Three-dimensional coupled-mode model and characteristics of low-frequency sound propagation in ocean waveguide with seamount topography

Large-scale topography, such as a seamount, substantially impacts low-frequency sound propagation in an ocean waveguide, limiting the application of low-frequency acoustic detecting techniques. A three-dimensional (3D) coupled-mode model is developed to calculate the acoustic field in an ocean waveguide with seamount topography and analyze the 3D effect. In this model, a correction is introduced in the bottom boundary, theoretically making the acoustic field satisfy the energy conservation. Furthermore, a large azimuth angle calculation range is obtained by using the operator theory and higher-order Padé approximation. Additionally, the model has advantages related to the coupling mode and parabolic equation theory. The couplings corresponding to the effects of range-dependent environment are fully considered, and the numerical implementation is kept feasible. After verifying the accuracy and reliability of the model, low-frequency sound propagation characteristics in the seamount environment are analyzed. The results indicate lateral variability in bathymetry can lead to out-of-plane effects such as the horizontal refraction phenomenon, while the coupling effect tends to restore the abnormal sound field and produces acoustic field diffraction behind the seamount. This model effectively considers the effects of the horizontal refraction and coupling, which are proportional to the scale of the seamount.     

A High-Efficiency Spectral Method for Two-Dimensional Ocean Acoustic Propagation Calculations

The accuracy and efficiency of sound field calculations highly concern issues of hydroacoustics. Recently, one-dimensional spectral methods have shown high-precision characteristics when solving the sound field but can solve only simplified models of underwater acoustic propagation, thus their application range is small. Therefore, it is necessary to directly calculate the two-dimensional Helmholtz equation of ocean acoustic propagation. Here, we use the Chebyshev–Galerkin and Chebyshev collocation methods to solve the two-dimensional Helmholtz model equation. Then, the Chebyshev collocation method is used to model ocean acoustic propagation because, unlike the Galerkin method, the collocation method does not need stringent boundary conditions. Compared with the mature Kraken program, the Chebyshev collocation method exhibits a higher numerical accuracy. However, the shortcoming of the collocation method is that the computational efficiency cannot satisfy the requirements of real-time applications due to the large number of calculations. Then, we implemented the parallel code of the collocation method, which could effectively improve calculation effectiveness.     

Computer modeling of sound fields in the ocean with fine-structured inhomogeneities

The results of a computer modeling of sound propagation in the ocean with fine-structured inhomogeneities are presented. The modeling was performed using a wave code based on the wide-angle approximation, which allows one to estimate the effects of sound field perturbations. These effects include the insonification of the geometric shadow zones and the abnormal attenuation of low-frequency sound in the course of its propagation in an oceanic waveguide. Calculations clearly demonstrate that the fine-structured inhomogeneities of the sound velocity considerably affect the sound propagation in the ocean.     

Complex Padé approximant operators for wide-angle beam propagation

The conventional rational Hadley(m, n) approximant of wide-angle beam propagator based on real Padé approximant operators incorrectly propagates the evanescent modes. In order to overcome this problem, two complex Padé approximants of wide-angle beam propagator are presented in this paper. The complex propagators of the first approach are obtained by using the same recurrence formula from the scalar Helmholtz equation of the conventional approximant method with a different initial value while those of the second method derived from Hadley(m, n) approximant of a square-root operator that has been rotated in the complex plane. These resulting approaches allow more accurate approximations to the Helmholtz equation than the well-known real Padé approximant. Furthermore, our proposed complex Padé approximant operators give the evanescent modes the desired damping.     

A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation

This paper presents a new non-overlapping domain decomposition method for the Helmholtz equation, whose effective convergence is quasi-optimal. These improved properties result from a combination of an appropriate choice of transmission conditions and a suitable approximation of the Dirichlet to Neumann operator. A convergence theorem of the algorithm is established and numerical results validating the new approach are presented in both two and three dimensions.     

Field transformational approach to three-dimensional scattering from two-dimensional rough surfaces

In 1985, Tappert and Nghiem-Phu introduced a field-transformation technique for computing rough surface scattering from a parabolic equation model utilizing a split-step Fourier marching algorithm. The approach was based on a two-dimensional parabolic equation with a standard operator approximation that was capable of computing scattering from a one-dimensional rough surface. Although this approach has been used extensively and effectively, extensions of this approach to higher order approximations or three-dimensional propagation have only recently been investigated. In this work, the expressions that incorporate higher-order approximations and three-dimensional scattering from two-dimensional rough surfaces are presented. The implications of some computationally necessary approximations are also provided.     

A converging equation of state of a weakly nonideal hydrogen plasma without mystery

A detailed independent derivation of the equation of state of a weakly nonideal hydrogen plasma is presented. The impetus for this work was the demand for high accuracy of the equation of state of the solar plasma in relation to the problems of modern helioseismology, accuracy sufficient for reproducing the velocity of sound on the Sun from optical measurement results with errors not exceeding 10^?4. The existing equations for the second virial coefficient in the expansion of the Helmholtz thermodynamic potential for a system of electrons and protons in powers of the activities of these particles involve certain procedures for the removal of the arising divergences that provoke questions and require independent verification. The suggested equation of state is used to qualitatively estimate the accuracy of various physical and chemical models. The speed of sound and adiabatic exponent calculated along the solar trajectory are presented for a model hydrogen plasma. The calculations were performed with the inclusion of relativistic corrections, electron degeneracy effects, radiation pressure in the plasma, Coulomb interaction in the Debye-Hückel approximation with diffraction and exchange corrections, and converging contributions of bound and scattering states.     

Sound propagation in inhomogeneous waveguides with sound-speed profiles using the multimodal admittance method

The multimodal admittance method and its improvement are presented to deal with various aspects in underwater acoustics, mostly for the sound propagation in inhomogeneous waveguides with sound-speed profiles, arbitrary-shaped liquid-like scatterers, and range-dependent environments. In all cases, the propagation problem governed by the Helmholtz equation is transformed into initial value problems of two coupled first-order evolution equations with respect to the modal components of field quantities(sound pressure and its derivative), by projecting the Helmholtz equation on a constructed orthogonal and complete local basis. The admittance matrix, which is the modal representation of Direchlet-to-Neumann operator, is introduced to compute the first-order evolution equations with no numerical instability caused by evanescent modes. The fourth-order Magnus scheme is used for the numerical integration of differential equations in the numerical implementation. The numerical experiments of sound field in underwater inhomogeneous waveguides generated by point sources are performed. Besides, the numerical results computed by simulation software COMSOL Multiphysics are given to validate the correction of the multimodal admittance method. It is shown that the multimodal admittance method is an efficient and stable numerical method to solve the wave propagation problem in inhomogeneous underwater waveguides with sound-speed profiles, liquid-like scatterers, and range-dependent environments. The extension of the method to more complicated waveguides such as horizontally stratified waveguides is available.     

Double-leaf microperforated panel space absorbers: A revised theory and detailed analysis

A double-leaf microperforated panel space absorber (DLMPP) is composed of two microperforated panels (MPPs) placed in parallel with an air-cavity in-between, without a back wall or any backing structure. This was proposed as a space sound absorber, which can be used for a sound absorbing screen or partition. A conventional MPP absorber with a rigid back wall is effective only around its resonance frequency, which is usually at middle frequencies, and not effective at low frequencies. However, a DLMPP can be effective also at low frequencies, because an additional sound absorption is produced by its acoustic flow resistance. In the authors’ previous work, theoretical analyses on the acoustic properties of a DLMPP were carried out using a simplified electro-acoustical equivalent circuit model. However, the equivalent circuit model includes an approximation, and more sophisticated theory is required for a better prediction and detailed discussion. In this paper, a revised theory for a DLMPP is presented: A Helmholtz integral formulation is employed to obtain a rigorous solution for more precise prediction of the absorptivity of a DLMPP. The result of the present revised theory is compared with that of the equivalent circuit model, and the difference between them is discussed. A parametric survey is made through numerical examples by the present revised theory to discuss its acoustic properties.     

Infrasonic sound pressure in dwellings at the Helmholtz resonance actuated by environmental noise and vibration

The Helmholtz resonator effect of a room with an open window or ventilation duct has been studied theoretically and experimentally. The effect results in a sound pressure buildup at infrasonic frequencies. For comparison, the frequencies of the standing-wave room resonances are above the infrasonic range for residential dwellings. The relations between the sound pressure inside a room and outside (environmental) sound pressure or vibration acceleration have been calculated for the third-octave frequency band incorporating the Helmholtz resonance frequency. The experiment on a small-scale model illustrated the Helmholtz resonator effect caused by environmental vibration.     

Limits of the paraxial approximation in laser beams

The validity of the paraxial approximation for laser beams in free space is studied via an integral criterion based on the propagation invariants of Helmholtz and paraxial wave equations. This approach allows one to determine the paraxial limit for beams with nondefined spot size and for beams described by more parameters in addition to typical longitudinal wavelength and transverse waist. As examples, the paraxiality of higher-order Hermite, Laguerre, and Bessel-Gaussian beams was completely determined. This method could be extended to nonlinear optics and Bose condensates.     

Thermodynamics and elastic properties of Ta from first-principles calculations

<正>Within the framework of the quasiharmonic approximation,the thermodynamics and elastic properties of Ta, including phonon density of states(DOS),equation of state,linear thermal expansion coefficient,entropy,enthalpy, heat capacity,elastic constants,bulk modulus,shear modulus,Young’s modulus,microhardness,and sound velocity, are studied using the first-principles projector-augmented wave method.The vibrational contribution to Helmholtz free energy is evaluated from the first-principles phonon DOS and the Debye model.The thermal electronic contribution to Helmholtz free energy is estimated from the integration over the electronic DOS.By comparing the experimental results with the calculation results from the first-principles and the Debye model,it is found that the thermodynamic properties of Ta are depicted well by the first-principles.The elastic properties of Ta from the first-principles are consistent with the available experimental data.     

Suppression of Helmholtz resonance using inside acoustic liner

When a Helmholtz resonator is exposed to grazing flow, an unstable shear layer at the opening can cause the occurrence of acoustic resonance under appropriate conditions. In this paper, in order to suppress the flow-induced resonance, the effects of inside acoustic liners placed on the side wall or the bottom of a Helmholtz resonator are investigated. Based on the one-dimensional sound propagation theory, the time domain impedance model of a Helmholtz resonator with inside acoustic liner is derived, and then combined with a discrete vortex model the resonant behavior of the resonator under grazing flow is simulated. Besides, an experiment is conducted to validate the present model, showing significant reduction of the peak sound pressure level achieved by the use of the side-wall liners. And the simulation results match reasonably well with the experimental data. The present results reveal that the inside acoustic liner can not only absorb the resonant sound pressure, but also suppress the fluctuation motion of the shear layer over the opening of the resonator. In all, the impact of the acoustic liners is to dampen the instability of the flow-acoustic coupled system. This demonstrates that it is a convenient and effective method for suppressing Helmholtz resonance by using inside acoustic liner.     

Sound generation due to the interaction of surface waves

Two opposite gravity-capillary waves of equal frequency give rise to the formation of a standing wave on the ocean surface and, thus, in the nonlinear approximation, generate a sound wave of twofold frequency with an amplitude proportional to the squared height of the surface wave [1]. This effect, being caused by the nonlinear interaction of opposite surface waves, can give rise to the radiation of sound waves in both ocean and atmosphere [2]. Opposite waves can appear in the ocean as a result of different ocean-atmosphere interactions and, in particular, as a result of the blocking of capillary waves on the slope of a gravity wave.     

由小斜率近似计算空气声经粗糙海面透射至深海中的声场（英文）

The first-order small slope approximation is applied to the problem of the sound transmission from an airborne source into deep ocean through a rough sea surface,and expressions are derived for the transmitted sound field and its coherent component.Numerical calculations are performed.The sea surface is assumed to be random rough with a PiersonMoskowitz spectrum and to have height variations in only one dimension.For the case of the airborne line source,the small slope approximation results are in good agreement with those from integral equations,and show that the mean of sound intensity at observation direction with shallow depression angle increases and approaches a limit as the root-mean-square surface height increases,while the coherent field intensity consistently decreases.For the case of the point source,the small slope approximation results show that the mean of sound intensity depends significantly on the source-receiver bearing angle,but the coherent field intensity is independent of this angle.     

由小斜率近似计算空气声经粗糙海面透射至深海中的声场

采用一级小斜率近似方法处理空气声经粗糙海面透射至深海中的声场问题,导出了透射场及其相干分量的表达式。假定海面高度一维变化且频谱满足PM谱,采用小斜率近似方法计算了相应的透射场。对于空气中的线源,小斜率近似与积分方程方法结果一致。当水下测量点距离较远且深度较浅时,平均声强随海面均方根高度增加而增加至一极限值,相干声强则随海面均方根高度增加而一致减小。对于空气中的点源,小斜率近似计算表明,水下平均声强还依赖于测量点相对于声源的方位,而相干声强则与测量点的方位无关。      

The impact of the neck material on the sound absorption performance of Helmholtz resonators

Helmholtz resonators with sound absorption materials filling the neck may have an improved sound absorption capacity. In this work, parallel perforated ceramics with different perforation diameters were installed into the neck of a Helmholtz resonator to improve its acoustic impedance to simultaneously achieve a better acoustic absorption coefficient and a wider absorption bandwidth. An experimental system was built to investigate the effect of the perforation diameters on the sound absorption performance of the resonator. It is found that nonlinear effects near the resonance frequency affect the resonator?s neck mouth impedance and further its sound absorption performance significantly. For frequency range 50–500 Hz, a model of the neck mouth impedance is developed based on a revised Forchheimer relationship. The experimental results are in good agreement with the theoretical model.     

On the Lorentz group SO(3, 1), geometrical supersymmetric action for particles, and square root operators

In this work the problem of the square-root quantum operators is analyzed from the theoretical group point of view. To this end, we considered the relativistic geometrical action of a particle in the superspace in order to quantize it and to obtain the spectrum of physical states with the Hamiltonian remaining in the natural square-root form. The generators of group SO(3, 1) are introduced and the quantization of this model is performed completely. The obtained spectrum of physical states and the Fock construction for the physical states from the Hamiltonian operator in square-root form was proposed, explicitly constructed, and compared with the spectrum and Fock construction obtained from the Hamiltonian in the standard form (i.e., quadratic in momenta). We show that the only states that the square-root Hamiltonian can operate with correspond to the representations with the lowest weights λ = 1/4 and 3/4 with four possible (nontrivial) fractional representations for the group decomposition of the spin structure. The text was submitted by the author in English.     

Multiple-order derivatives of a waveguide acoustic field with respect to sound speed, density, and frequency

An adjoint perturbative method is used to derive expressions for the first- through third-order derivatives of a pressure field with respect to sound speed, density, and frequency, for the restricted case of a laterally homogenous waveguide in which environmental parameters are only a function of depth. By using a normal-mode Green's function, the three-dimensional spatial correlation required by the standard acoustic adjoint equation can be reduced to a set of one-dimensional depth integrals. The resulting expressions for the first-order derivative are similar to those obtained by previous perturbative approaches based on the depth-separated wave equation, but the approach followed here permits straightforward extension to higher-order derivatives. Explicit evaluations of the expressions for a representative shallow-water waveguide model are in excellent agreement with numerical finite-difference computations. An analysis of the expressions as a function of source-receiver range finds the contributions to the mode amplitude derivatives to be non-negligible at ranges less than a few modal interference lengths, for parameters associated with the ocean bottom. Therefore, linear perturbative inversion methods that perturb only horizontal wavenumbers and not mode amplitudes should either be used with caution or modified to incorporate the expressions presented here.     

Sound absorption of microperforated panel mounted with helmholtz resonators

Microperforated panel (MPP) absorbers have been widely used in noise reduction and are regarded as a promising alternative to the traditional porous materials. However, the absorption bandwidth of a single-layer MPP is insufficient to compete with the porous materials. In order to improve the sound absorption ability of the single-layer MPP, MPP mounted with Helmholtz resonators (MPPHR) is introduced. Based on the MPP, Helmholtz resonators theory and electro-acoustical equivalent circuit principle, sound absorption properties of MPPHR are studied. Simulation and experimental results show that MPPHR have two peak frequencies and one anti-resonant frequency. The low-frequency peak is dependent on the Helmholtz resonators, while the high frequency peak is close to the peak of the single-layer MPP. The low-frequency sound absorption peaks move to low frequency with the neck length and the volume of Helmholtz resonators increasing. The high-frequency sound absorption peaks move to high frequency with the volume of Helmholtz resonators cavity increasing. Multiple Helmholtz resonator parallel MPP structure can provide more sound absorption than single MPPHR at low frequency range due to the introduction of more additional sound absorption peaks.