Highly nonlinear internal solitary waves over the continental shelf of the northwestern South China Sea

Large amplitude internal solitary waves (ISWs) often exhibit highly nonlinear effects and may contribute significantly to mixing and energy transporting in the ocean. We observed highly nonlinear ISWs over the continental shelf of the northwestern South China Sea (19A degrees 35'N, 112A degrees E) in May 2005 during the Wenchang Internal Wave Experiment using in-situ time series data from an array of temperature and salinity sensors, and an acoustic Doppler current profiler (ADCP). We summarized the characteristics of the ISWs and compared them with those of existing internal wave theories. Particular attention has been paid to characterizing solitons in terms of the relationship between shape and amplitude-width. Comparison between theoretical prediction and observation results shows that the high nonlinearity of these waves is better represented by the second-order extended Korteweg-de Vries (KdV) theory than the first-order KdV model. These results indicate that the northwestern South China Sea (SCS) is rich in highly nonlinear ISWs that are an indispensable part of the energy budget of the internal waves in the northern South China Sea.

A study of internal solitary waves observed on the continental shelf in the northwestern South China Sea

Based on in-situ time series data from the acoustic Doppler current profiler (ADCP) and thermistor chain in Wenchang area, a sequence of internal solitary wave (ISW) packets was observed in September 2005, propagating northwest on the continental shelf of the northwestern South China Sea (SCS). Corresponding to different stratification of the water column and tidal condition, both elevation and depression ISWs were observed at the same mooring location with amplitude of 35 m and 25 m respectively in different days. Regular arrival of the remarkable ISW packets at approximately the diurnal tidal period and the dominance of diurnal internal waves in the study area, strongly suggest that the main energy source of the waves is the diurnal tide. Notice that the wave packets were all riding on the troughs and shoulders of the internal tides, they were probably generated locally from the shelf break by the evolution of the internal tides due to nonlinear and dispersive effects.

复杂介质中地震波场数值模拟研究——基于广义正交多项式迭积微分算子法

In this paper, we propose a new numerical modeling method – Convolutional Forsyte Polynomial Differentiator (CFPD), aimed at simulating seismic wave propagation in complex media with high efficiency and accuracy individually owned by short-scheme finite differentiator and general convolutional polynomial method. By adjusting the operator length and optimizing the operator coefficient, both global and local informations can be easily incorporated into the wavefield which is important to invert the undersurface geological structure. The key issue in this paper is to introduce the convolutional differentiator based on Forsyte generalized orthogonal polynomial in mathematics into the spatial differentiation of the first velocity-stress equation. To match the high accuracy of the spatial differentiator, this method in the time coordinate adopts staggered grid finite difference instead of conventional finite difference to model seismic wave propagation in heterogeneous media. To attenuate the reflection artifacts caused by artificial boundary, Perfectly Matched Layer (PML) absorbing boundary is also being considered in the method to deal with boundary problem due to its advantage of automatically handling large-angle emission. The PML formula for acoustic equation and first-order velocity-stress equation are also derived in this paper. There is little difference to implement the PML boundary condition in all kind of wave equations, but in Biot media, special attenuation factors should be taken. Numerical results demonstrate that the PML boundary condition is better than Cerjan absorbing boundary condition which makes it more suitable to hand the artificial boundary reflection. Based on the theories of anisotropy, Biot two-phase media and viscous-elasticity, this paper constructs the constitutive relationship for viscous-elastic and two-phase media, and further derives the first-order velocity-stress equation for 3D viscous-elastic and two-phase media. Numerical modeling using CFPD method is carried out in the above-mentioned media. The results modeled in the viscous-elastic media and the anisotropic pore elastic media can better explain wave phenomena of the true earth media, and can also prove that CFPD is a useful numerical tool to study the wave propagation in complex media.

特大地震激发地球自由振荡的数值模拟研究

Large earthquakes, such as the Chile earthquake in 1960 and the Sumatra-Andaman earthquake on Dec 26, 2004 in Indonesia, have generated the Earth’s free oscillations. The eigenfrequencies of the Earth’s free oscillations are closely related to the Earth’s internal structures. The conventional methods, which mainly focus on calculating the eigenfrequecies by analytical ways, and the analysis on observations can not easily study the whole processes from earthquake occurrence to the Earth’s free oscillation inspired. Therefore, we try to use numerical method incorporated with large-scale parallel computing to study on the Earth’s free oscillations excited by giant earthquakes. We first give a review of researches and developments of the Earth’s free oscillation, and basical theories under spherical coordinate system. We then give a review of the numerical simulation of seismic wave propagation and basical theories of spectral element method to simulate global seismic wave propagation. As a first step to study the Earth’s free oscillations, we use a finite element method to simulate the propagation of elastic waves and the generation of oscillations of the chime bell of Marquis Yi of Zeng, by striking different parts of the bell, which possesses the oval crosssection. The bronze chime bells of Marquis Yi of Zeng are precious cultural relics of China. The bells have a two-tone acoustic characteristic, i.e., striking different parts of the bell generates different tones. By analysis of the vibration in the bell and the spectrum analysis, we further help the understanding of the mechanism of two-tone acoustic characteristics of the chime bell of Marquis Yi of Zeng. The preliminary calculations have clearly shown that two different modes of oscillation can be generated by striking different parts of the bell, and indicate that finite element numerical simulation of the processes of wave propagation and two-tone generation of the chime bell of Marquis Yi of Zeng is feasible. These analyses provide a new quantitative and visual way to explain the mystery of the two-tone acoustic characteristics. The method suggested by this study can be applied to simulate free oscillations excited by great earthquakes with complex Earth structure. Taking into account of such large-scale structure of the Earth, small-scale low-precision numerical simulation can not simply meet the requirement. The increasing capacity in high-performance parallel computing and progress on fully numerical solutions for seismic wave fields in realistic three-dimensional spherical models, Spectral element method and high-performance parallel computing were incorporated to simulate the seismic wave propagation processes in the Earth’s interior, without the effects of the Earth’s gravitational potential. The numerical simulation shows that, the results of the toroidal modes of our calculation agree well with the theoretical values, although the accuracy of our results is much limited, the calculated peaks are little distorted due to three-dimensional effects. There exist much great differences between our calculated values of spheroidal modes and theoretical values, because we don’t consider the effect the Earth’ gravitation in numerical model, which leads our values are smaller than the theoretical values. When , is much smaller, the effect of the Earth’s gravitation make the periods of spheroidal modes become shorter. However, we now can not consider effects of the Earth’s gravitational potential into the numerical model to simulate the spheroidal oscillations, but those results still demonstrate that, the numerical simulation of the Earth’s free oscillation is very feasible. We make the numerical simulation on processes of the Earth’s free oscillations under spherically symmetric Earth model using different special source mechanisms. The results quantitatively show that Earth’s free oscillations excited by different earthquakes are different, and oscillations at different locations are different for free oscillation excited by the same earthquake. We also explore how the Earth’s medium attenuation will take effects on the Earth’s free oscillations, and take comparisons with the observations. The medium attenuation can make influences on the Earth’s free oscillations, though the effects on lower-frequency fundamental oscillations are weak. At last, taking 2008 Wenchuan earthquake for example, we employ spectral element method incorporated with large-scale parallel computing technology to investigate the characteristics of seismic wave propagation excited by Wenchuan earthquake. We calculate synthetic seismograms with one-point source model and three-point source model respectively. Full 3-D visualization of the numerical results displays the profile of the seismic wave propagation with respect to time. The three-point source, which was proposed by the latest investigations through field observation and reverse estimation, can better demonstrate the spatial and temporal characteristics of the source rupture processes than one-point source. Primary results show that those synthetic signals calculated from three-point source agree well with the observations. This can further reveal that the source rupturing process of Wenchuan earthquake is a multi-rupture process, which is composed by at least three or more stages of rupture processes. In conclusion, the numerical simulation can not only solve some problems concluding the Earth’s ellipticity and anisotropy, which can be easily solved by conventional methods, but also finally solve the problems concluding topography model and lateral heterogeneity. We will try to find a way to fully implement self-gravitation in spectral element method in future, and do our best to continue researching the Earth’s free oscillations using the numerical simulations to see how the Earth’ lateral heterogeneous will affect the Earth’s free oscillations. These will make it possible to bring modal spectral data increasingly to bear on furthering our understanding of the Earth’s three-dimensional structure.

SCANNING ACOUSTIC MICROSCOPE FOR CHARACTERIZATION OF ARTERIAL PLAQUE

Unstable arterial plaque is likely the key component of atherosclerosis, a disease which is responsible for two-thirds of heart attacks and strokes, leading to approximately 1 million deaths in the United States. Ultrasound imaging is able to detect plaque but as of yet is not able to distinguish unstable plaque from stable plaque. In this work a scanning acoustic microscope (SAM) was implemented and validated as tool to measure the acoustic properties of a sample. The goal for the SAM is to be able to provide quantitative measurements of the acoustic properties of different plaque types, to understand the physical basis by which plaque may be identified acoustically. The SAM consists of a spherically focused transducer which operates in pulse-echo mode and is scanned in a 2D raster pattern over a sample. A plane wave analysis is presented which allows the impedance, attenuation and phase velocity of a sample to be de- termined from measurements of the echoes from the front and back of the sample. After the measurements, the attenuation and phase velocity were analysed to ensure that they were consistent with causality. The backscatter coefficient of the samples was obtained using the technique outlined by Chen et al [8]. The transducer used here was able to determine acoustic properties from 10-40 MHz. The results for the impedance, attenuation and phase velocity were validated for high and low-density polyethylene against published results. The plane wave approximation was validated by measuring the properties throughout the focal region and throughout a range of incidence angles from the transducer. The SAM was used to characterize a set of recipes for tissue-mimicking phantoms which demonstrate indepen- dent control over the impedance, attenuation, phase velocity and backscatter coefficient. An initial feasibility study on a human artery was performed.

An acoustic correction method for extracting sound signals

Sound waves are propagating pressure fluctuations and are typically several orders of magnitude smaller than the pressure variations in the flow field that account for flow acceleration. On the other hand, these fluctuations travel at the speed of sound in the medium, not as a transported fluid quantity. Due to the above two properties, the Reynolds averaged Navier-Stokes (RANS) equations do not resolve the acoustic fluctuations. Direct numerical simulation of turbulent flow is still a prohibitively expensive tool to perform noise analysis. This paper proposes the acousticcorrectionmethod, an alternative and affordable tool based on a modified defect correction concept, which leads to an efficient algorithm for computational aeroacoustics and noise analysis.

Parametric study of nonlinear electrostatic waves in two-dimensional quantum dusty plasmas

The nonlinear properties of two-dimensional cylindrical quantum dust-ion-acoustic (QDIA) and quantum dust-acoustic (QDA) waves are studied in a collisionless, unmagnetized and dense (quantum) dusty plasma. For this purpose, the reductive perturbation technique is employed to the quantum hydrodynamical equations and the Poisson equation, obtaining the cylindrical Kadomtsev–Petviashvili (CKP) equations. The effects of quantum diffraction, as well as quantum statistical and geometric effects on the profiles of QDIA and QDA solitary waves are examined. It is found that the amplitudes and widths of the nonplanar QDIA and QDA waves are significantly affected by the quantum electron tunneling effect. The addition of a dust component to a quantum plasma is seen to affect the propagation characteristics of localized QDIA excitations. In the case of low-frequency QDA waves, this effect is even stronger, since the actual form of the potential solitary waves, in fact, depends on the dust charge polarity (positive/negative) itself (allowing for positive/negative potential forms, respectively). The relevance of the present investigation to metallic nanostructures is highlighted.

Alfvén Waves in the Lower Solar Atmosphere

The flow of energy through the solar atmosphere and the heating of the Sun's outer regions are still not understood. Here, we report the detection of oscillatory phenomena associated with a large bright-point group that is 430,000 square kilometers in area and located near the solar disk center. Wavelet analysis reveals full-width half-maximum oscillations with periodicities ranging from 126 to 700 seconds originating above the bright point and significance levels exceeding 99%. These oscillations, 2.6 kilometers per second in amplitude, are coupled with chromospheric line-of-sight Doppler velocities with an average blue shift of 23 kilometers per second. A lack of cospatial intensity oscillations and transversal displacements rules out the presence of magneto-acoustic wave modes. The oscillations are a signature of Alfvén waves produced by a torsional twist of ±22 degrees. A phase shift of 180 degrees across the diameter of the bright point suggests that these torsional Alfvén oscillations are induced globally throughout the entire brightening. The energy flux associated with this wave mode is sufficient to heat the solar corona.

Arbitrary amplitude ion-acoustic solitary excitations in the presence of excess superthermal electrons

Velocity distribution functions with an excess of superthermal particles are commonly observed in space plasmas, and are effectively modeled by a kappa distribution. They are also found in some laboratory experiments. In this paper we obtain existence conditions for and some characteristics of ion-acoustic solitary waves in a plasma composed of cold ions and kappa-distributed electrons, where kappa>3/2 represents the spectral index. As is the case for the usual Maxwell-Boltzmann electrons, only positive potential solitons are found, and, as expected, in the limit of large kappa one recovers the usual range of possible soliton Mach numbers, viz., 1 < M < 1.58. For lower values of kappa, modeling the presence of a greater superthermal component, the range of accessible Mach numbers is reduced. It is found that the amplitude of the largest possible solitons that may be generated in a given plasma (corresponding to the highest allowed Mach number for the given plasma composition) falls off with decreasing kappa, i.e., an increasing superthermal component. On the other hand, at fixed Mach number, both soliton amplitude and profile steepness increase as kappa is decreased. These changes are seen to be important particularly for kappa < 4, i.e., when the electrons have a "hard" spectrum.

Electrostatic solitary waves in the presence of excess superthermal electrons: modulational instability and envelope soliton modes

The nonlinear dynamics of electrostatic solitary waves in the form of localized modulated wavepackets is investigated from first principles. Electron-acoustic (EA) excitations are considered in a two-electron plasma, via a fluid formulation. The plasma, assumed to be collisionless and uniform (unmagnetized), is composed of two types of electrons (inertial cold electrons and inertialess kappa-distributed superthermal electrons) and stationary ions. By making use of a multiscale perturbation technique, a nonlinear Schrodinger equation is derived for the modulated envelope, relying on which the occurrence of modulational instability (MI) is investigated in detail. Stationary profile localized EA excitations may exist, in the form of bright solitons (envelope pulses) or dark envelopes (voids). The presence of superthermal electrons modifies the conditions for MI to occur, as well as the associated threshold and growth rate. The concentration of superthermal electrons (i.e., the deviation from a Maxwellian electron distribution) may control or even suppress MI. Furthermore, superthermality affects the characteristics of solitary envelope structures, both qualitatively (supporting one or the other type, for different.) and quantitatively, changing their characteristics (width, amplitude). The stability of bright and dark-type nonlinear structures is confirmed by numerical simulations.

Electron-scale electrostatic solitary waves and shocks: the role of superthermal electrons

The propagation of electron-acoustic solitary waves and shock structures is investigated in a plasma characterized by a superthermal electron population. A three-component plasma model configuration is employed, consisting of inertial (“cold”) electrons, inertialess ? (kappa) distributed superthermal (“hot”) electrons and stationary ions. A multiscale method is employed, leading to a Korteweg-de Vries (KdV) equation for the electrostatic potential (in the absence of dissipation). Taking into account dissipation, a hybrid Korteweg-de Vries-Burgers (KdVB) equation is derived. Exact negative-potential pulse- and kink-shaped solutions (shocks) are obtained. The relative strength among dispersion, nonlinearity and damping coefficients is discussed. Excitations formed in superthermal plasma (finite ?) are narrower and steeper, compared to the Maxwellian case (infinite ?). A series of numerical simulations confirms that energy initially stored in a solitary pulse which propagates in a stable manner for large ? (Maxwellian plasma) may break down to smaller structures or/and to random oscillations, when it encounters a small-? (nonthermal) region. On the other hand, shock structures used as initial conditions for numerical simulations were shown to be robust, essentially responding to changed in the environment by a simple profile change (in width).

A Physically-Constrained Source Model For FDTD Acoustic Simulation

The Finite Difference Time Domain (FDTD) method is becoming increasingly popular for room acoustics simulation. Yet, the literature on grid excitation methods is relatively sparse, and source functions are traditionally implemented in a hard or additive form
using arbitrarily-shaped functions which do not necessarily obey the physical laws of sound generation. In this paper we formulate
a source function based on a small pulsating sphere model. A physically plausible method to inject a source signal into the grid
is derived from first principles, resulting in a source with a near-flat spectrum that does not scatter incoming waves. In the final
discrete-time formulation, the source signal is the result of passing a Gaussian pulse through a digital filter simulating the dynamics of the pulsating sphere, hence facilitating a physically correct means to design source functions that generate a prescribed sound field.

Dynamical characteristics of solitary waves, shocks and envelope modes in kappa-distributed non-thermal plasmas: an overview

Space plasmas provide abundant evidence of highly energetic particle population, resulting in a long-tailed non-Maxwellian distribution. Furthermore, the first stages in the evolution of plasmas produced during laser-matter interaction are dominated by nonthermal electrons, as confirmed by experimental observation and computer simulations. This phenomenon is efficiently modelled via a kappa-type distribution. We present an overview, from first principles, of the effect of superthermality on the characteristics of electrostatic plasma waves. We rely on a fluid model for ion-acoustic excitations, employing a kappa distribution function to model excess superthermality of the electron distribution. Focusing on nonlinear excitations (solitons), in the form of solitary waves (pulses), shocks and envelope solitons, and employing standard methodological tools of nonlinear plasmadynamical analysis, we discuss the role of excess superthermality in their propagation dynamics (existence laws, stability profile), geometric characteristics and stability. Numerical simulations are employed to confirm theoretical predictions, namely in terms of the stability of electrostatic pulses, as well as the modulational stability profile of bright- and dark-type envelope solitons.

Dust-ion-acoustic supersolitons in dusty plasmas with nonthermal electrons

Supersolitons are a recent addition to the literature on large-amplitude solitary waves in multispecies plasmas. They are distinguished from the usual solitons by their associated electric field profiles which are inherently distinct from traditional bipolar structures. In this paper, dust-ion-acoustic modes in a dusty plasma with stationary negative dust, cold fluid protons, and nonthermal electrons are investigated through a Sagdeev pseudopotential approach to see where supersolitons fit between ranges of ordinary solitons and double layers, as supersolitons always have finite amplitudes. They therefore cannot be described by reductive perturbation treatments, which rely on a weak amplitude assumption. A systematic methodology and discussion is given to distinguish the existence domains in solitary wave speed and amplitude for the different solitons, supersolitons and double layers, in terms of compositional parameters for the plasma model under consideration. © 2013 American Physical Society.

Re-examining the Cairns-Tsallis model for ion acoustic solitons

Recently, a hybrid distribution function was proposed to describe a plasma species with an enhanced superthermal component. This combines a Cairns-type "nonthermal" form with the Tsallis theory for nonextensive thermodynamics. Using this alternative model, the propagation of arbitrary amplitude ion acoustic solitary waves in a two-component plasma is investigated. From a careful study of the distribution function it is found that the model itself is valid only for a very restricted range in the q-nonextensive parameter and the nonthermality parameter, a. Solitary waves, the amplitude and nature of which depend sensitively on both q and a, can exist within a narrow range of allowable Mach numbers. Both positive and negative potential structures are found, and coexistence may occur. © 2013 American Physical Society.