Nonuniform Sound Speed Research Articles

Overflow waters in the western Irminger Sea modify deep sound speed structure and convergence zone propagation

Deep sound speed structure in the western Irminger Sea is found to be highly dynamic in comparison to the adiabatic (uniform) sound speed gradient underpinning data assimilation and modeling efforts around the globe. A beamed source parabolic equation model is used to illustrate how the resulting non-uniform sound speed structure at 1 to 1.5 km in depth and sound speed inversion near the seafloor produce observable effects on acoustic signals between a shallow source and shallow vertical line array at convergence zone ranges. Beamforming analysis shows that a uniform sound speed gradient leads to “ideal” interference patterns that do not capture or represent modeled convergence zone properties, such as location, strength, and sharpness. Overall findings suggest that in situ information about sound speed below 1 km is necessary for low frequency, long-range propagation studies, particularly in areas of complex thermohaline circulation.

On acoustic reflection from a seabed exhibiting a non-uniform sound speed profile, with relevance to fine-grained sediments.

An analysis of the plane wave reflection coefficient of the seabed, R, is developed for two upward-refracting sediment sound speed profiles: the two-parameter linear and the three-parameter inverse-square, both extending to infinite depth. For the linear profile, it turns out that |R| = 1, representing total reflection for all grazing angles and all frequencies, signifying that in this special case, |R| is insensitive to the gradient. The implication is that if |R| is to return information about the shape of a profile, the gradient must change with depth, either smoothly through the presence of second- and/or higher-order depth derivatives or discontinuously at, say, an interface between sediment layers. The inverse-square is an example of a profile with a smoothly varying gradient, for which a general, closed-form expression for R is derived, valid for all grazing angles and all frequencies. When the sound speed ratio is less than unity, representative of a fine-grained sediment (mud), |R| exhibits two frequency regimes, designated high and low, separated by a transition frequency, fT. In each of these regimes, |R| exhibits a frequency-dependent angle of intromission, which exhibits high- and low-frequency limiting values, differing by approximately 3.5°, depending on the geo-acoustic parameters of the sediment.

On two-dimensional acoustic-entropy waves in a mean flow with uniform velocity and laterally varying sound speed

Acoustic-entropy waves are considered as linear, compressive perturbations of a non-dissipative non-homentropic uniform flow. The acoustic-entropy wave equation for the pressure satisfies a modified convected wave equation with non-uniform sound speed. In the case of plane flow with a linear entropy shear profile the exact solution is obtained in terms of Bessel functions of an exponential variable. The acoustic-entropy waves in a uniform flow with a linear entropy shear are considered in: (i) a parallel sided duct; (ii) an unbounded boundary over a flat wall; (iii) a boundary layer of finite thickness matched to a uniform free stream.

Prediction of far-field wind turbine noise propagation with parabolic equation.

Sound propagation of wind farms is typically simulated by the use of engineering tools that are neglecting some atmospheric conditions and terrain effects. Wind and temperature profiles, however, can affect the propagation of sound and thus the perceived sound in the far field. A better understanding and application of those effects would allow a more optimized farm operation towards meeting noise regulations and optimizing energy yield. This paper presents the parabolic equation (PE) model development for accurate wind turbine noise propagation. The model is validated against analytic solutions for a uniform sound speed profile, benchmark problems for nonuniform sound speed profiles, and field sound test data for real environmental acoustics. It is shown that PE provides good agreement with the measured data, except upwind propagation cases in which turbulence scattering is important. Finally, the PE model uses computational fluid dynamics results as input to accurately predict sound propagation for complex flows such as wake flows. It is demonstrated that wake flows significantly modify the sound propagation characteristics.

A time-domain finite volume approach for prediction of muffler transmission loss including thermal effects

A time-domain finite volume approach is presented for predicting the transmission loss of muffler including thermal effects with non-uniform sound speed field and density field, in which the acoustic wave equation in heterogeneous media is solved by using unstructured finite volume method with the temperature field specified or solved by some commercial code. An improved time-domain impulse method based on the absorbing boundary condition is applied to predict the acoustic attenuation characteristics of mufflers. The approach is validated by numerical simulations of a simple expansion chamber muffler and a complex muffler with five chambers. The predicted results agree well with the corresponding experimental ones and numerical ones obtained by finite element method with commercial code SYSNOISE. The results of both mufflers under different thermal conditions indicate that the temperature distribution has a significant influence on transmission loss. According to the analysis of a complex muffler with ideal medium, it is shown that the variation of working conditions can obviously affect density and sound speed distributions but have little influence on transmission loss. On the other hand, the obtained transmission loss with the solved temperature field deviates much from the one with specified uniform temperature field.

Scattering from extended targets in range-dependent fluctuating ocean-waveguides with clutter from theory and experiments

Bistatic, long-range measurements of acoustic scattered returns from vertically extended, air-filled tubular targets were made during three distinct field experiments in fluctuating continental shelf waveguides. It is shown that Sonar Equation estimates of mean target-scattered intensity lead to large errors, differing by an order of magnitude from both the measurements and waveguide scattering theory. The use of the Ingenito scattering model is also shown to lead to significant errors in estimating mean target-scattered intensity in the field experiments because they were conducted in range-dependent ocean environments with large variations in sound speed structure over the depth of the targets, scenarios that violate basic assumptions of the Ingenito model. Green's theorem based full-field modeling that describes scattering from vertically extended tubular targets in range-dependent ocean waveguides by taking into account nonuniform sound speed structure over the target's depth extent is shown to accurately describe the statistics of the targets' scattered field in all three field experiments. Returns from the man-made targets are also shown to have a very different spectral dependence from the natural target-like clutter of the dominant fish schools observed, suggesting that judicious multi-frequency sensing may often provide a useful means of distinguishing fish from man-made targets.

Second Harmonic Component in Focused Gaussian Beam Propagating through Nonuniform Sound-Speed Layer

The fundamental and second harmonic components in a focused sound transmitting through a layer of an inhomogeneous medium with a nonuniform sound speed are analyzed. The nonlinear wave equation including the perturbation of the sound speed is solved with a successive approximation. The influence of the nonuniformity on the measurement of the acoustic nonlinearity parameter B/A in biological samples inserted in the focal region is also investigated. The axial sound-speed variation causes the relative uncertainty of the measured B/A to be the same as the rate of the sound speed within the sample. On the other hand, since the sound beam is refracted owing to the lateral variation of the sound speed, the second harmonic amplitude of the sound detected with the receiver noticeably decreases. Thus, the B/A is underestimated by half the rate of change of the sound speed within a lateral range equivalent to the sample thickness.

Second Harmonic Component in Focused Gaussian Beam Propagating through Nonuniform Sound-Speed Layer

The fundamental and second harmonic components in a focused sound transmitting through a layer of an inhomogeneous medium with a nonuniform sound speed are analyzed. The nonlinear wave equation including the perturbation of the sound speed is solved with a successive approximation. The influence of the nonuniformity on the measurement of the acoustic nonlinearity parameter B/A in biological samples inserted in the focal region is also investigated. The axial sound-speed variation causes the relative uncertainty of the measured B/A to be the same as the rate of the sound speed within the sample. On the other hand, since the sound beam is refracted owing to the lateral variation of the sound speed, the second harmonic amplitude of the sound detected with the receiver noticeably decreases. Thus, the B/A is underestimated by half the rate of change of the sound speed within a lateral range equivalent to the sample thickness.

2Pb4-4 Second Harmonic Component in Focused Sound Beam through a Layer with Nonuniform Sound-Speed(Poster Session)

2Pb4-4 Second Harmonic Component in Focused Sound Beam through a Layer with Nonuniform Sound-Speed(Poster Session)

Scattering from extended targets in a range-dependent fluctuating ocean waveguide from theory and experiments where the sonar equation is invalid.

Bi-static, long-range measurements of acoustic scattered returns from vertically extended, air-filled cylindrical targets were made during three separate ONR-sponsored field experiments in fluctuating continental shelf environments. We show that the sonar equation estimates of mean scattered intensity from these targets lead to large errors, differing by an order of magnitude from both our measurements and waveguide scattering theory. This is because the sonar equation approximation is not applicable to targets large compared to the acoustic wavelength in an ocean waveguide. We find that use of the Ingenito scattering model also leads to significant errors in estimating mean target scattered intensity in our field experiments because they were conducted in range-dependent ocean environments with large variations in sound speed structure over the depth of the targets, scenarios that violate the basic assumptions of the Ingenito model. Here we describe scattering from extended cylindrical targets in a range-dependent fluctuating ocean waveguide using a Green’s theorem based full-field model that takes into account nonuniform sound speed structure over the target’s depth extent. We show that this model accurately describes the statistics of the acoustic field scattered by the targets in all three field experiments.

Sound Transmission from a Source Outside a Nonisothermal Boundary Layer

The transmission of sound from a source outside a nonisothermal high-speed boundary layer is considered. The sound source is assumed to lie in a uniform stream and matched to a zero velocity at the wall by a linear velocity profile. The unidirectional shear mean flow is assumed to be isentropic but nonhomentropic, so that the entropy, the sound speed, and the temperature can vary fromone streamline to the other. The condition of homoenergetic flow, or constant enthalpy, is used to relate the sound speed to themeanflowvelocity and specify the temperature profile in the boundary layer. Compared with a homentropic boundary layer, for which sound refraction is due to the shear flow alone, a nonhomentropic boundary layer introduces additional refraction due to the nonuniform sound speed and the associated temperature gradients. It is shown that for a high speed, even in isentropic conditions, the nonhomentropic effects of temperature gradients and the nonuniform sound speed can cause significant sound attenuation (viz., for the same sound source outside the boundary layer, the acoustic pressure at the wall can be substantially reduced). This agrees qualitativelywith the results from testingpropfans at high subsonic speeds,which showed significant sound attenuation in the fuselage boundary layer.

On the Propagation of Sound in a High-Speed Non-Isothermal Shear Flow

The propagation of sound in shear flows is relevant to the acoustics of wall and duct boundary layers, and to jet shear layers. The acoustic wave equation in a shear flow has been solved exactly only for a plane unidirectional homentropic mean shear flow, in the case of three velocity profiles: linear, exponential and hyperbolic tangent. The assumption of homentropic mean flow restricts application to isothermal shear flows. In the present paper the wave equation in an plane unidirectional shear flow with a linear velocity profile is solved in an isentropic non-homentropic case, which allows for the presence of transverse temperature gradients associated with the ***non-uniform sound speed. The sound speed profile is specified by the condition of constant enthalpy, i.e. homenergetic shear flow. In this case the acoustic wave equation has three singularities at finite distance (besides the point at infinity), viz. the critical layer where the Doppler shifted frequency vanishes, and the critical flow points where the sound speed vanishes. By matching pairs of solutions around the singular and regular points, the amplitude and phase of the acoustic pressure in calculated and plotted for several combinations of wavelength and wave frequency, mean flow vorticity and sound speed, demonstrating, among others, some cases of sound suppression at the critical layer.

In vivo simulation of shock wave lithotripsy: Wave focusing in inhomogeneous materials.

Shock wave generation and focusing in electrohydraulic, electromagnetic, and piezoelectric lithotripters are simulated numerically. Inhomogeneities associated with wave propagation in vivo are modeled using data from The Visible Human Project. The approximate time‐domain relaxation model of Yang and Cleveland (2005) was used to simulate attenuation and dispersion in the tissuelike media. The simulations utilize a MUSCL‐type shock capturing scheme with adaptive mesh refinement (AMR). In vitro focal region pressure measurements compare favorably with available experimental data for each lithotripter type. Preliminary in vivo simulation results show significant dispersion associated with the nonuniform sound speed, including increases of up to 50% in focal pressure amplitudes and the presence of multiple pressure minima/maxima in the focal waveform. We will also discuss the extension of the AMR framework to account for cavitation via a previously developed ensemble‐averaged continuous two‐phase flow model.

Webster's Horn Equation Revisited

The problem of low-frequency sound propagation in slowly varying ducts is systematically analyzed as a perturbation problem of slow variation. Webster's horn equation and variants in bent ducts, in ducts with nonuniform soundspeed, and in ducts with irrotational mean flow, with and without lining, are derived, and the entrance/exit plane boundary layer is given. It is shown why a varying lined duct in general does not have an (acoustic) solution.

Low-frequency acoustics of bubble plumes formed in fresh water and salt water

Experiments aimed at comparing the acoustics of bubble plumes formed in salt water and fresh water were performed in a laboratory tank and natural bodies of water. The plumes were generated as a vertical stream of water, with a diameter of millimeter order and velocity ranging to about 10 m/s, penetrated a free water surface. The acoustic signals were measured with hydrophones in different positions, amplified, and digitally sampled. The measured power spectra revealed well-defined, nonuniformly spaced resonance peaks at frequencies below about 1 kHz. A theory based on a conical bubble plume, with a nonuniform sound speed profile acting as a resonant cavity, predicts the frequencies of the resonance peaks and shows remarkable agreement with the experimentally measured values for both salt water and fresh water bubble plumes. Though the bubbles contained in the salt water bubble plumes are much smaller than those in the fresh water plumes, the resonance frequencies are largely unaffected, consistent with the observation that the plumes in both cases are nearly identical in size and geometry for the same incoming velocity and air-entrainment rate. The acoustic levels in salt water were lower, indicating possible differences in attenuation or driving mechanisms. [Work supported by ONR.]

Low-frequency acoustic resonances in the bubble plume formed by a plunging water jet

As a jet of water penetrates a free water surface, air is entrained in the form of bubbles which produce sound by various mechanisms, including both individual and collective oscillations. The low-frequency acoustic emissions of the bubble clouds entrained and dispersed by vertical continuous and transient fresh water jets impinging from varying heights into a fresh water receiving pool in a large laboratory tank were studied both theoretically and experimentally for jet velocities ranging to about 10 m/s, and jet diameters of millimeter order. The acoustic signals were measured with hydrophones in different positions, amplified, and digitally sampled. The measured power spectra revealed well-defined, nonuniformly spaced resonance peaks at frequencies below about 1 kHz. A theory based on a conical bubble plume, with a nonuniform sound speed profile, acting as a resonant cavity predicts the frequencies of the resonance peaks and shows remarkable agreement with the experimentally measured values. Further, time-frequency analysis gives bubble size distributions and shows the driving source for the resonant cavity to be large secondary bubbles formed through coalescence, which become acoustically active through deformation or break-up as they are re-entrained by the downstream flow in a failed attempt to rise to the surface.

Low-frequency acoustic emissions of a plunging water jet. Part II. Theory

A theory of low-frequency acoustic emissions of a plunging water jet is developed and presented. A plunging liquid jet impinging on a free liquid surface entrains air and produces a bubble cloud with a well-defined geometry. At low frequencies the resulting bubble cloud has a substantially lower sound speed than the surrounding single phase medium. The cloud is modeled as a conical resonant cavity having the apex at the plunging point, with nonuniform sound speed profile and acoustically hard boundaries. Analytical estimates for the eigenfrequencies, based on the wave equation and a simplified void fraction profile, provide insight into the dependence of the resonance frequencies on various system parameters. A more realistic numerical model that includes advection by the surrounding flow and a more appropriate void fraction profile gives remarkable agreement with measured values and scalings for the eigenfrequencies. Further improvements can be made by including turbulent transport and dissolution in the model but at the cost of including additional parameters. Considering the complicated nature of the system, very strong overall agreement of the presented models is found, thus allowing inversions to be performed for important quantities related to the gas transfer, such as the entrainment rate and the void fraction profile.

Application of wavefront coordinates to acoustic ray tracing

Acoustic wave propagation is considered by transforming the equations of inviscid compressible flow to a coordinate system defined by the wavefront geometry. These equations are linearised and equations for the trajectory of rays are derived in the high frequency limit. The formulation in terms of the new coordinates facilitates a rapid derivation of an expression for the transmission loss associated with propagation along a ray. The form of the equations permits easy and robust calculation of sound propagation through media characterised by a non-uniform sound speed and demonstrates the utility of the coordinate system defined by the natural geometry of the wavefront.

On surface-generated ambient noise in an upward refracting ocean

Naturally generated ambient noise in the ocean is created by breaking waves, spray and precipitation. Each of these mechanisms produces a pulse of sound that propagates down into the depths of the ocean, and the superposition of all such pulses from across the whole sea surface constitutes the ambient noise field. Since the noise is a stochastic phenomenon, its properties are described in terms of statistical quantities, the most useful being the power spectral density at a point and the cross-spectral density between two points in the field. If these second-order statistical measures are independent of absolute position, the noise field is said to be spatially homogeneous. In the rare case of an isovelocity, deep ocean, the noise field at depths greater than a wavelength or so beneath the surface is spatially homogeneous, consisting of a random superposition of plane waves. A non-uniform sound speed profile, however, introduces wave-front curvature which modifies the situation significantly. the noise exhibits strong spatial homogeneity over length scales that are comparable with the apertures of typical acoustic arrays. Apart from the implications with regard to array performance, this is important in connection with certain aspects of acoustical oceanography, whereby information on the oceanographic environment is extracted from the noise field (Buckinghamet al.1992). Such information is accessible only if the structure of the noise field is well understood. The problem lies in determining the spatial and spectral properties of the noise in a profile. Fundamental to the noise analysis is the Green’s function for the channel, which characterizes the propagation conditions; and yet for most non-uniform sound speed profiles the analysis of the Green's function is intractable. However, there is one profile, designated the inverse-square profile, for which a complete, exact solution for the field has been developed (Buckingham 1991). The inverse-square profile is monotonic increasing with depth, giving rise to upward refractive propagation. Such a profile is found in several ocean environments: the polar oceans, where the temperature and hence the sound speed show a minimum at the surface; the mixed surface layer, extending to a depth of order 100 m in the open ocean; and the ocean-surface bubble layer, occupying the first ten metres or so beneath the surface. An analysis of the noise field in the presence of an inverse square profile, based on the solution for the Green’s function, shows that the cross-spectral density of the noise in the vertical consists of three components: a normal mode sum, representing noise originating largely in distant sources; a direct path contribution, from sources that are more or less overhead; and a near-surface term that is negligible at depths greater than a wavelength. In the theoretical noise spectrum , the normal mode and direct path components are prominent, dominating, respectively, at low and high frequencies. The cross-over frequency depends on the parameters of the profile and attenuation in the medium, but for polar oceans is in the region of several hundred hertz. At a much lower frequency, around 10 Hz, where the polar profile ceases to support normal mode propagation, a minimum appears in the theoretical spectrum . This is the result of a very rapid fall off in the normal mode component of the noise and a slow rise of the direct path component with decreasing frequency. Each of the three components of the vertical cross-spectral density exhibits strong spatial inhomogeneity. This is exemplified by the dramatic dependence of the cross-spectrum on both the mean depth of the sensors and frequency. Although such behaviour adds complexity to the structure of the noise field, this could be advantageous since it allows the possibility of performing inversions on noise cross-spectral data to determine properties of the medium. Recent measurements of low-frequency (50-2000 Hz) and very low-frequency (5-200 Hz) ambient noise spectra in the marginal ice zone of the Greenland Sea, where the sound speed profile is of the inverse-square form, have been compared with the predictions of the new noise theory. There is evidence in the measured spectra that both the normal mode and direct path components of the noise are present with the predicted relative levels. A minimum around 10 Hz is a ubiquitous feature of the VLF spectra, and the LF spectra show a change of slope close to 400 Hz, both of which are in accord with the theory. Along the ice edge a highly non-uniform (spatial) distribution of energetic sources is known to be present, whose effects in the observed spectra are consistent with arguments developed from the inverse-square noise analysis.