Axisymmetric Waves in Isothermal Accretion Discs with Vertical Self-Gravity

We extend the research of axisymmetric waves in accretion discs with three-dimensional structure to the case that vertical self-gravity of the discs is included. We derive and analyze the dispersion relation and solve the eigenfunctions numerically. The following results have been reached: vertical self-gravity expands the forbidden region of the wave propagation. As the influence of the vertical self-gravity increases, the group velocities of the waves get smaller and the vertical nodes of the wave shrink to the middle plane of the disc.     

The Pulsational Instability of Non-Isothermal Magnetized Accretion Disk with Self-Gravity in the Transition Zone

By analyzing the fifth-order dispersion relation, the influence of coupled magnetic field and self-gravity on the pulsational instability of gas pressure dominated accretion disk is investigated. Our main results are that the viscous modes become more stable with the increase of self-gravity, magnetized field and viscosity, while they enhance the instabilities of acoustic modes. The effect of self-gravity to the instability is much greater than that of magnetic field in transition zone of the accretion disk. Especially, the self-gravity affects the thermal-modes and acoustic modes strongly. Finally, we discuss our results.     

Experimental observation of motion of edge dislocations in Ge/Ge<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Si<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>/Si(001) (<Emphasis Type="Italic">x</Emphasis> = 0.2–0.6) heterostructures

The rotating magnetohydrodynamic flows of a thin layer of astrophysical and space plasmas with a free surface in a vertical external magnetic field are considered in the shallow water approximation. The presence of a vertical external magnetic field changes significantly the dynamics of wave processes in an astrophysical plasma, in contrast to a neutral fluid and a plasma layer in an external toroidal magnetic field. There are three-wave nonlinear interactions in the case under consideration. Using the asymptotic method of multiscale expansions, we have derived nonlinear equations for the interaction of wave packets: three magneto- Poincare waves, three magnetostrophic waves, two magneto-Poincare and one magnetostrophic waves, and two magnetostrophic and one magneto-Poincare waves. The existence of decay instabilities and parametric amplification is predicted. We show that a magneto-Poincare wave decays into two magneto-Poincare waves, a magnetostrophic wave decays into two magnetostrophic waves, a magneto-Poincare wave decays into one magneto-Poincare and one magnetostrophic waves, and a magnetostrophic wave decays into one magnetostrophic and one magneto-Poincare waves. There are the following parametric amplification mechanisms: the parametric amplification of magneto-Poincare waves, the parametric amplification of magnetostrophic waves, the amplification of a magneto-Poincare wave in the field of a magnetostrophic wave, and the amplification of a magnetostrophic wave in the field of a magneto-Poincare wave. The instability growth rates and parametric amplification factors have been found for the corresponding processes.     

Scattering of a Rayleigh surface acoustic wave by a small-size inhomogeneity in a solid half-space

We use the Born approximation of the perturbation method to solve the problem of scattering of a harmonic Rayleigh surface acoustic wave by a weak-contrast inhomogeneity that is small compared with the wavelength and is located in a solid half-space near its boundary. The material of the inhomogeneity differs from the material of the half-space only in its density. The Rayleigh wave incident on the inhomogeneity is excited by a monochromatic surface force source acting normally to the half-space boundary. We derive expressions for the displacement fields in the scattered spherical compressional and shear (SV- and SH-polarized) waves. Scattering of the Rayleigh wave into a Rayleigh wave is studied in detail. We find expressions for the vertical and horizontal components of the displacement vector in the scattered Rayleigh wave as well as its radiated power. It is shown that the field of the scattered surface wave is mainly formed by vertical oscillations of the inhomogeneity in the field of the incident wave. In this case, the radiated power for the scattered Rayleigh wave formed by vertical motion of the inhomogeneity in the incident-wave field depends on the depth of the inhomogeneity as the fourth power of the function describing the well-known depth dependence of the vertical displacements in the Rayleigh surface wave. Correspondingly, the dependence of the radiated power for the scattered Rayleigh wave formed by horizontal motion of the inhomogeneity depends on its location depth as the fourth power of the depth dependence of the horizontal displacements in the Rayleigh surface wave. We perform calculations of the ratio between the powers of the scattered and incident Rayleigh waves for different ratios between the velocities of the compressional and shear waves in a solid. It is shown that the radiated power for the scattered surface wave decreases sharply with increasing depth of the subsurface-inhomogeneity location. Thus, the scattering of a Rayleigh wave into a Rayleigh wave is fairly efficient only when the location depth of the inhomogeneity does not exceed about one-third of the wavelength of the shear wave in an elastic medium.     

Angle-tuned signal-resonated optical parametric oscillator based on periodically poled lithium niobate

We demonstrate an angle-tuned signal-resonated optical parametric oscillator (OPO) with periodically poled lithium niobate (PPLN) pumped by a diode-pumped Nd:YVO4 laser. 1499.8 - 1506.6 nm of signal wavelength is achieved at 140℃ by rotating a 29-μm period PPLN from 0° - 10.22° in the x-y plane while keeping the pump wave vertical to the resonator mirrors. Two pairs of the signal and idler waves of the same wavelengths can be achieved symmetrically for each pair of angles of rotation with same absolute value and opposite sign. Theoretical analyses on angle-tuned PPLN-OPO with pump wave vertical to the resonator mirrors are presented and in good agreement with our experimental results. It is also found that all interacting waves in the cavity (not inside the crystal) are always collineax for PPLN-OPO with the pump wave vertical to the resonator mirrors while phase-matching is noncollinear within the crystal.     

Rossby waves in the magnetic fluid dynamics of a rotating plasma in the shallow-water approximation

We have studied rotating magnetohydrodynamic flows of a thin layer of astrophysical plasma with a free boundary in the β-plane. Nonlinear interactions of the Rossby waves have been analyzed in the shallow-water approximation based on the averaging of the initial equations of the magnetic fluid dynamics of the plasma over the depth. The shallow-water magnetohydrodynamic equations have been generalized to the case of a plasma layer in an external vertical magnetic field. We have considered two types of the flow, viz., the flow in an external vertical magnetic field and the flow in the presence of a horizontal magnetic field. Qualitative analysis of the dispersion curves shows the presence of three-wave nonlinear interactions of the magnetic Rossby waves in both cases. In the particular case of zero external magnetic field, the wave dynamics in the layer of a plasma is analogous to the wave dynamics in a neutral fluid. The asymptotic method of multiscale expansions has been used for deriving the nonlinear equations of interaction in an external vertical magnetic field for slowly varying amplitudes, which describe three-wave interactions in a vertical external magnetic field as well as three-wave interactions of waves in a horizontal magnetic field. It is shown that decay instabilities and parametric wave amplification mechanisms exist in each case under investigation. The instability increments and the parametric gain coefficients have been determined for the relevant processes.     

Breakdown of self-similarity at the crests of large-amplitude standing water waves

We study the limiting behavior of large-amplitude standing waves on deep water using high-resolution numerical simulations in double and quadruple precision. While periodic traveling waves approach Stokes's sharply crested extreme wave in an asymptotically self-similar manner, we find that standing waves behave differently. Instead of sharpening to a corner or cusp as previously conjectured, the crest tip develops a variety of oscillatory structures. This causes the bifurcation curve that parametrizes these waves to fragment into disjoint branches corresponding to the different oscillation patterns that occur. In many cases, a vertical jet of fluid pushes these structures upward, leading to wave profiles commonly seen in wave tank experiments. Thus, we observe a rich array of dynamic behavior at small length scales in a regime previously thought to be self-similar.     

Electroseismic waves excited by vertical magnetic dipole in borenole

Acoustic and electromagnetic fields are coupled in a fluid saturated porous medium due to seismoelectric effect. Seismoelectric well logging method has been proposed to detect deep target formation utilizing such effect. Because of uncoupling of SH waves with P-SV waves, a simple and forthright way to get shear waves information is possible, especially for soft or slow formation whose shear wave velocity is lower than the velocity of borehole fluid. We consider the wave fields excited by a vertical magnetic dipole (VMD) source. Two methods are used to simulate, one is the coupled method based on Pride model and the other is the uncoupled method. For two methods, the frequency wavenumber domain representations of the acoustic field and associated seismoelectric field are formulated. The full waveforms of acoustic waves and electromagnetic wave induced SH waves excited by VMD source in the time domain propagation in borehole are simulated and analyzed.     

Hall Currents and the Rayleigh-Taylor Instability of a Finitely Conducting Plasma in the Presence of Coriolis Forces

We have studied the effect of rotation on the development of Rayleigh-Taylor instability of an incompressible, viscous, Hall, finitely conducting plasma of variable density. The solution is developed, through variational methods, for a semi-infinite plasma in which the density varies exponentially along the vertical. It is found that the system is unstable for all wave numbers when the effects of magnetic resistivity are included. The effects of coriolis forces and viscosity on the growth rate of the unstable system are found to be stabilizing while that of Hall currents is destabilizing. Finite conductivity affects the growth rate of the unstable mode differently for the smaller and larger values of the wave numbers, destabilizing for the waves of large wave length and stabilizing for waves of small wave length.     

Nonlinear Shock and Kink Waves with Complete Coriolis Force in Earth's Atmosphere

Nonlinear waves in a Boussinesq fluid model which includes both the vertical and horizontal components of Coriolis force are studied by using the semi-geostrophic approximation and the method of travelling-wave solution. Taylor series expansion has been employed to isolate the characteristics of the linear Rossby waves and to identify the nonlinear shock and kink waves. The KdV-Burgers and the compound KdV-Burgers equations are derived, their shock wave and kink wave solution are also obtained.     

Nonlinear transformation of wave packets in weakly dispersive media

We study the propagation of nonlinear modulated waves in weakly dispersive media within the framework of the Korteveg- de Vries equation. It is shown that strong generation of overtones and mean flow by the modulated packet results in asymmetry of the wave packet envelope with respect to both horizontal and vertical axes and makes the envelope skewed. The motion of the wave packet is accompanied by the emission of low-frequency and high-frequency waves that propagate in different directions from the packet. As a result, the mean amplitude of the wave packet decreases with distance. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 4, pp. 354–358, April 1999.     

Superdiffusive wave front propagation in a chemical active flow

We present experiments on the propagation of a wave front in a fluid forced by Faraday waves. The vertical periodical modulation of the acceleration induces flows in the system that modifies the Belousov-Zhabotinsky (BZ) chemical reaction dynamics. Phase waves spreading through standing waves with different symmetries results in superdiffusion. The anomalous diffusion is characterized in terms of a non-integer transport exponent which is compared with exponents resulting from tracer particles trajectories undergoing rapid, distant jumps called Lévy flights.     

直立防波堤上部分反射的三阶双色双向水波理论

为充分克服以往直立防波堤上立波波浪力的内在局限性和刻画直立防波堤堤前的多色多向波,提出一种可包含经典二维长峰波解和三维单色单向短峰波解的部分反射的三阶双色双向水波理论,并从中推断出适用于高阶多色多向波系统的一项普适法则——偶数阶频率为零,奇数阶频率个数构成一等比数列.     

套管中模式波的响应特征*

在固井质量评价中主要利用套管中模式波的幅度或衰减变化反映水泥的胶结状况,不同测井仪器在套管中激发的模式波的类型不同,研究套管中各模式波的传播特征和影响因素可充分挖掘测量数据的潜在应用价值。CBL和SBT等测井仪器在套管中主要激发拉伸波,类同于平板中的零阶对称Lamb波,水泥环封隔测井仪器的斜入射模式在套管中主要激发套管弯曲波,类同于平板中的零阶反对称Lamb波,垂直入射模式激发套管共振波,类同于平板中的高阶对称Lamb波。该文重点分析了这些模式波的衰减特征及其对微环的响应,套管弯曲波在套后耦合轻质水泥时对微环不敏感,但在套后耦合常规水泥或重水泥时,其衰减明显高于胶结良好的状况;拉伸波对微环的存在最为敏感;套管共振波对微环不敏感。     

Horseshoe-like patterns in first-order 3D random Gauss-Lagrange waves with directional spreading

The Gauss–Lagrange model for ocean waves describes the vertical and horizontal movements of water particles as three correlated Gaussian fields. The model can produce irregular waves, asymmetric in both vertical and horizontal direction, and by judicious choice of a single skewness parameter the front–back asymmetry can be regulated to realistic values. In this paper, it is shown that this additive model for shallow waters can also produce horseshoe-like patterns around moderate to high wave crests. Such phenomena are usually analyzed and described as nonlinear interaction effects between different frequencies. The tool in the paper is a Slepian model for the three-dimensional movements conditioned on a wave crest     

THz wave polarization-controlled spectroscopic imaging for anisotropic materials

We present a polarization-controlled terahertz (THz) wave spectroscopic imaging modality to investigate the anisotropy of the detected materials. The polarization of the emitted THz wave is controlled by changing the relative phase between the fundamental and second-harmonic waves in the two-color laser-induced air plasma THz generation configuration. The THz wave polarization direction is extracted by measuring the two electric field amplitudes when the polarization of the incident wave is controlled to be horizontal and vertical. The anisotropy of the industrial Sprayed-On-Foam-Insulation (SOFI) is characterized by measuring its azimuthal angle dependent THz polarization response. This work demonstrates that THz wave polarization-controlled imaging technique can be used for highly sensitive industrial nondestructive inspection and biological related characterization.     

Conventional electromagnetic acoustic transducer development for optimum Lamb wave modes

Lamb waves are normally utilized for inspecting thin metal sheets. Wheel type probes using piezoelectric oscillators have generally been used as the sensors for Lamb waves. Recently, the electromagnetic acoustic transducer (EMAT) has been developed and is beginning to be used as a Lamb wave detector. We have developed a useful type of transducer for Lamb waves. The new EMAT consists of a meander coil with a narrow distance of 2.5 mm and has a symmetrical structure in the vertical direction for both surface sides. The new EMAT can generate Lamb waves with variable wavelengths corresponding to the frequency range from approximately 300 kHz to 2.5 MHz and multiple modes, and can also generate selected symmetrical and anti-symmetrical mode Lamb waves. It is demonstrated that the optimum Lamb wave mode could be produced by the appropriate positioning of the EMATs and controlling the phase (same or inversed) of the electrical signal driving the device. The described EMAT can be used to examine steel (or other material) sheets of different thickness. It is also shown that the S0 (0.3 MHz) mode Lamb wave is the most effective for the deepest (up to 6 mm) penetration.     

Turbulence of near-inertial waves in the continuously stratified fluid

By using the normal form of continuously stratified “primitive” equations of geophysical fluid dynamics with density (in the ocean), or potential temperature (in the atmosphere) playing the role of the vertical coordinate, we decouple vortex and wave motions in the system, introduce normal variables, and derive the effective Hamiltonian for waves with frequencies close to the inertial frequency (near-inertial waves, NIW). We then apply the weak turbulence approach to the random-phase ensembles of these waves. We show how the anisotropic scale-invariance of NIW may be exploited in order to obtain the stationary power-law spectra. The non-decay anisotropic scale-invariant dispersion laws of the NIW-type were not studied previously in the weak-turbulence literature.     

Surface gravity waves in deep fluid at vertical shear flows

Special features of surface gravity waves in a deep fluid flow with a constant vertical shear of velocity is studied. It is found that the mean flow velocity shear leads to a nontrivial modification of the dispersive characteristics of surface gravity wave modes. Moreover, the shear induces generation of surface gravity waves by internal vortex mode perturbations. The performed analytical and numerical study show that surface gravity waves are effectively generated by the internal perturbations at high shear rates. The generation is different for the waves propagating in the different directions. The generation of surface gravity waves propagating along the main flow considerably exceeds the generation of surface gravity waves in the opposite direction for relatively small shear rates, whereas the latter wave is generated more effectively for high shear rates. From the mathematical standpoint, the wave generation is caused by non-self-adjointness of the linear operators that describe the shear flow.     

Acoustic waves in random fields

The effect of space- and time-dependent random mass density, velocity, and pressure fields on frequencies and amplitudes of acoustic waves is considered by means of the analytical perturbative method. The analytical results, which are valid for weak fluctuations and long wavelength sound waves, reveal frequency and amplitude alteration, the effect of which depends on the type of random field. In particular, the effect of a random mass density field is to increase wave frequencies. Space-dependent random velocity and pressure fields reduce wave frequencies. While space-dependent random fields attenuate wave amplitudes, their time-dependent counterparts lead to wave amplification. In another example, sound waves that are trapped in the vertical direction but are free to propagate horizontally are affected by a space-dependent random mass density field. This effect depends on the direction along which the field is varying. A random field, which varies along the horizontal direction, does not couple vertically standing modes but increases their frequencies and attenuates amplitudes. These modes are coupled by a random field which depends on the vertical coordinate, but the dispersion relation remains the same as in the case of the deterministic medium.