Modeling acoustic vector fields for inverse problems

Although the ocean environment in shallow water is very complex, there still exists stable interference pattern for broadband low frequency sound propagation. The waveguide invariant concept is introduced to describe the broadband interference structure of the acoustic pressure field in a waveguide and now it is widely used in underwater acoustic signal processing. Acoustic vector sensor can measure the particle velocity in the ocean and provides more information for the underwater sound field. In this paper, the interference phenomena of broadband vector acoustic signals in shallow water are investigated by numerical simulation. Energy spatial‐frequency distributions are shown for energy flux density vector obtained by combination of pressure and particle velocity signals and they are analyzed according to normal mode theory. Comparisons of the interference structure between the scale acoustic field and vector acoustic field also have been made. The waveguide invariant concept is extended to describe the interference structure of vector acoustic field in shallow water. A method for extraction of the waveguide invariant from interference patterns in vector acoustic field spectrograms is presented, which can be used in matched‐field processing and geoacoustic inversion. It is shown that this method may have more advantages than the traditional methods which calculate the waveguide invariant using measured sound pressure in the ocean.

The present paper examines the temporal evolution of acoustic fields by modeling forward propagation subject to sea surface dynamics with time scales of less than a second to tens of seconds. A time-evolving rough sea surface model is combined with a rough surface formulation of a parabolic equation model for predicting time-varying acoustic fields. Surface waves are generated from surface wave spectra, and stepped in time using a Runge-Kutta integration technique applied to linear evolution equations. This evolving, range-dependent surface information is combined with other environmental parameters and input to the acoustic model, giving an approximation of the time-varying acoustic field. The wide-angle parabolic equation model manages the rough sea surfaces by molding them into the boundary conditions for calculations of the near-surface acoustic field. This merged acoustic model is validated using concurrently-collected acoustic and environmental information, including surface wave spectra. Data to model comparisons demonstrate that the model is able to approximate the ensemble-averaged acoustic intensity at ranges of about a kilometer for acoustic signals of around 15 kHz. Furthermore, the model is shown to capture variations due to surface fluctuations occurring over time scales of less than a second to tens of seconds.

We present the first simultaneous mapping of two-dimensional, time-dependent velocity and pressure fields in a plane Couette flow pervaded by a transverse magnetic field. While electromagnetic forces are strongest in fluids of high electric conductivity such as liquid metals, their opacity excludes optical optical measurement methods. We circumvent this difficulty using a transparent electrolyte (Sulfuric acid), whose weaker conductivity is offset by higher magnetic fields. We describe an experimental rig based on this idea, where the Couette flow is entrained by a tape immersed in sulfuric acid and positioned flush onto the bore of large superconducting magnet, so that most of the flow is pervaded by a sufficiently homogeneous transverse magnetic field. Velocity and pressure fields are obtained by means of a bespoke PIV system, capable of recording the fluid's acceleration as well as its velocity. Both fields are then fed into a finite difference solver that extracts the pressure field from the magnetohydrodynamic governing equations. This method constitutes the first implementation of the pressure PIV technique to an MHD flow. Thanks to it, we obtain the first experimental velocity and pressure profiles in an MHD Couette flows and show that the transitional regime between laminar and turbulent states is dominated by near-wall, isolated, anisotropic perturbations.

A steady-state, nonlinear nearfield acoustical holography procedure, based on the Westervelt Wave Equation (WWE), was developed by the authors of this article to accurately reconstruct nonlinear acoustic “pressure” fields. Here, a “transient,” nonlinear acoustic holography algorithm is introduced that can be used to reconstruct three-dimensional, nonlinear acoustic pressure as well as particle velocity fields from two-dimensional acoustic pressure data measured on a measurement plane. This procedure is based on the Kuznetsov Wave Equation (KWE) that is directly solved by applying temporal and spatial Fourier Transforms to the KWE. When compared to the WWE-based procedure, the proposed procedure can be used to reconstruct acoustic particle velocity fields in addition to acoustic pressure fields. It can also be applied to multi-frequency source cases where each frequency component can contain both linear and nonlinear components. The KWE-based procedure is validated by conducting four numerical simulations with: (1) an infinite-size panel vibrating at a single frequency, (2) a pulsating sphere with a bifrequency excitation, (3) a finite-size, vibrating panel generating bended wave rays, and (4) an ultrasound transducer with a transient excitation. The numerical results show that holographically projected acoustic fields match well with directly calculated ones.

An experimental investigation of the influence of a leading edge separation region on the unsteady aerodynamic problem for thin, symmetric airfoils exposed to periodic gusting was performed in a subsonic indraft wind tunnel. Two leading edge shapes for the airfoil were used to examine the influence of flow separation both in the unsteady velocity and pressure fields. It is shown that flow separation near the leading edge causes a sharp increase in the unsteady RMS velocity and unsteady surface pressure variation associated with the gust frequency. This also causes a departure from the expectation that the gust information is convected downstream by the freestream in the velocity field. In the absence of such a separation region, velocity and surface pressure results closely resemble inviscid theoretical predictions and expectations. Accurate prediction of unsteady pressure is crucial in estimating the acoustic production of the system.

Modern acoustic intensity measurement techniques began in the early 1980's with the realization that the imaginary part of the cross-spectral density was directly related to the active intensity component along the axis between two closely-spaced pressure microphones. Since acoustic intensity is a vector quantity, it was obvious that one would like to measure all three orthogonal components and to graphically represent acoustic power flow through space. Needing an interesting topic for a Ph.D. thesis at Penn State (and a way of funding it ..., thank-you US Navy), the task of investigating and developing the estimation of the acoustic intensity vector field fortunately came my way. This talk will present some of the early interesting and fun things that came out of working on in-air acoustic vector sensors. It will conclude with some more recent developments that have direct connections to the early acoustic vector probes that were built, tested, and used at Penn State.

Through in-pressure sensor array signal processing, the signal arrival angle can be estimated by the estimation of signal parameters via rotational invariance techniques (ESPRIT) if we regard the whole array as two sub-arrays with the same structure. The estimation angles arrived at by ESPRIT have a left-right ambiguity because of the inverse trigonometric function operation. An acoustic vector sensor array (AVSA), which measures particle velocity and pressure at the same time and point of the acoustic field, offers significant potential. The traditional ESPRIT algorithm can also be used for an AVSA with left-right ambiguity. A new algorithm with omnibearing and an high accuracy based on ESPRIT using an AVSA was proposed in this paper. An analytic particle velocity, which composes by acoustic vector sensor x-axis and y-axis velocities, embeds the signal angle in its phase. The signal broadside can be known by the ESPRIT based on analytic particle velocity and pressure sub-arrays. The estimation angle containing broadside information can be used as the driving angle for combined particle velocity. According to the signal broadside, an average cross-variance matrix of pressure and combined velocity was constructed. The signal angle can be estimated by ESPRIT based on this new combined cross-variance matrix. Theoretical analysis and computer simulations show that the proposed algorithm has no left-right ambiguity and also has higher accuracy than the analytic particle velocity algorithm in the case of low signal-to-noise ratio (SNR). The algorithm is based on pressure and particle velocity combined processing, which can suppress interference better than existing algorithms in isotropic noise. The algorithm is also based on the analytic particle velocity ESPRIT, which has no left-right ambiguity. So the new algorithm has better performance than the existing algorithms.

Multiple-resolution scheme in finite-volume code for active or passive scalar turbulence

In the free field, making full use of scalar and vector information of acoustic field can bring many advantages for acoustic measurement, but under the conditions of the existence of sound baffle, the sound field should be distorted due to the superposition of diffraction wave. Taking the soft spherical baffle as background, the sphere scattering model is established, the diffraction pressure field and particle velocity field under the condition of different frequency, distance and incident angle is analyzed. The effect of diffraction wave on sound pressure and particle velocity is determined by the amplitude of diffraction wave and the phase difference between the diffraction wave and the incident wave, which is related with the frequency, distance and incident angle. The effect of diffraction wave on sound pressure and the particle velocity components in y axis is strong only on near field and high frequency, but for particle velocity component in x axis, on near field, the effect is always strong both at high and low frequency. The effect of diffraction wave can be ignored only in the far field for particle velocity component in x axis. The description of reference for influences on the directivity of vector sensor by soft ball boundary is not consistent with us.

In the present study, a new non-contact remote method is developed to reconstruct the location and amplitude of a harmonic source distribution in a fluid based on the associated acoustic pressure field on a measurement surface which is in contact with the fluid. An inverse or backward projection method based on the Singular Value Decomposition (SVD) method is utilized to reconstruct the source distribution that created the acoustic pressure field. Point source distributions located above an axisymmetric rigid plane and line source distributions located outside infinite rigid circular and elliptical cylinders are investigated. Numerical results show that the backward projection method is able to locate and to determine the strength of harmonic near-field sources in the external fluid which are separated by less than 0.01 of a wavelength. The reconstruction of the harmonic normal velocity and pressure surface distributions on a three-dimensional body based on the associated acoustic pressure field on a measurement surface located outside the body is addressed next. Prescribed normal velocity distributions on a spherical shell are investigated as special cases of interest. The case of different ratios of length to radius cylindrical shells with hemispherical end caps is also investigated. Numerical results for the reconstruction of normal velocity and pressure fields on the surface of the body show excellent agreement with the prescribed normal velocity and pressure fields over a wide normalized frequency range. Finally, the backward projection of the acoustic pressure field on the internal surface of a body to determine the internal harmonic source distributions which generated the field is considered. Axisymmetric source distributions in an infinite rigid circular cylinder duct are investigated. Monopole sources, dipole sources, and quadrupole sources are addressed. Numerical results show that the backward projection method is able to locate and to determine the strength of harmonic source distribution which are separated by less than 0.004 of a wavelength.

We now present exact solutions to some flow problems obtained by solving the governing differential equations. Though exact solutions are known to only a small number of problems due to the complexity of the governing equations, these solutions are very valuable not only for the insight that they offer, but also as a means of testing the accuracy of numerical schemes such as the one presented in [49]. All the solutions that are presented in this chapter have been obtained by guessing (fully, or in terms of some function to be determined) the velocity field. If one guesses the stress field, then of course, one would have to check the compatibility conditions presented in Vol. I; the same compatibility conditions derived for linear elasticity hold, with the rate of deformation tensor and velocity playing the roles of the linearized strain tensor and displacements, respectively.

During the last few years it became feasible to record in the marine environment the reflection seismograms of the acoustic pressure field along two horizontal streamers emersed one below the other. This enables a more exact treatment of the wave equation as a second‐order partial differential equation requiring two boundary conditions such as the pressure field and its gradient. According to Green's representation theorem, if the actual source is located above the two streamers, the wave field can be reconstructed for any point below them provided the medium parameters are known. Alternatively, if the dual acoustic field, namely, the pressure and particle velocity, is measured along a single horizontal streamer placed below the source, both dual fields may be reconstructed. As a first step to demonstrate the power of processing simultaneously the dual fields, we show how the source signature estimation, deghosting and deconvolution can be deterministically derived. As far as we know these processes cannot be done with a single set of boundary conditions.

Solving an acoustic wave equation using a parabolic approximation is a popular approach for many existing ocean acoustic models. Commonly used parabolic equation (PE) model programs, such as the range-dependent acoustic model (RAM), are discretized by the finite difference method (FDM). Considering the idea and theory of the wide-angle rational approximation, a discrete PE model using the Chebyshev spectral method (CSM) is derived, and the code is developed. This method is currently suitable only for range-independent waveguides. Taking three ideal fluid waveguides as examples, the correctness of using the CSM discrete PE model in solving the underwater acoustic propagation problem is verified. The test results show that compared with the RAM, the method proposed in this paper can achieve higher accuracy in computational underwater acoustics and requires fewer discrete grid points. After optimization, this method is more advantageous than the FDM in terms of speed. Thus, the CSM provides high-precision reference standards for benchmark examples of the range-independent PE model.

The Shallow Water Acoustic Modeling (SWAM'99) Workshop was organized to examine the ability of various acoustic propagation models to accurately predict sound transmission in a variety of shallow water environments designed with realistic perturbations. In order to quantify this, tests of reciprocity, convergence, and stability must be considered. This paper presents the results of an established parabolic equation model based on the split-step Fourier algorithm. The test cases examined in this paper include a simple isospeed water column over a flat bottom with geoacoustic parameter variations, a randomly sloping bottom with geoacoustic parameter variations, and a canonical shallow water profile perturbed by internal waves over a flat, homogeneous bottom. Source configurations were generally held constant but numerous single frequency and broadband runs were performed. Model testing is emphasized with specific criteria for accurate solutions being specified. Random perturbations are added to one test case to examine the influence of environmental uncertainty on the details of the propagation. The results indicate that point-wise accurate solutions to the acoustic field in shallow water cannot be achieved beyond a few kilometers. This is partly due to the inaccuracies of the split-step Fourier algorithm employed in these shallow water scenarios and the treatment of the bottom interface boundary conditions, but also due to the inherent variability caused by uncertain environmental specification. Thus, more general features of the acoustic field should be emphasized at longer ranges.

Two-dimensional acoustic particle velocity and acoustic pressure, concurrent with atmospheric data, were collected during a series of field tests. It was found that for short propagation distances, the particle velocity field remained unsaturated (little variation in amplitude and phase) for higher frequencies than did the pressure field. Theoretical comparisons are made to examine the physical effects of the propagation environment on the particle velocity field statistics.