dependent acoustic model using the representer method: Theoretical derivations

This study presents the theoretical framework for variational data assimilation of acoustic pressure observations into an acoustic propagation model, namely, the range dependent acoustic model (RAM). RAM uses the split-step Padé algorithm to solve the parabolic equation. The assimilation consists of minimizing a weighted least squares cost function that includes discrepancies between the model solution and the observations. The minimization process, which uses the principle of variations, requires the derivation of the tangent linear and adjoint models of the RAM. The mathematical derivations are presented here, and, for the sake of brevity, a companion study presents the numerical implementation and results from the assimilation simulated acoustic pressure observations.

Time‐domain solutions for Rayleigh and Stoneley waves using the single‐scattering parabolic equation method.

The parabolic equation method implemented with the single‐scattering correction accurately handles range‐dependent environments in elastic layered media. Interfaces between elastic media may be treated efficiently by subdividing into a series of two or more single‐scattering problems [Kusel et al., J. Acoust. Soc. Am. 121, 808–813 (2007)]. In addition to environmental waveguide parameters, the procedure uses several computational parameters. The impacts of the number of interfacial scattering problems, an iteration scheme convergence parameter, and the number of iterations for convergence are shown on the accuracy and efficiency of the method. In particular, selection criteria for these parameters are developed. Fourier transforms and syntheses generate time‐domain solutions for seismic applications of interest. Examples for model waveguides show features of Rayleigh and Stoneley wave propagation, and comparisons with solutions from other methods are shown. [Work supported by the ONR.]

Inaccurate results from benchmark accurate ocean acoustic propagation models: It’s the implementation, not the model

Despite numerous publications that document the benchmark accuracy of several ocean acoustic propagation models, some users of these models continue to get inaccurate results. The problem is not with the model, but with the implementation of the model. The most common mistake in implementing range‐dependent acoustic models (e.g., parabolic equation models) is the selection of model parameters (e.g., step size, grid spacing, attenuating bottom depth). Another common mistake is lack of sufficient environmental data to the model. The number of implementation errors could be significantly reduced, if the user would abandon the erroneous belief that the model is a ‘‘black box’’ that will always produce the correct answer in a single run. Knowledgeable users methodically vary the input parameters and make repeated runs until model convergence is evident. It is possible to preselect model parameters, and couple the acoustic model with its environmental databases, so that a general user can obtain an accurate res...

FDTD modeling of low‐frequency sea surface reverberation in the presence of a near‐surface bubble layer

There exists a well‐documented discrepancy between the low to moderate frequency (150 Hz<f<1.5 kHz), low‐grazing angle (<30 degrees) reverberation‐derived backscattering strengths collected at sea and the predictions provided by rough surface scattering models. One of the central features of the data/model comparisons in this regime is the strong wind speed dependence exhibited in the data and the very weak wind speed dependence predicted by surface scattering models. In a previous study [Keiffer et al., J. Acoust. Soc. Am. 97, 227–234 (1995)], a heuristic model was used to explore the hypothesis that bubble‐induced refraction may modify the insonification of the air/sea interface and significantly enhance the surface reverberation in this frequency range. In the present work, a finite difference time domain (FDTD) solution to the linear acoustic wave equation is exercised in numerical experiments designed to unambiguously demonstrate the significant impact that near‐surface, bubble‐induced refraction can...

Dynamic coupling of primitive equation soliton models and acoustic propagation models via acoustic mode analysis

Simulation studies of acoustic mode conversions resulting from underwater acoustic fields propagating through solitons in the Strait of Messina have indicated a novel way of coupling oceanographic models with ocean acoustic models using dynamic feedback from the acoustic analysis. A weakly nonhydrostatic primitive equation model was used to generate simulations of oceanographic soliton fields in the Strait of Messina. The soliton fields were used to study acoustic mode conversions as the acoustic field passed through the solitons and propagated upslope. Conversion into modes having higher bottom loss have shown resonance effects similar to that observed in the Yellow Sea. Oceanographic parameters were adjusted so that amplitude and phase of the first two wavelengths of the simulated soliton fields were in agreement with measured soliton data. However, identical acoustic signals propagated through the simulated and measured soliton fields produced different acoustic mode structures. Oceanographic parameter...

Anomalous signal loss in the Yellow Sea, revisited: Coupling the acoustics with model‐generated oceanographic realizations

In a seminal paper, Zhou et al. [J. Acoust. Soc. Am. 90, 2042–2054 (1991)] introduced the concept of large anomalous signal loss due to a resonance effect caused by solitons (internal waves traveling along the thermocline). They assumed that solitons were present and produced a remarkable comparison between acoustic model predictions and their acoustic measurements taken over a four‐year period. They did not take sufficient oceanographic measurements to confirm the existence of solitons. Numerous investigators have tried to duplicate their pioneering work in similar shallow‐water environments with solitons present. Signal reduction, mode conversions, and resonance‐like effects have been observed, but signal loss of the magnitude measured by Zhou et al. have not been observed. We have used a primitive equation soliton model and the tidal flow near the Shandong peninsula to generate soliton simulations that flow into the Yellow Sea near the region where Zhou et al. made their acoustic measurements. We are p...

Results from a simulation study of mode coupling due to acoustic wave‐soliton interactions

There is a strong interest in understanding the interactions between ocean acoustic waves and shallow water solitons. Central to these interactions are the acoustic mode conversions caused by the solitons. Such mode conversions potentially occur each time the acoustic wave and soliton interact; however, at certain combinations of acoustic‐oceanographic wavelengths, the interactions can produce large losses in acoustic signal. Mode coupling results will be discussed from simulation studies that examined the signal loss due to interactions with solitons in the Strait of Messina. Coupled mode formulations were avoided so that interpretations of results were not dependent upon any particular mode coupling scheme. Rather, the full‐wave, two‐way, finite‐element model, FFRAME, was used to produce numerically accurate predictions of the complex pressure field as it passed through the soliton. This complex field was then decomposed into its component wave numbers via an FFT to determine the mode structure. This si...

A search algorithm to predict the resonance frequency of a shallow‐water soliton packet

Recently a number of researchers have performed acoustic simulations of shallow‐water regions that contain large amplitude internal waves (solitons). Their results have confirmed earlier findings: (a) mode conversions, due to acoustic interactions with soliton packets, can produce a large loss in acoustic transmission; (b) this loss occurs within a narrow band of acoustic frequencies (about the resonance frequency); and, (c) the transmission loss is most prominent when there is strong coupling between the lower‐order (water‐borne) propagation modes and the higher‐order, very lossy (bottom interacting) modes. Using this knowledge, development of a search algorithm has begun to predict the resonance frequency of a shallow‐water soliton packet. In this proof‐of‐concept work, a shallow‐water soliton model was used to generate replicas of the soliton fields in the Strait of Messina. The allowable acoustic mode conversions were calculated and correlated with the dominate spatial wave numbers of the soliton pack...