Simulation Of Acoustic Propagation Research Articles

Finite‐difference time‐domain simulation of acoustic propagation through a dispersive oceanic bubble cloud

Accurate modeling of pulse propagation and scattering is a problem in many disciplines. For the case of an acoustic wave propagating in a two‐dimensional non dispersive medium, a routine second‐order in time and space finite‐difference‐time‐domain (FDTD) scheme representation of the linear wave equation can be used to solve for the acoustic pressure. However, when the medium is dispersive, one is required to take into account the frequency‐dependent attenuation and phase speed. Until recently, to include the dispersive effects one typically solved the problem in the frequency domain and then Fourier transformed into the time domain. However, by using a theory proposed by Blackstock [D. T. Blackstock, J. Acoust. Soc. Am. 77, 2050 (1985)], the linear wave equation has been modified by adding an additional term that takes into account the dispersive nature of the medium. In this work a fourth‐order (in time and space) 2‐D FDTD scheme, which includes attenuation and dispersion via the convolution operator, is used to model backscattering of broadband signals from a dispersive composite subsurface bubble cloud composed of two different plumes underlying a random rough sea surface. [Work supported by ONR/NRL.]

Finite-difference time-domain simulation of acoustic propagation in dispersive medium: An application to bubble clouds in the ocean

Accurate modeling of pulse propagation and scattering is a problem in many disciplines (i.e. electromagnetics and acoustics). For the case of an acoustic wave propagating in a two-dimensional non-dispersive medium, a routine 2nd order in time and space Finite-Difference Time-Domain (FDTD) scheme representation of the linear wave equation can be used to solve for the acoustic pressure. However when the medium is dispersive, one is required to take into account the frequency dependent attenuation and phase speed. Until recently to include the dispersive effects one typically solved the problem in the frequency domain and not in the time domain. The frequency domain solutions were Fourier transformed into the time domain. However by using a theory first proposed by Blackstock [D.T. Blackstock, J. Acoust. Soc. Am. 77 (1985) 2050. [1]], the linear wave equation has been modified by adding an additional term (the derivative of the convolution between the causal time-domain propagation factor and the acoustic pressure) that takes into account the dispersive nature of the medium. In the case of acoustic propagation through water, the water environment becomes strongly dispersive due to the presence of air bubbles that are present below the air–water interface.

Large eddy simulation of a forward–backward facing step for acoustic source identification

The feasibility of using a commercial CFD code for large eddy simulation (LES) is investigated. A first test on homogeneous turbulence decay allows a fine-tuning of the eddy viscosity with respect to the numerical features of the code. Then, a flow over forward–backward facing step at Reynolds number Re h =1.7×10 5 is computed. The results found show good agreement with the new LDA data of Leclercq et al. [Forward backward facing step pair: aerodynamic flow, wall pressure and acoustic characterization. AIAA-2001-2249]. The acoustic source term, recorded from the LES and to be fed into a following acoustic propagation simulation, is found to be largest in the separation from the forward step. The source terms structures are similar to the vortical structures generated at the front edge of the obstacle and advected downstream. Structures generated from the backward step rapidly break down into smaller scale structures due to the background turbulence.

Acoustic effects of near-bottom soliton packets

The winter 1997 Primer4 experiment was conducted on the shelfbreak and continental slope south of Cape Code in the Middle Atlantic Bight. Internal solitary waves were surveyed with rapid-sampling thermistor chains, current meters, and an upward looking ADCP. Using the available environmental data we have simulated the generation of these near-bottom solitary internal waves in this region using a forcing tidal velocity of 0.3 m/s to initiate the primitive equation Lamb model. The simulated soliton packets compare favorably in period and amplitude with the measured data taken in the winter 1997 Primer4 experiment. Previously, resonance effects leading to anomalous signal losses have been observed in numerous simulations of acoustic propagation through near-surface soliton packets. The objective of this work is to determine if similar resonance effects are caused by the interaction of the acoustic field with these near-bottom soliton packets. In contrast to our previous acoustic simulations, it was necessary to place the acoustic source and receivers above the thermocline for these near-bottom soliton packet studies. Simulation results will be presented that illustrate the similarities and differences between the acoustic effects produced by the near-surface and near-bottom soliton packets. [Work supported by ONR/NRL.]

Estimates of the prevalence of anomalous signal losses in the Yellow Sea derived from acoustic and oceanographic computer model simulations

The results from collocated oceanographic and acoustic simulations in a region of the Yellow Sea near the Shandong peninsula have been presented [Chin-Bing et al., J. Acoust. Soc. Am. 108, 2577 (2000)]. In that work, the tidal flow near the peninsula was used to initialize a 2.5-dimensional ocean model [K. G. Lamb, J. Geophys. Res. 99, 843–864 (1994)] that subsequently generated internal solitary waves (solitons). The validity of these soliton simulations was established by matching satellite imagery taken over the region. Acoustic propagation simulations through this soliton field produced results similar to the anomalous signal loss measured by Zhou, Zhang, and Rogers [J. Acoust. Soc. Am. 90, 2042–2054 (1991)]. Analysis of the acoustic interactions with the solitons also confirmed the hypothesis that the loss mechanism involved acoustic mode coupling. Recently we have attempted to estimate the prevalence of these anomalous signal losses in this region. These estimates were made from simulating acoustic effects over an 80 hour space-time evolution of soliton packets. Examples will be presented that suggest the conditions necessary for anomalous signal loss may be more prevalent than previously thought. [Work supported by ONR/NRL and by a High Performance Computing DoD grant.]

On verification of the new criterion of adiabaticity by numerical simulation of acoustic propagation through the polar front

To assess the adiabaticity of acoustic propagation in the ocean is very important for acoustic field calculation (forward problem) and tomographic retrieving (inverse problem). A new criterion of adiabaticity is proposed recently (Shang et al., 2001). In this paper, numerical simulation has been conducted for acoustic propagation through the Polar Front to verify the new criterion. Numerical results on the f (frequency)-m (mode number) plan demonstrate that the new criterion works very well for this extremely non-gradual ocean structure.

Time-domain simulation of acoustic propagation in a lined duct

An inviscid, spatial time-domain numerical simulation is employed to compute acoustic wave propagation in a duct treated with an acoustic liner. The motivation is to assess the effects on sound attenuation of bias flow passed through the liner for application to noise suppression in jet engine nacelles. Physically, the liner is composed of porous sheets with backing air cavities. The mathematical model lumps the sheets' presence into a continuous empirical source term which modifies the right-hand side of the momentum equations. This source term specifies the time-domain characteristics of the frequency-domain resistance and reactance of the liner's component sheets. Nonlinear behavior of the liner sheets at high sound pressure levels is included in the form of the source term. The source term constants are empirically matched to frequency-domain impedance data via a one-dimensional numerical impedance tube simulation. The resulting liner model is then incorporated into a two-dimensional Euler solver and used for simulations of a realistic duct configuration. Sound pressure levels and axially transmitted power are computed to assess the attenuation effects of various magnitudes of bias flow. Simulation results are compared to available experimental data from a geometrically similar lined duct.

A new method for calculating temporal intensity correlations in partially saturated scattering

Intensity correlations in time for acoustic scattering from internal waves are investigated using path integral methods. A new perturbative procedure for calculating the temporal intensity autocorrelation 〈I(x,0)I(x,t)〉, valid in the partially saturated scattering regime, is introduced. Partial saturation describes a situation in which smaller scales of the scatterer cause the geometrical raypath to fracture into myriad microrays but where the larger scales lead to correlation between these micromultipaths. This situation is of particular relevance in acoustic propagation through internal waves due to the wide range of vertical scales as well as the separability of the internal wave power spectrum. It is shown that the perturbative method being introduced has greater accuracy as well as a wider range of applicability than the standard method [Flatté et al., J. Acoust. Soc. Am. 77, 1723–1731 (1985)]. A computer simulation of acoustic propagation through an evolving internal wave field has been implemented to provide a basis for comparison with the theory. Application to calculation of higher moments of intensity will be discussed. [Work supported by ONR.]

Acoustic diagnostic for the polar front

The Polar frontal zone is known to have the highest contrast between properties of the divided water masses in Nordic seas. Acoustically, it is a strongly range-dependent environment. Numerical simulations of acoustic propagation in the frequency range of 20–200 Hz have been conducted for typical cases by using the IFD-PE and KRAKEN codes. The adiabaticity is strongly frequency dependent. For lower frequency, the inverted results of the frontal parameters based on the adiabatic modal travel time and modal horizontal refraction data can be obtained analytically using a simple ‘‘few parameter model’’ proposed by Kuz’kin [Acoust. Phys. 39(4), 402 (1993)]. The possibility of estimating the frontal parameters for a more complex realistic model will also be discussed. [Work supported by ONR and NOAA.]

Simulation of ultrasonic imaging with linear arrays in causal absorptive media

Rigorous and efficient numerical methods are presented for simulation of acoustic propagation in a medium where the absorption is described by relaxation processes. It is shown how FFT-based algorithms can be used to simulate ultrasound images in pulse-echo mode. General expressions are obtained for the complex wavenumber in a relaxing medium. A fit to measurements in biological media shows the appropriateness of the model. The wavenumber is applied to three FFT-based extrapolation operators, which are implemented in a weak form to reduce spatial aliasing. The influence of the absorptive medium on the quality of images obtained with a linear array transducer is demonstrated. It is shown that, for moderately absorbing media, the absorption has a large influence on the images, whereas the dispersion has a negligible effect on the images.

Simulation studies of narrow-band and cw acoustic propagation through a shallow-water internal wave

The effects of a shallow-water, solitary internal wave on cw and narrow-band acoustic propagation have been studied using computer simulations. Numerous observations have been made of solitary internal waves in shallow water. These internal waves travel along the near-surface thermocline for some distance without loss of coherence. Due to their prevalence, they have been cited as the likely cause of the anomalous effects observed in some recent shallow-water acoustic measurements. In order to test this hypothesis, computer simulations of acoustic propagation through an internal wave have been made using an ocean-acoustic PE propagation computer model (EFEPE), fast Fourier transformations (FFTs), and beamforming algorithms. A narrow band of frequencies was used with the center frequency at 250 Hz. The resulting frequency-dependent fields were then converted into the time domain via an FFT. Beamforming algorithms were used to analyze the field structure. Examples will be shown that contrast the internal wave effects on cw propagation and on narrow-band propagation. [Work supported by ONR and NRL.]

Underwater acoustic propagation simulation using a 3-D sea-surface scattering model and a 2-D propagation model

A three-dimensional time-domain sea-surface scattering model based on the wedge assemblage method has been incorporated into a two-dimensional frequency-domain propagation model based on the parabolic equation (PE) method. The sea-surface scattering model computes the time-domain scattering acoustic field using multiple realizations of sea-surface spectra to give a realistic stochastic 3-D sea-surface scattering prediction. The interfacing of the two models is achieved by obtaining the output from the sea-surface scattering model as a function of mode propagation angle and redistributing the scattered field into the proper modes in the propagation model. This new field is then marched forward by the PE model until the next significant sea-surface scattering event occurs where the interfacing method is again employed. Examples will be presented using various interfacing schemes.

Long-range, range-dependent, acoustic propagation simulation using a full-wave, finite-element model coupled with a one-way parabolic equation model

A full-wave, range-dependent, ocean acoustic propagation and scattering model based on the finite-element (FE) method [J. E. Murphy and S. A. Chin-Bing, Math. Comput. Modeling 11, 70–74 (1988)] has been combined with a range-dependent, one-way parabolic equation (PE) model to simulate long-range (> 100 km) ocean acoustic propagation. This hybrid FE/PE model has the advantage that it includes the coupled effects of the full-wave, range-dependent, forward propagated and backscattered fields where full-wave effects are important, while allowing for the much faster computational marching method of the PE model in those ocean regions where full-wave effects are not significant. The FE/PE hybrid model also uses the FE full-wave, range-dependent solution from the source out to a specified range at which the pressure field serves as the initial field input to the PE model. This PE starting field is most useful when the source is near a severely range-dependent boundary. Numerical examples are given and comparisons made with the more “exact” coupled mode and finite-element models that illustrate the increased accuracy of this hybrid FE/PE model over the one-way propagation models. [Work supported by ONR and NORDA.]

Numerical simulation of acoustic propagation at a fluid-solid interface

Propagation of acoustic pulses in the neighborhood of the interface between fluid and solid half-spaces is investigated numerically using the finite difference technique. The solid half-space may be homogeneous, or it may comprise several distinct solids of differing acoustical properties. The solid-solid interface may have arbitrary orientation with respect to the fluid-solid interface. Plots of the displacement fields clearly illustrate the wavefronts, headwaves, and surface modes near the fluid-solid interface. In the case of the inhomogeneous solid, reflection, transmission, and mode conversions at the solid-solid interface, and subsequent interactions with the fluid-solid interface give rise to a multiplicity of decay pulses. The origin and physical significance of each of these decay pulses is made evident by the displacement field pilots.

Satellite remote sensing and underwater acoustics: What you see is not necessarily what you get

Continuing efforts in satellite systems and analysis methodology may soon result in routine production of ocean weather maps for substantial regions of the world's oceans. Such maps might illustrate positions of such mesoscale features as ocean fronts and eddies and be available to the acoustician on a routine basis. (In fact such products are presently available for the Gulf Stream region.) However, the use of such maps without guidance as to the acoustic significance of these features may have limited utility to an acoustician deciding on the deployment of an acoustic system, and may indeed serve to mislead. A front or eddy that may be clearly visible to a satellite sensor may not be acoustically significant to the system under consideration. Even if the mesoscale feature has acoustic impact, the surface expression of the feature may not coincide with the acoustically important portion of the feature. Alternately, acoustically relevant mesoscale anomalies may not be visible to a satellite sensor. To illustrate these cautions, oceanographic data taken by the U.S. Naval Oceanographic Office Ocean Measurements Program in the Northeast Atlantic and Norwegian Sea are utilized in conjunction with numerical acoustic propagation simulations. This region is typical of areas where significant mesoscale activity occurs and oceanographic sampling is sparse, so that satellite remote sensing may be very useful in predicting acoustic system performance. However, examples presented illustrate that significant work must be done before a useful satellite oceanographic product can be turned into a useful acoustic product. [Work supported by the U.S. Naval Oceanographic Office.]

Optical simulation of acoustic propagation through deterministic and internal wave sound speed variations

We make use of an argon‐ion laser operating at 4880/ Å to model portions of the 406‐Hz MIMI experiments. Our simulation covers a range of 250 km. The Garret‐Munk internal wave model is used to construct two‐dimensional sound speed profiles at 15‐rain intervals. Each profile is recorded as a separate photographic plate. The plates are imaged using a high‐intensity ruby laser beam to differentially heat a fluid. The argon‐ion laser beam propagates through the light speed variations caused by the heating. The modeled rms sound speed fluctuation at the sound channel is approximately 0.01%. Phase and intensity measurements are made. Our results are compared with numerical models and extrapolated experimental results. Using the deterministic sound speed profiles reported by Clark and Kronengold, [J. Acoust. Soc. 56, 171–1083 (1974)], we present measurements of intensity as a function of range and depth. [Work supported by the Office of Naval Research.]

Some results of an optical simulation of acoustic propagation in the ocean

We are generating analog models of sound propagation in a variable sound‐speed ocean by using a previously described system [L. E. Estes and G. Fain, J. Acoust. Soc. Am. 62, S17(A) (1977)] that propagates a CW laser beam through a differentially heated fluid. The differential heating is effected at the correct wavelength scale by imaging a negative with the appropriate gray scale onto the fluid. The energy source is a high power pulse laser. The negative typically requires 500 000 resolution elements. It is exposed using a computer directed electromechanical deflection and acousto‐optical modulation system to control a low power CW laser. Essentially any pattern can be placed on the film. During operation a photographic measure of sound intensity at all ranges and depths is made. A simultaneous measurement of the velocity distribution is made using a Mach‐Zehnder interferometer. Results presented include range independent profiles that are compared to analytic solutions and range dependent profiles which are compared to a full diffraction theory numerical model. [Work supported by the Office of Naval Research.]

Optical simulation of acoustic propagation in the ocean

We have constructed, using lasers and optical components, a simulator for acoustic waves propagating in a nonhomogeneous two-dimensional ocean. The resulting wavelength scaling provides for the contraction of tens of kilometer ocean distances to centimeter distances on the optical bench. Ocean velocity profiles which vary in range and depth are created by inducing a temperature distribution in a fluid with a high velocity-temperature gradient. This is produced by imaging a transparency (with the desired distribution) using a high-power-pulse ruby laser onto the fluid. A blue dye in the fluid selectively absorbs the ruby light. The acoustic beam is simulated by a cw blue argon-ion laser and the source and receiver patterns are generated via appropriate optics. Subwavelength-size scatters make the blue beam visible from the side providing a photographic measure of sound intensity at all ranges and depths. A simultaneous measurement of the light velocity profile is made using a Michelson interferometer. The timing of the experiment consists of a 1-msec ruby pulse immediately followed by a 1-msec shuttering of the sound wave simulating and interferometer laser beams. [Work supported by the Office of Naval Research.]