On study of the theory and algorithm of the three dimensional coupled mode-parabolic equation

A fast algorithm of sound propagation in three dimensional underwater environments is presented. On the basis of the generalized phase integral (WKBZ) theory and the beam displacement ray mode (BDRM) theory, the coupled mode parabolic equation (CMPE) theory of sound propagation in range dependent underwater environment is extended for three dimensional (3D) problems. The CMPE3D solution is expressed in terms of the normal modes     

Inversion for the sea bottom acoustic parameters by using the group time delays and amplitude of normal mode

The group time delays and amplitudes of the normal mode are derived using the normal mode filter. The sea bottom sound speed, density and attenuation are inversely deduced by matching the group time delays and the amplitude of the normal mode. A genetic algorithm (GA) is used for optimization search in the parameter space. The inverted attenuation has the nonlinear frequency relationship a = 0.29f1.91 dB/m (the unit of frequency is kHz) in the frequency range 200 - 500 Hz. The theoretical transmission loss calculated using the deduced parameters matches the experiment data very well.     

Stability and a fast calculation method of travel speed of pulse peak in convergence zone

A long-range sound propagation experiment was conducted in the West Pacific Ocean in summer 2013.The signals received by a towed array indicate that the travel speed of pulse peak(TSPP)in the convergence zones is stable.Therefore,an equivalent sound speed can be used at all ranges in the convergence zones.A fast calculation method based on the beam-displace-ment ray-mode(BDRM)theory and convergence zone theory is proposed to calculate this equivalent sound speed.The computation speed of this proposed method is over 1000 times faster than that of the conventional calculation method based on the normal mode theory,with the computation error less than 0.4%compared with the experimental result.Also,the effect of frequency and sound speed profile on the TSPP is studied with the conventional and fast calculation methods,showing that the TSPP is almost independent of the frequency and sound speed profile in the ocean surface layer.     

The WKBZ mode approach to pulsed propagation in ocean channels

In the paper, the WKBZ normal mode approach has been applied to the propagation of the pulsed energy and waveform in ocean channels. The numerical results in two different channels are given. Comparison between the WKBZ and conventional normal mode codes shows that the WKBZ mode approach is a fast and accurate method and the running time by the WKBZ approach is reduced by about two orders of magnitude.     

Normal mode propagation of impulsive soundwith moving source and receiver

A representation of impulsive sound propagation with a moving source and receiver in an ocean waveguide is derived based on the normal mode theory. The Doppler shift of individual normal mode of narrow-band pulse is analyzed. A Doppler matched condition and Doppler compensation intervals are obtained based on the analysis of the correlation between the emitted and received signals. An experiment of long-range impulse propagation at 55km in a shallow water is used to verify the theoretical results of the Doppler shift compensation.     

Extraction of mode attenuation coefficient from low frequency reverberation signal

A method of extracting normal mode attenuation coefficient from low frequency reverberation signal has been proposed.Pseudo-inverse normal mode filtering method is implemented to get single mode reverberation field firstly.Based on the assumption of separability of modal back-scattering matrix,effective back-scattering matrix element can be calculated using single mode average reverberation intensity.Finally,mode attenuation coefficient is extracted by comparing effective back-scattering matrix elements at different ranges.The extracted mode attenuation coefficients are used to predict sound transmission loss at the same experiment area. Results show that the predicted transmission loss agrees well with the measured data.This method avoids the difficult of treating the coupling between bottom scattering attenuation and normal mode propagation attenuation.Research on extraction of mode attenuation coefficient from low frequency reverberation signal is useful for both geoacoustic inversion and rapid underwater environment assessment.     

Characteristics of the transmission spectrum of the long period fiber gratings based on the coupling of core mode to the higher order cladding modes

The characteristics of the transmission spectrum of the Long-period fiber gratings (LPFGs) based on the coupling of core mode to a higher order cladding mode (HE mode) are investigated using the coupled mode theory. This kind of LPFGs is different from that based on the coupling of core mode to a lower order cladding mode because of the effect of the coupling of core mode to EH cladding mode. When the cladding mode order is higher, the coupling coefficients of core mode to HE and EH cladding modes are comparable and both of the propagation constants of HE and EH cladding modes approach, so the spectrum has an additional loss peak. The bandwidth of LPFG based on the coupling of core mode to different cladding mode differs greatly. With the change of the mode orders from lower to higher, the transmission spectrum changes from narrow to wide and more narrow.     

SCATTERING NEAR FIELD OF A RECTANGULAR COMPOSITE PLATE IMMERSED IN WATER

According to the extensive theory of flexural vibration of elastic-viscoelastic composite platesystem in a previous paper,the vibration and scattering sound near field of an immersed rectangularelastic-viscoelastic composite plate in an underwater sound are studied.The solution for deflectionof the composite plate is expanded into a series in terms of normal mode,whatever plate is vibratingin water under the influence of incident sound wave.The interaction between normal modes owingto sound field coupling is taken into consideration.As a function of(kl_1,r;m,n;p,q),the couplingcoefficients between(m,n);(p,q)modes of vibration are calculated numerically.Whith these coef-ficients,the vibration of composite plate and the sound irradiation from which may be characterized(where k is wave number,l_1,is length of one parallel edges,r=1_2/l_1 is parametric variable,l_2 is lengthof another parallel edges).And then,the complex values of amplitude of normal modes for flexuralmotion of a Steel-Rubber bilaminar plate     

A Method of Measuring the In Situ Seafloor Sound Speed using Two Receivers with WarDing Transformation

We present a method of measuring the in situ superficial seafloor sound speed by using two receivers deployed vertically in sediment, based on the dispersion characteristic of normal modes in shallow water. Warping transfor- mation is adopted to extract the first normal mode from the broadband propagation signals. Some experimental results which could validate the method are shown. One of the advantages of the method is that the seafloor sound speed can be solved directly from the relative vertical transmission loss of the first normal mode without the exact priori information of the environmental parameters such as the sound speed profile, the water-column depth and the source location.     

Influence of warm eddies on sound propagation in the Gulf of Mexico

An automatic detection method is employed to identify and track eddies in the Gulf of Mexico. The physical parameters of the eddies, such as lifespan, radius, and distribution position are first examined and used to determine the spatio–temporal evolution of a strong warm eddy separated from the Mexico current. Then, the influence of this strong warm eddy on sound propagation during its lifespan are comprehensively analyzed with the parabolic equation and explained by using the normal mode and ray theories. Additionally, the influence of mesoscale eddies on the redistribution of total depth-integrated energy among the normal modes in the deep water is also discussed. The variation of arrival angle is investigated to explain the spreading acoustic energy caused by eddies. Overall, the results show that warm eddies can change the propagation paths and cause the convergence zone to broaden and approach the sound source. Moreover,the warm eddy can disperse sound energy and cause the total depth-integrated energy to incline to a lower normal mode.Throughout the whole of these three periods(eddy generating, eddy maturing, and eddy terminating), the fluctuation in the transmission loss is up to 30 dB(depending on the relative location of eddy center to the source).     

Inversion of acoustic mode coupling coefficient matrix

It is found that the normal mode amplitude time series consist of multi-frequency component by analyzing the structure of acoustical signal when internal wave propagation exists, and each frequency is the product of internal wave speed and the normal mode wave number difference between acoustical receivers and source. The amplitude of each component is proportional to the acoustic mode coupling coefficient. The structure of the normal mode coefficient time series is still complex even the internal waves do not reshape when they propagate from the acoustical receivers to the source. A method is presented to compute the AMCCM by the feature of IWs' motion and the relation between the AMCCM and the acoustical signal fluctuation amplitude. The IWs data measured in the 2001 Asia experiment (ASIAEX2001) is used to check the accuracy of this method by numerical simulation. It is show that the method is accurate to compute the AMCCM.     

Estimation of boundary parameters and prediction of transmission loss based upon ray acoustics

1 IntroductionThe sea and its boundaries (the sea surface and the sea floor) can exert a profound influenceon the acoustic energy propagation through the action of reflection, scattering and absorption.The performance of an underwater acoustic system is related to the sound propagation in thesea. transmission Loss (TL) is an important parameter used to describe quantitatively thecharacteristics of the underwater sound propagation. Prediction of TL plays an important rolein forecasting acoust…     

A coupled-mode sound propagation model with complex effective depth

A coupled-mode sound propagation model with complex effective depth is presented,in order to involve the effect of branch line integral for acoustic field in a range-dependent waveguide.The equations of motion and continuity are used to obtain the coupled equations,which satisfy boundary conditions in the waveguide with varying topography and contain one coupling matrix.Meanwhile,the couplings between discrete and continuous spectrum are dealt with based on complex effective depth theory.Numerical simulations show that the accuracy of transmission loss is improved by the coupled mode model when eigenvalues of trapped modes are located near the branch point.The acoustic field in a non-horizontally stratified waveguide can be calculated efficiently and accurately by this model,and the energy corresponding to trapped modes,leaky modes and branch line integral can be considered adequately.     

A study on the multi-freedom broadband impedance model for time-domain simulations

The purpose of this paper is to construct a general broadband impedance model, which is suited for predicting acoustic propagation problems in time domain.A multi-freedom broadband impedance model for sound propagation over impedance surfaces is proposed and the corresponding time domain impedance boundary condition is presented.Basing on the extended Helmholtz resonator,the multi-freedom impedance model is constructed through combing with a sum of rational functions in the form of general complex-conjugate pole-residue pairs and it is proved that the impedance model is well posed.The impedance boundary condition can be implemented into a computational aeroacoustics solver by a recursive convolution technique, which results in a fast and computationally efficient algorithm.The two dimensional and three dimensional benchmark problems are selected to validate the accuracy of the proposed impedance model and time domain simulations.The numerical results are in good agreement with the reference solutions.It is demonstrated that the proposed impedance model can be used to describe the broadband characteristics of acoustic liners,and the corresponding time domain impedance boundary condition is viable and accurate for the prediction of sound propagation over broadband impedance surfaces.     

Numerical prediction of envelope line-spectrum intensity in underwater acoustic waveguides

In order to predict the detectible range and region of passive sonar in underwater channel,the attenuation causes of envelope line-spectrum height during vessel noise propagation are analyzed and an approach of numerical prediction is proposed.In the paper a model for vessel radiated noise is established by a periodically locally stationary random process,two formulae of the envelope line-spectrum height with and without background-noise are deduced, therefore the attenuation rule of the envelope line-spectrum height is obtained.It is shown that the transmission loss of the sound level of the envelope line-spectrum is same as the sound level of the stationary spectrum,but the decrease of envelope line-spectrum height depends on a modified scale of amplitude modulation depth which is variable with the ratio of signal to noise. An approach of numerical prediction for envelope line-spectrum height is as follows:first,the transmission loss of the stationary radiated noise is derived using the numerical approaches of normal modes or wavenumber integration or PE etc.,then the ratio of signal to noise on sound field is calculated,finally the decrease of envelope line-spectrum height is obtained according to the modified scale,and the envelope line-spectrum height in sound field is predicted.The theory and the numerical prediction approach possess certain innovation,practicality,simplicity and suitability for engineering.     

AN EXPERIMENTAL INVESTIGATION OF TURNING-POINT CONVERGENCE-ZONES IN A DEEP SOUND CHANNEL IN THE SOUTH CHINA SEA

in October 1983,an experiment was carried out to investigate the characteristics of turning-point convergence-zones and of underwater sound propagation in a deep sound channel in the SouthChina Sea by using explosive sound sources.In this paper,we present the experimental results forthe source depths of 200 m and 500 m.By using the theory on the turning-point convergence-zoneand parabolic approximation,the measured data are analysed.For low-frequencies the measuredpositions and convergence-gains of zones coincide with calculated results quite well.     

Theoretical Prediction of the Acoustical Nonlinear Field Radiated from a Concave Focusing Source with a Wide Aperture Angle

We propose a time-domain theoretical approach to predict the acoustic nonlinear field radiated from a concave focusing spherical source with a wide aperture angle. The nonlinear sound propagation is theoretically described by an accurate mathematical model including the continuity and momentum equations. Numerical calculation is implemented by using the finite difference time domain algorithm in the oblate spheroidal coordinate system. To examine the validity of the theoretical model, we calculate the sound fields radiated from concave spherical focusing transducers with aperture angles 30° and 40° and the results are compared with those obtained by the SBE solution.     

The numerical simulation of the average reverberation intensities in shallow water

A reverberation model for estimating the average reverberation inten-sity in layered shallow water is presented.The reverberation intensity is calculated interms of ray theory for short range and normal mode theory for long range.Thecalculation accuracy has been improved by taking into account the effect of complexeigenvalues on the incident normal mode field.From the comparison between dif-ferent scattering models it has been shown that the separable bistatic-backscatteringmodel is acceptable.This makes it possible to calculate reverberation by using onlythe monostatic-backscattering coefficient and to save greatly the computing time.     

Progress of Project ＂Basic Characteristics of an A=2 Tokamak Reactor-like Plasma＂ during 2006

This report consists of two main research activities ： The first one is the study of MHD ballooning stability of tokamak plasmas, the second is about some fundamental aspect in the ECR wave propagation and power deposition. Main results are summarized here in three parts briefly. In the first part, the instabilities of tokamak plasma in the negative shear regime is studied and characteristics of the unstable mode is described, the scaling law of the growth rate over plasma parameters is given. In the second part, by using the restrict Solov＇ev configuration, the correctness of the usual s,α model in ballooning mode theory is analyzed. In the third part, the deposition of the power density of the ECR ordinary wave in the HL-2A plasma is calculated.     

Investigation of long-range sound propagation in surface ducts

Understanding the effect of source-receiver geometry on sound propagation in surface ducts can improve the performance of near-surface sonar in deep water. The Lloyd-mirror and normal mode theories are used to analyze the features of surface-duct propagation in this paper. Firstly, according to the Lloyd-mirror theory, a shallow point source generates directional lobes, whose grazing angles are determined by the source depth and frequency. By assuming a part of the first lobe to be just trapped in the surface duct, a method to calculate the minimum cutoff frequency （MCF） is obtained. The presented method is source depth dependent and thus is helpful for determining the working depth for sonar. Secondly, it is found that under certain environments there exists a layer of low transmission loss （TL） in the surface duct, whose thickness is related to the source geometry and can be calculated by the Lloyd-mirror method. The receiver should be placed in this layer to minimize the TL. Finally, the arrival angle on a vertical linear array （VLA） in the surface duct is analyzed based on normal mode theory, which provides a priori knowledge of the beam direction of passive sonar.