Surface waves in a micropolar elastic solid containing voids

The present paper investigates the effect of voids on the propagation of surface waves in a homogeneous micropolar elastic solid medium which contains a distribution of vacuous pores (voids). The general theory for surface wave propagation in micropolar elastic media containing voids has been presented. Particular cases of surface waves (Rayleigh’s, Love’s and Stoneley’s) in micropolar media which contain vacuous pores have been deduced from the above general theory. Discussions have been made in each case to highlight the effect of voids and micropolar character of the material medium separately. Their joint effect has also been studied in details. Modulation of Rayleigh wave velocity has been studied numerically. It is observed that Love waves are not affected by the presence of voids.     

Internal solitary wave-induced flow over a corrugated bed

A combined numerical and experimental study of the propagation of an internal solitary wave (ISW) over a corrugated bed is presented, in which the amplitude and the wavelength of the corrugated bed, together with the wave amplitude and wave speed of the ISW, have been varied parametrically. Both ISWs of elevation and depression have been considered. The wave-induced currents over the corrugated bed cause flow separation at the apex of the corrugations and a sequence of lee vortices forms as a result. These vortices develop fully after the main wave has passed over the topographic feature, resulting in deformation of the overlying pycnocline and, in some instances, significant vertical mixing. It is found that the intensity of the vortex formation is dependent on both the amplitude and wavelength of the bottom topography. In the case of an ISW of depression, the generation of vertically (upward)-propagating vortices is seen to result in entrainment of fluid from a bottom boundary jet (Carr and Davies, Phys Fluids 18:016601, 2006), while, in the elevation case, a second mechanism is present to induce significant turbulent mixing in the water column. It occurs when the bottom corrugations reach into, or are very near, the pycnocline at rest. Large waves of elevation that are stable on approach to the corrugations exhibit evidence of a spatio-temporally developing shear instability as they interact with the bottom corrugation. The shear instability takes the form of billows that have a vertical extent that can reach 50% of the wave amplitude.     

Hydro-elastic wave proliferation over an impermeable seabed with bottom deformation

ABSTRACT

A hydro-elastic frame has been considered to investigate the proliferation of waves over small base deformation on an infinitely extended flexible seabed. The flexible base surface is assumed as a thin elastic plate of very small thickness and it depends on the Euler–Bernoulli beam equation. For any particular frequency, there are two different modes of time-harmonic propagating wave exists rather than one mode of propagating wave along the positive horizontal direction. The waves with smaller wavenumber spread along the free-surface of the sea (say, free-surface mode) and the waves with higher wavenumber spread along the flexible base surface (say, flexural mode). A simplified perturbation approach is utilised to bring down the entire equations which govern the original boundary value problem (bvp) to a less complex bvp for the first-order velocity potential function. The first-order potential function along with the first-order reflection and transmission coefficients for both modes are calculated by a procedure based upon Fourier transform approach. A shape of sinusoidal swells flexible base surface is taken as an example to approve the scientific results. It is observed that when the train of normal incident propagating wave spreads over base distortion because of either the free-surface unsettling influence or the flexural wave movement in the sea, the reflected and transmitted energy are always feasible to be exchanged from one particular wave mode to another wave mode. Furthermore, we notice that the realistic changes in the flexural rigidity behaviour on the flexible base surface of the sea have a significant effect on the problem of water wave proliferation over small base deformation. Moreover, the energy conservation equation is derived with the help of the Green's integral theorem. The results for the values of reflection and transmission coefficients obtained for both the free-surface unsettling influence as well as flexural wave movement in the fluid are found to satisfy the energy conservation equation almost accurately.     

Effect of surface wave propagation in a four-layered oceanic crust model

Dispersion of Rayleigh type surface wave propagation has been discussed in four-layered oceanic crust. It includes a sandy layer over a crystalline elastic half-space and over it there are two more layers—on the top inhomogeneous liquid layer and under it a liquid-saturated porous layer. Frequency equation is obtained in the form of determinant. The effects of the width of different layers as well as the inhomogeneity of liquid layer, sandiness of sandy layer on surface waves are depicted and shown graphically by considering all possible case of the particular model. Some special cases have been deduced, few special cases give the dispersion equation of Scholte wave and Stoneley wave, some of which have already been discussed elsewhere.     

Convection in a rotating,laterally heated annulus pattern velocities and amplitude oscillations

Abstract

The velocities of the wave patterns relative to the rotating annulus have been measured with either increasing or decreasing positive radial temperature gradients and different rotation rates, with the fluid in thermal equilibrium and in contact with a rigid lid. The pattern velocities are dependent on initial conditions except in the unique areas of the stability diagram, where the velocities observed with either increasing or decreasing ΔT, overlap. The pattern velocities change discontinuously with each wave number transition, with a particularly large discontinuity at the transition from two to one wave. The frequency of the amplitude oscillations of the waves has been measured also. It has been found that the period of the oscillation of the three wave pattern is inversely proportional to the period of the pattern velocity, which means that in this case the ratio of the frequency of amplitude oscillation and the frequency of the pattern revolution is incommensurate.     

Passive and hybrid mitigation of potential near-fault inner pounding of a self-braking seismic isolator

A seismic isolated structure is usually a long-period structural system, which may encounter a low-frequency resonance problem when subjected to a near-fault earthquake that usually has a long-period pulse-like waveform. This long-period wave component may result in an enlargement of the base displacement and a decrease of the isolation efficiency. To overcome this problem, a rolling-based seismic isolator, referred to as roll-n-cage (RNC) isolator, has been recently proposed. The RNC isolator has a built-in buffer (braking) mechanism that limits the peak isolator displacements under severe earthquakes and prevents adjacent structural pounding. This paper addresses the problem of passive and hybrid mitigation of the potential inner pounding of the self-braking RNC isolator under near-fault earthquakes. Numerical results show that the RNC isolator can intrinsically limit the isolator displacements under near-fault earthquakes with less severe inner pounding using additional hysteretic damping and active control forces.     

Observations of coastal cliff base waves,sand levels,and cliff top shaking

Concurrent observations of waves at the base of a southern California coastal cliff and seismic cliff motion were used to explore wave–cliff interaction and test proxies for wave forcing on coastal cliffs. Time series of waves and sand levels at the cliff base were extracted from pressure sensor observations programmatically and used to compute various wave impact metrics (e.g. significant cliff base wave height). Wave–cliff interaction was controlled by tide, incident waves, and beach sand levels, and varied from low tides with no wave–cliff impacts, to high tides with continuous wave–cliff interaction. Observed cliff base wave heights differed from standard Normal and Rayleigh distributions. Cliff base wave spectra levels were elevated at sea swell and infragravity frequencies. Coastal cliff top response to wave impacts was characterized using microseismic shaking in a frequency band (20–45 Hz) sensitive to wave breaking and cliff impacts. Response in the 20–45 Hz band was well correlated with wave–cliff impact metrics including cliff base significant wave height and hourly maximum water depth at the cliff base (r² = 0.75). With site‐specific calibration relating wave impacts and shaking, and acceptable anthropogenic (traffic) noise levels, cliff top seismic observations are a viable proxy for cliff base wave conditions. The methods presented here are applicable to other coastal settings and can provide coastal managers with real time coastal conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

Radio signal propagation effects in a nonstationary ionosphere based on the numerical solution of the one-dimensional wave equation

The goal of this work is to solve Maxwell equations analytically and numerically in a one-dimensional case under the conditions of a nonstationary medium. Analytical solutions to the Maxwell equations have been obtained in two partial cases of the linear and quadratic time dependence of medium permittivity. Since the number of models for which the wave equation can be solved analytically is limited, it becomes also necessary to apply numerical methods, specifically the method of finite differences, in a time domain Finite Difference Time Domain method. The effects of the decameter wave dynamic reflection from structures with considerable spatial gradients (the scales of which are comparable with the sounding pulse wavelength) have been studied based on this method. It has been shown that the spectrum can broaden and a Doppler frequency shift of a reflected signal can originate can take place.     

Dynamic stiffness of foundation embedded in layered halfspace based on wave propagation in cones

An Erratum has been published for this article in Earthquake Engineering & Structural Dynamics 33(6) 2004, 793. The dynamic stiffness of a foundation embedded in a multiple‐layered halfspace is calculated postulating one‐dimensional wave propagation in cone segments. In this strength‐of‐materials approach the sectional property of the cone segment increases in the direction of wave propagation. Reflections and refractions with waves propagating in corresponding cone segments occur at layer interfaces. Compared to rigorous procedures the novel method based on cone segments is easy to apply, provides conceptual clarity and physical insight in the wave propagation mechanisms. This method postulating one‐dimensional wave propagation in cone segments with reflections and refractions at layer interfaces is evaluated, calculating the dynamic stiffness of a foundation embedded in a multiple‐layered halfspace. For sites resting on a flexible halfspace and fixed at the base, engineering accuracy (deviation of ±20%) is achieved for all degrees of freedom with a vast parameter variation. The behaviour below the cut‐off frequency in an undamped site fixed at its base is also reliably predicted. The accuracy is, in general, better than for the method based on cone frustums, which can lead to negative damping. Copyright © 2003 John Wiley & Sons, Ltd.     

Harmonic wave diffraction by two circular cavities in a poroelastic formation

This study investigates the dynamic interaction of time harmonic plane waves with a pair of parallel circular cylindrical cavities of infinite length buried in a boundless porous elastic fluid-saturated medium. The novel features of Biot dynamic theory of poroelasticity along with the appropriate wave field expansions, the pertinent boundary conditions, and the translational addition theorems for cylindrical wave functions are employed to develop a closed-form solution in the form of infinite series. The analytical results are illustrated with numerical examples in which two empty cavities are insonified by a fast compressional or a shear wave at end-on incidence. The basic dynamic field quantities such as the hoop stress amplitude and the radial displacement of the elastic frame are evaluated and discussed for representative values of the parameters characterizing the system. The effects of the proximity of the two cavities, the incident wave frequency and type are examined. Particular attention has been focused on multiple scattering interactions in addition to the slow wave coupling effects which is known to be the primary distinction of the scattering phenomenon in poroelasticity from the classical elastic case. Limiting case involving two empty cylindrical cavities in an elastic solid is considered and excellent agreement with a well-known solution is established.     

Seismic wave scattering effects under different canyon topographic and geological conditions

Based on our numerical model for wave scattering problems due to P and SV wave incidences and the frequency domain analysis procedure, the effect of canyon topographic and geologic conditions on ground motion due to P and SV earthquake wave incidences has been extensively studied in this paper. The numerical results from this research illustrated that: (1) canyon topographic and geologic conditions can dramatically affect both peak value and frequency contents of the free field motion along the canyon surface during an earthquake; (2) a canyon may be subjected to stronger ground motion when its predominant frequency is in coincidence with the predominant frequency of the incident earthquake wave; (3) a stronger wave mode conversion effect can be induced by a steeper canyon bank or a softer weathered stratum on the canyon surface in the case of an earthquake wave incidence; (4) compared with harmonic wave incidences, the amplification effect of a canyon on the incident earthquake wave is a little weaker due to the average self-healing effect of the earthquake wave.     

Wave emission during a plasma density jump in the auroral zone of the topside ionosphere according to the APEX satellite data

The intensity of the wave emission in the 0.1–10 MHz band measured in the ionosphere (the APEX satellite experiment) has been presented. A jump of the plasma density and an increase in the emission intensity at a plasma frequency have been registered at altitudes of ～1300 km in the topside auroral ionosphere. The emission intensity in the whistler-mode band nonmonotonically increased along the satellite trajectory near the plasma jump wall. It has been indicated that waveguides could be formed near the wall during damping of electrostatic oscillations generated by precipitating electron fluxes. A spatially nonmonotonous separation of waveguides from the plasma inhomogeneity stretched along geomagnetic field lines is possible in this case.     

TTI介质有限差分逆时偏移的稳定性探讨

在沉积学中,可假设在相同时期的沉积层具有相近的物理性质和演化过程.因此,沿层传播的地震波和垂直于地层传播的地震波具有各向异性的特点.在纵波资料的处理中,考虑各向异性对逆时偏移的影响,通常假设介质的横波速度为零,这样可以得到纵波在TTI介质中的传播方程,但是该方程在实际计算中仍存在数值稳定性问题.本文加入横波分量可有效解决数值稳定性问题,并选取适当的横波速度减小对纵波成像的影响,实现地震波在TTI介质中的逆时偏移.实际测算表明,P-SV波的方程中包含横波分量,若假设SV的速度为零,则会导致方程的差分格式不稳定;若加入SV波,选择合适的SV波速度可以使SV波的全区各向异性和反射系数达到极小,并可有效的抑制SV波对纵波勘探的影响.本文的方法是一种稳定的TTI介质中的逆时偏移方法.     

Propagation of one-dimensional unloading waves in materials exhibiting yielding delay phenomena

Summary The nature of possible unloading waves in materials exhibiting yielding delay phenom ena has been discussed in this paper. The differential equation governing the propagation of the waves, has been solved by this method of characteristics. In this case also as in materials not exhibiting yielding delay phenomena, the unloading wave propagates with the velocity of elastic waves, if it is a wave of discontinuity, and if the load is suddenly increased the unloading wave travels with plastic wave velocity.     

YC地区转换波数据处理及裂隙预测

裂隙介质的横波响应能提供对裂隙走向与密度一种直接测量.为了探测YC地区裂隙型储层特征,在该区进行了纵波源三分量数据采集.经过精细地处理,YC地区转换波成像质量得到了改善.以此为基础,对该区的裂隙特征进行了预测.预测结果与本区的应力场分析和钻井揭示的裂隙特征比较吻合.本文所介绍的一些关键转换波资料处理技术、解释方法和分析结论对今后陆地转换波勘探有一定借鉴作用.     

Steep wave,turbulence, and sediment concentration statistics beneath a breaking wave field and their implications for sediment transport

A new methodology based on wavelet analysis is used to estimate steep wave statistics under depth-limited conditions and the corresponding high concentration sediment statistics. Steep waves here are defined as wave crests within the wavelet transform exceeding a root mean square derived acceleration threshold. The method is applied to laboratory data obtained in a large-scale wave-flume experiment conducted in 2005 at Oregon State University's O. H. Hinsdale Wave Research Laboratory from an acoustic Doppler velocimeter and a fiber optic backscatter sensor array above a mobile sand bed. The steep wave and high concentration statistical results for the erosive condition suggest that sand suspensions are intermittent when a wave-breaking timescale (the ratio of breaking wave height and rms wave velocity) is used to detect the concurrence among steep wave, high velocity turbulent fluctuations, and sand concentration events near the bed. More importantly, at 1 cm above the bed, though the accretive case has more steep wave events, the erosive case has more steep waves and concurrent high concentration events, suggesting a more intense breaking wave process near the sensors. The use of a longer time window, based on the dominant wave period in the detection process of steep wave and high concentration events at 1 cm above the bed, does not change the resulting statistics for the erosive condition. However, increased percentages of high concentration events correlated with steep wave and high velocity turbulence events for the accretive condition are obtained. These increased percentages are conjectured to be due to advection of non-local turbulent events and sediment concentration peaks from upstream.     

Rayleigh wave propagation in a two-layer anisotropic media

Summary The possibility of propagation of Rayleigh waves in an incompressible crust of constant density and rigidity varying exponentially with depth lying on a semi-infinite transversely isotropic base has been discussed in this paper. Frequency equation has been derived and numerical calculations are made. The result obtained in this case is compared with that ofNewlands [3]²) andDutta [4].     

Hydroacoustic wave in the external alternating magnetic field

The electromagnetic fields induced by hydroacoustic waves, propagating in a liquid conducting medium in an alternating magnetic field, have been considered. The equation, relating the induced magnetic field to the undisturbed antenna field and acoustic wave parameters, has been obtained. The spatial—temporal pattern of the induced field has been constructed in the case when acoustic wave propagates along a direct line with an alternating current.     

On the stability of a non-convolutional perfectly matched layer for isotropic elastic media

The multi-axial perfectly matched layer (M-PML) is a material boundary condition for wave propagation problems in unbounded domains. It is obtained by extending the formulation of the split-field perfectly matched layer to a more general absorptive medium, for which damping profiles are specified along all dimensions of the problem. Under the hypothesis of small damping, it has been demonstrated that the stability of the system of partial differential equations of the M-PML can be related to the ratio of the damping profiles, and stable M-PML terminations for isotropic and orthotropic elastic media have been constructed. In the present work, we use the Routh–Horwitz determinants to demonstrate that the conclusions regarding the stability of M-PML for isotropic media for small damping are in fact valid for the more general case of damping coefficients of any (positive) value. The effectiveness of the M-PML is demonstrated by constructing stable terminations for the abovementioned media. The stability analysis is presented for 2-D in-plane (P-SV) wave propagation in elastic isotropic continua.     

A note on the approximate determination of the dispersion of Love waves in a laterally nonhomogeneous layer lying over a homogeneous half-space

Rayleigh's principle and the concept of the local wave number have been utilised for the approximate determination of the dispersion of Love waves propagating in a laterally heterogeneous layer lying over a homogeneous half-space. The shear wave velocity and the rigidity in the surface layer have been assumed to decrease with the increase of the lateral distance from the origin. The range of validity of the dispersion equation obtained by this method has been examined critically. It was found that: (a) for existence of Love waves the minimum value of shear wave velocity in the layer must be less than that in the matter below, and (b) the phase velocity of Love waves decreases with the increase of the lateral distance from the origin.