Linear Sound Speed Research Articles

Localisation for underwater acoustic networks with a piece-wise linear sound speed profile

ABSTRACT Underwater agent localisation is a precondition for plenty of ocean applications. The variation of the underwater sound speed (USS) is one of the main factors that constrain the performance of underwater localisation. In this paper, a scheme is designed to reduce the agent localisation error arising from the USS variation in deep water and an agent localisation algorithm named ‘localisation with a piecewise linear USS' (LPL) is proposed. According to the characteristics of a real USS in deep water, a piecewise linear USS model is introduced to approximate the real USS. The agent above under the ‘sound fixing and ranging’ (SOFAR) channel are both considered. The LPL algorithm consists of three parts: initial value estimation, horizontal distance estimation and localisation. Considering the piecewise linear USS profile, the proposed LPL algorithm improves the performance for localisation with 60% more precision than the state-of-the-art methods.

Finite amplitude wave propagation through bubbly fluids

The existence of only a few bubbles could drastically reduce the acoustic wave speed in a liquid. Wood’s equation models the linear sound speed, while the speed of an ideal shock waves is derived as a function of the pressure ratio across the shock. The common finite amplitude waves lie, however, in between these limits. We show that in a bubbly medium, the high frequency components of finite amplitude waves are attenuated and dissipate quickly, but a low frequency part remains. This wave is then transmitted by the collapse of the bubbles and its speed decreases with increasing void fraction. We demonstrate that the linear and the shock wave regimes can be smoothly connected through a Mach number based on the collapse velocity of the bubbles.

On plane-wave reflection from a two-layer marine sediment: A surficial layer with linear sound speed profile overlying an iso-speed basement.

An analysis of plane wave reflection is developed for a two-layer sediment, the top layer consisting of a fine-grained material (mud) with an upward refracting linear sound speed profile. Beneath is a homogeneous basement, and above is homogeneous seawater. A rather curious, exact analytical expression for the reflection coefficient is derived, involving easy to evaluate integrals over finite limits, of the modified Bessel functions of low-integer order. The expression is generally valid for any linear profile with positive gradient in the surficial mud layer and for any sound speed in the basement, either greater than or less than that in the seawater. For "fast" basements, a critical angle always exists that is independent of the sound speed in the mud layer. With a "slow" basement, a quasi-angle of intromission may exist, which depends only weakly on both frequency and the gradient of the profile in the mud, a conclusion that may be relevant to the conditions of the Seabed Characterization Experiment (2017) performed over the New England Mud Patch. With both types of basement, fast and slow, the reflection coefficient, as a function of grazing angle, exhibits fluctuations that are strongly frequency dependent, associated with resonances and anti-resonances in the mud layer.

Lagrangian description of cosmic fluids: Mapping dark energy into unified dark energy

We investigate the appropriateness of the use of different Lagrangians to describe various components of the cosmic energy budget, discussing the degeneracies between them in the absence of nonminimal couplings to gravity or other fields, and clarifying some misconceptions in the literature. We further demonstrate that these degeneracies are generally broken for nonminimal coupled fluids, in which case the identification of the appropriate on-shell Lagrangian may become essential in order characterize the overall dynamics. We then show that models with the same on-shell Lagrangian may have different proper energy densities and use this result to map dark energy models into unified dark energy models in which dark matter and dark energy are described by the same perfect fluid. We determine the correspondence between their equation of state parameters and sound speeds, briefly discussing the linear sound speed problem of unified dark energy models as well as a possible way out associated to the nonlinear dynamics.

Maximum Entropy Derived Statistics of Sound-Speed Structure in a Fine-Grained Sediment Inferred From Sparse Broadband Acoustic Measurements on the New England Continental Shelf

Marginal probability distributions for parameters representing an effective sound-speed structure of a fine-grained sediment are inferred from a data ensemble maximum entropy method that utilizes a sparse spatially distributed set of received pressure time series resulting from multiple explosive sources in a shallow-water ocean environment possessing significant spatial variability of the seabed. A remote sensing seabed acoustics experiment undertaken in March 2017 off the New England Shelf was designed so that multiple independent analyses could infer the statistical properties of the seabed. The current analysis incorporates the measured horizontal variability from interpretations of a subbottom profiling survey of the experimental area. An idealized range- and azimuth-dependent parameterization of the seabed is derived from identification of horizons within the seabed that define multiple sediment layers. A sparse set of explosive charges were deployed on circular tracks with radii of about 2, 4, and 6.5 km with an acoustic array at the center to correlate a set of random measurements to physical acoustic processes that characterize the seabed. The mean values of a surface sound speed ratio and a linear sound speed gradient for the fine-grained sediment layer derived from 12 data samples processed in the 25-275-Hz band provide an estimate of the effective sound-speed structure in a 130-km <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> area. The inferred sediment sound speed values are evaluated by predicting measured time series data not used in the statistical inference, and are also compared to historical measurements. Finally, the low-frequency maximum entropy estimate of the sediment sound speed along with physical measurements derived from piston core measurements are utilized to estimate the sediment grain bulk modulus.

A three-dimensional bistatic reverberation model of underwater explosion by interface scattering at variable sound speeds

Underwater reverberation is a main limitation of the sonar performance and thereby the reverberation level estimation becomes crucial. In this study, based on the Lambert law and ray theory, a model for predicting 3D bistatic reverberation performance by interface scattering at linear sound speed profile is established and then verified through the underwater explosion experiments. The Influences of source and receiver positions, and relative sound speed gradient on reverberation performance are further investigated. The results indicate that: (1) the proposed model can predict the short-range mean reverberation level effectively, with the deviation 2–4 dB and describe the whole reverberation level distribution in some details; (2) at the early reverberation phase, the interference effects between the interface scattering sounds are considerable and a dominating interface exists; the counterbalance between the losses by scattering, spreading and medium absorption results in the local high-intensity zones close to corresponding interfaces, respectively; (3) as the sound source moves towards some interface, associated local high-intensity zone gradually expands, while the other one shrinks; if the sound speed approaches are constant, an extra local high-intensity zone will appear between the previous two but with a lower magnitude.

Estimating rates of coherent leakage from a variety of ocean surface duct types

In prior work, we obtained a semi-empirical algorithm for the rate of leakage from a mixed layer surface duct with linear sound speed gradients both within and below the duct. Realistic surface ducts are, however, likely to include zones of nonlinear sound speed gradient. In this paper, we made an initial test of whether the leakage rate is strongly dependent on the shape of the sound speed profile or whether it may be adequately approximated based on consideration of the trapping frequency alone. We used a normal mode model to obtain the rate of leakage for each of several nonlinear surface ducts for which the sound speed profiles can be expressed analytically. In each case, the leakage has been compared with that for a duct with a linear gradient, obtained using the algorithm above. In this comparison, the different ducts have been designed so that they all have the same trapping frequency, the same gradient at the top of the respective profiles, and the same sound speed gradient below the duct.

Broadband unidirectional acoustic transmission based on piecewise linear acoustic metamaterials

In this paper, a broadband unidirectional acoustic transmission based on inhomogeneous metamaterial shell with radial piecewise linear sound speed distribution is proposed. Acoustic rays in the case of external and internal incidences from the shell are deduced by geometric acoustic theory to show the unidirectional acoustic propagation in the polar coordinate system. Numerical full-wave simulations reveal that one way transmission has the intensity-independent unidirectional transmission feature over a wide frequency range. Finally, a scheme for realization of the proposed one way transmission model is designed and simulated by using multilayered materials, suggesting its potential applications in noise control, acoustic rectifiers, wave absorption and related fields.

Source motion modeling for high-speed aircraft noise propagation

A continuous source motion model has been developed to represent a cruising aircraft traveling at high altitudes. The numerical implementation is based on the Lorentz transform (LT) and a Fast Field Program (FFP) formulation, which is used to compute the sound fields due to a monopole point source traversing in a horizontally stratified atmosphere parallel to a ground surface. To reduce the computational expenses, a one-dimensional LT-FFP is performed to obtain the pressure time-history for overhead flight conditions. The continuous source motion model is compared against a heuristic model which applies a Doppler shift to the stationary source sound field. A linear sound speed profile was selected to simplify the ray model implementation. A parametric study involving the source Mach number and source emission frequency has been performed in a variety of environmental conditions. The differences in the predicted maximum sound pressure levels between the two models can be as large as 9 dB under certain cond...

Averaged transmission loss expressions in shallow water waveguides with sandy‐silty sediments.

Relatively simple approximations for transmission loss in shallow water based on ray theory were presented by Marsh and Schulkin (1962), Weston (1971), Smith (1974), and Rogers (1981). Formulas for averaged transmission loss versus range in stratified shallow water waveguides over sandy‐silty sediments are derived entirely from mode theory. Results are contrasted with other mode based expressions obtained by Brekhovskikh (1960) and Grachev (1983). Convenient expressions for loss in Pekeris waveguides are developed by approximating the mode number dependence of the attenuation coefficients as quadratic, which is valid in Westons’s mode stripping region. Similar loss expressions for environments with downward refracting linear sound speed profiles are constructed using modal attenuation coefficient approximations for the “limiting mode” of Denham (1969). This quantity illustrates how changes in environmental parameters, particularly thermocline strength and depth, produce corresponding changes in averaged transmission loss. The loss formulas have several terms, each having a natural physical interpretation, and each is compared with the well known results of Rogers from ray theory. The corresponding expressions have the same parameter dependence, thereby providing a modal foundation for Rogers’s formulas. [Work partially supported by the ONR.]

Propagation of sound and supersonic bright solitons in superfluid Fermi gases in BCS-BEC crossover

We investigate the linear and nonlinear sound propagations in a cigar-shaped superfluid Fermi gas with a large particle number. We first solve analytically the eigenvalue problem of linear collective excitations and provide explicit expressions of all eigenvalues and eigenfunctions, which are valid for all superfluid regimes in the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation (BCS-BEC) crossover. The linear sound speed obtained agrees well with that of a recent experimental measurement. We then consider a weak nonlinear excitation and show that the time evolution of the excitation obeys a Korteweg de Vries equation. Different from the result obtained in quasi-one-dimensional case studied previously, where subsonic dark solitons are obtained via the balance between quantum pressure and nonlinear effect, we demonstrate that bright solitons with supersonic propagating velocity can be generated in the present three-dimensional system through the balance between a waveguidelike dispersion and the interparticle interaction. The supersonic bright solitons obtained display different physical properties in different superfluid regimes and hence can be used to characterize superfluid features of the BCS-BEC crossover.

Spectral properties of the interference head wave

The interference head wave propagating through a sediment with a linear sound speed gradient is studied as a function of the parameter zeta, which is itself a function of acoustic frequency f, sediment sound speed and its gradient, and range. For zeta<1 the amplitude spectrum of the interference head waves goes as |S(f)|/f, where S(f) is the source spectrum. For increasing zeta beyond unity a more complicated modulation of S(f) ensues, which is explained by a channel transfer function H1(f), constructed analytically from a summation of terms involving zeroth-order refracted waves (referred to as a ray approach). For zeta greater than or approximately equal to 2 this summation compares well with a wave theory result for the interference head wave involving a fluid-fluid boundary. The amplitude spectrum of the interference head wave in the absence of sediment attenuation is |S(f)| x |H1(f)| and it is essential to know these to obtain an estimate of sediment attenuation from field observations. Examples of |S(f)| x |H1(f)| are presented for which H1(f) is computed directly using the ray approach and indirectly using the parabolic wave equation. A brief discussion on the application of these results towards the inversion of sediment attenuation is given.

Closed Form Bistatic Reverberation and Target Echoes With Variable Bathymetry and Sound Speed

Some existing closed-form expressions for target echo and reverberation, assuming classical mode-stripping and Lambert's law in isovelocity water, are extended to the case of uniform slope bathymetry combined with range-independent linear sound speed and bistatic geometry. The analytical, or extremely fast numerical, calculation of signal-to-reverberation-ratio provides insight useful for sonar design, and operational research. There are three types of path, each of which may be important at some range: Those that only interact with one boundary, those that always interact with both boundaries and those that sometimes interact with both. Each provides a separate closed-form contribution. The earlier finding, that with Lambert's law the reverberation tends to follow the same range trend as the target echo, is slightly modified by the addition of refraction. The stronger reverberation from the low sound speed side of the duct tends to fall off slightly less slowly than the target echo according to the strength of the refraction. Some graphical examples show that the very large parameter space can be handled very easily

Mass, momentum, and energy transfer by the propagation of acoustic solitary waves

This paper considers the mass, momentum, and energy transfer accompanied by the propagation of the acoustic solitary wave in a gas-filled tube. As was demonstrated previously [J. Acoust. Soc. Am. 99, 1971-1976 (1996); Phys. Rev. Lett. 83, 4053-4056 (1999)], the propagation of the solitary waves is made possible by connecting a periodic array of Helmholtz resonators axially with the tube. The solitary wave can convey the mass, momentum, and energy steadily with a constant speed that is subsonic but nearly equal to the linear sound speed. It is emphasized that the quantities transferred are of first order in magnitude. Formulating the basic equations in the conservation form, the total amount of the mass, momentum, and energy transferred is obtained by using the solitary-wave solutions. It has the upper bounds determined by the limiting solitary wave, which are proportional to the size of the resonator and the inverse of its natural frequency. In evaluating the energy transfer, a clear distinction should be made between the gas-dynamic energy and the acoustic energy. The former, which contains the first-order quantity whereas the latter begins with the quadratic ones, is to be used to determine the energy transfer in the form of heat (internal energy) associated with the mass transfer.

Snell’s law of refraction and sound rays for a moving medium

Fermat’s principle of least time is used to calculate a new law of refraction for a stratified medium moving horizontally with different temperatures in each layer. This new law of refraction includes velocity of sound, wind speed, and the angle between the vectorial sum of sound velocity and the wind speed. This new equation is compared with the usual approximations for the different refraction laws of a moving medium occasionally mentioned in literature as ‘‘Snell’s law for a moving media.’’ The sound rays in a moving thermically stratified medium are refracted more or less (dependent on either upwind or downwind sound propagation), then calculated according to the ‘‘Snell’s law.’’ For upward-oriented sound rays and a moderate thermical stratification with high wind speeds, the difference in the angle of refraction between the new refraction law and the usual approximation is roughly 3 degrees and neglectable for grazing incidence. The sound ray trajectories expressed as analytical equations for a constant sound velocity combined with a wind speed profile proportional to height; the results are shown in a figure. Furthermore, the sound ray trajectories for a linear sound speed profile combined with a linear height-dependent wind speed profile are calculated and shown graphically.

Influence of ground effect and refraction on road traffic noise

Ground effect and refraction modify geometrical spreading. In the present study a simplified model of ground effect is applied. Refraction is analyzed for the motionless atmosphere with a linear sound speed profile. Noise generated by constant speed road traffic is assessed by the time-average sound level, L AeqT -. The model of L AeqT prediction contains free parameters that are estimated from noise measurements at the site in question. The model makes possible the prediction of L AeqT at an altitude of a few tens of meters above the ground surface, within the range of a few hundred meters from the road. Contours of L AeqT = constant in the vertical plane represent the radiation pattern of road traffic noise.

The evolution of strongly modulated, low-frequency, moderate-amplitude wave packets in a dispersive plasma

The evolution of strongly modulated wave packets in a dispersive plasma that propagate parallel to the magnetic field is studied. Modulation effects are shown to reduce significantly (≊30%) the rate of spreading from that due to dispersion alone. For fluidlike behavior, nonlinearity has its greatest impact on evolution when the linear sound speed and initial wave packet speeds are well matched, resulting in a strong coupling between the wave magnetic and sonic components. Ion kinetic processes reduce the impact of nonlinearity and cause the rate of spreading to approach that expected from dispersion alone as the ratio of ion and electron temperatures, Ti/Te→4. For β≳1 and Ti/Te∼1, the coupled waveforms correspond qualitatively to kinetic treatments of the derivative nonlinear Schrödinger (DNLS) equation.

Weak shock interaction with a free-slip interface at low grazing angles

Theoretical/numerical investigations with the nonlinear progressive wave equation (NPE) model predict qualitative differences between behavior of a planar weak shock and a linear acoustic wave of similar time signature incident downward at small grazing angle onto a free-slip interface between two fluids. For the linear case, the model agrees well with an appropriate analytic benchmark solution. For the nonlinear cases considered, initial conditions evolve toward (a) supercritical reflection (steady wave with no Mach stem development) or (b) subcritical reflection (self-similar behavior with Mach stem development). When the horizontal phase speed c0 of the incident wave barely exceeds the linear sound speed cL of the lower medium, an intermediate state can be obtained in which the incident shock discontinuity terminates on the interface; wave energy below the interface runs ahead and reforms a deep penetrating shock ahead of and below the interface disturbance. When c0 is below cL, the shock discontinuity terminates at the interface and does not reform in the lower medium.

Heuristic model for outdoor sound propagation based on an extension of the geometrical ray theory in the case of a linear sound speed profile

In the case of outdoor sound propagation at relatively short ranges, it is reasonable to assume that sound follows straight ray paths. At longer ranges, refraction due to temperature and wind gradients results in ray paths that are curved, and calculations using straight rays are no longer valid and lead to erroneous results. In addition, atmospheric turbulence plays an ever-increasing role by degrading the coherence of the sound field. In this paper, the theory valid for propagation from a point source above an impedance plane is extended to include the effects of curved rays and the loss of coherence due to atmospheric turbulence. The model assumes a sound speed gradient that varies linearly with height above the ground. This assumption allows an analytical determination of the travel times of the curved rays and the modified angle of incidence of the ground-reflected paths. The additional reflected rays that may appear in the presence of a positive gradient are included in the calculation. The assumption also permits the determination of the position of the shadow zone in the presence of a negative gradient. The total sound pressure level is computed by summing the contribution from all the rays. In this summation, a fluctuating index of refraction is used to take into account the partial coherence between the rays caused by the effects of atmospheric turbulence. If the receiver is in the shadow zone, a diffraction theory based on a residue series solution is used to compute the sound levels. The results of calculations using the model are compared with experimental results.

A fast and accurate bistatic bottom reverberation model

A simple bistatic reverberation model has been developed to model low‐frequency, wideband, bottom, or surface reverberation. The model allows for arbitrary separation of source and receiver in both range and depth, and accommodates both source and receiver beam patterns. Total reverberation is computed by the incoherent summation of the incremental contributions from each three‐dimensional ray path connecting the source, scattering element, and receiver. Simplified ray path calculations are made with either a constant or a linear sound speed profile, assuming spherical spreading along each ray, and specular reflection from the flat, horizontal boundary interfaces. Acoustic characteristics of the surface and bottom are assumed to be completely represented by the reflection loss and scattering strength functions. A realistic representation of generalized bistatic scattering [D. D. Ellis and D. R. Haller, J. Acoust. Soc. Am. Suppl. 182, S124 (1987)] has been successfully used to model reverberation from expl...