A general analytical solution for flow to a single horizontal well by Fourier and Laplace transforms

The objective of this paper is to present an analytical solution for describing the head distribution in an unconfined aquifer with a single pumping horizontal well parallel to a fully penetrating stream. The Laplace-domain solution is developed by applying Fourier sine, Fourier and Laplace transforms to the governing equation as well as the associated initial and boundary conditions. The time-domain solution is obtained after taking the inverse Laplace transform along with the Bromwich integral method and inverse Fourier and Fourier sine transforms. The upper boundary condition of the aquifer is represented by the free surface equation in which the second-order slope terms are neglected. Based on the solution and Darcy’s law, the equation representing the stream depletion rate is then derived. The solution can simulate head distributions in an aquifer infinitely extending in horizontal direction if the well is located far away from the stream. In addition, the solution can also simulate head distributions in confined aquifers if specific yield is set zero. It is shown that the solution can be applied practically to evaluate flow to a horizontal well.     

Boundary element simulation of scattering of elastic waves by 3-D cracks

Numerical modelling techniques are now becoming common for understanding the complicated nature of seismic wave propagation in fractured rock. Here the Indirect Boundary Element Method (IBEM) is applied to study scattering of elastic waves by cracks. The problem addressed in this paper is the diffraction of P and S waves by open 3-D cracks of arbitrary shape embedded in a homogeneous isotropic medium. The IBEM yields the value of the jump of displacements between opposite surfaces of the crack, often called Crack Opening Displacement (COD). This is used to evaluate the solution away from the crack. We use a multi-regional approach which consists of splitting a surface S into two identical surfaces S⁺ and S⁻ chosen such that the crack lies at the interface. The resulting integral equations are not hyper-singular and wave propagation within media that contain open cracks can be rigorously solved. In order to validate the method, we compare results of displacements of a penny-shaped crack for a vertical incident P-wave with the classic results by Mal (1970) obtaining excellent agreement. This comparison gives us confidence to study cases where no analytic solutions exist. Some examples of incidence of P or S waves upon cracks with various shapes are depicted and the salient aspects of the method are also discussed. Both frequency and time-domain results are included.     

Scattering of SH waves from a partially debonded rigid elliptic cylinder

Scattering of SH waves by an embedded rigid elliptic cylinder of finite length, which is partially debonded from elastic soil is studied. The debonding regions are modeled as multiple elliptic arc-shaped interface cracks with non-contacting faces. The scattered wave field is expressed as a Mathieu function expansion with unknown coefficients. The mixed boundary conditions of the problem lead to a set of singular integral equations of the first type in terms of the dislocation density functions of the cracks. A quadrature method is used to solve these integral equations numerically. The results for dynamic stress intensity factors, far-field pattern of the displacement and scattering cross sections are presented. We particularly discuss the effects of the ratio of the short radius to long radius of the cylinder.     

Propagation of partially coherent non-stationary random waves in a viscoelastic layered half-space

This paper presents a highly accurate method based on the precise integration method (PIM) and on the pseudo excitation method (PEM). The method computes the propagation behaviour of partially coherent non-stationary random waves in a viscoelastic, transversely isotropic solid, which consists of a multi-layered soil resting on a homogeneous semi-infinite space. The excitation source is a local rupture between two layers, which causes a partially coherent non-stationary random field. The analysis of non-stationary random wave propagation is transformed into that for deterministic waves by using PEM. The resulting governing equations in the frequency-wavenumber domain are linear ordinary differential equations, which are solved very precisely by using PIM. The evolutionary power spectral densities of the ground level responses are investigated and some typical earthquake phenomena are explained.     

Interaction of waves,currents and tides,and wave-energy impact on the beach area of Sylt Island

Erosion due to waves is an important and actual problem for most coastal areas of the North Sea. The objective of this study was to estimate the impact of wave action on the coastline of Sylt Island. From a 2-year time series (November 1999 to October 2001) of hydrological and wave parameters generated with a coupled wave–current modelling system, a period comprising storm ‘Anatol’ (3–4 December 1999) is used to investigate the effects of waves on currents and water levels and the input of wave energy into the coastline. The wave-induced stress causes an increase of the current velocity of 1 m/s over sand and an additional drift along the coast of about 20 cm/s. This produces a water level increase of more than 20 cm in parts of the tidal basin. The model system also calculates the wave energy input into the coastline. Scenario runs for December 1999 with a water level increase of 50 cm and wind velocity increased by 10% show that the input of the wave energy into the west coast of Sylt Island increases by 30% compared to present conditions. With regard to the forecasted near-future (Woth et al., Ocean Dyn 56:3–15, 2006) increase of strong storm surges, the scenario results indicate an increased risk of coastal erosion in the surf zone of Sylt Island.     

Spatiotemporal spectrum and momentum flux of the stratospheric gravity waves generated by a typhoon

The simulation results of Typhoon Matsa (2005) by using the Weather Research and Forecasting (WRF) model show that pronounced stratospheric gravity waves (GWs) are generated in the vicinity of the typhoon. Using the model output, we investigate the spatial structures and the temporal variations of the GWs through a three dimensional (3-d) spectral analysis, i.e. the spectrum with respect to two horizontal wavenumbers and frequency. We further derive the momentum flux carried by the GWs. Spectral investigation results show that the power spectral density (PSD) of the GWs exhibits a single-peaked spectrum, which consists primarily of a distinct spectrum at horizontal wavelength of ~1000km, time period of 12-18h, and vertical wavelength of 7-9km. This spectrum is different from the spectra of GWs generated by deep convections disclosed by the previous researches. Both the PSD and momentum flux spectrum are prominent in positive k h portion, which is consistent with the fact that the GWs propagate in the upstream of mean flow. Large momentum flux is found to be associated with the GWs, and the net zonal momentum flux is 0.7845×10 3 Pa at 20km height, which can account for ~26% of the momentum flux that is required in driving the QBO phenomenon.     

Two-phase SPH modelling of waves caused by dam break over a movable bed

This paper describes the application of the Smoothed Particle Hydrodynamics（SPH） method for modeling two dimensional waves caused by dam break over a movable bed in two dimensions.The two phase SPH method is developed to solve the Navier-Stokes equations.Both fluid and sediment phases are described by particles as weakly compressible fluids and the incompressibility is achieved by the equation of state.The sediment phase is modeled as a non-Newtonian fluid using three alternative approaches of artificial viscosity and Bingham Model.In this paper,the new formulations for two-phase flows are proposed.The numerical results obtained from the developed SPH model show acceptable accuracy with comparison to experimental data.     

Observations of acoustic-gravity waves in the ionosphere generated by severe tropospheric weather

Atmospheric waves influence the dynamics and energetic budget of the upper atmosphere. Using the continuous HF Doppler sounder, we study the wave activity in the ionosphere during tropospheric convective storms in western and central part of the Czech Republic. The study is focused on acoustic-gravity waves in the period range 2–30 minutes. We discuss possible methods of distinguishing the waves emitted by meteorological sources from waves of different origin, particularly waves of geomagnetic origin. In two cases out of twenty-five analysed, we found waves in the infrasonic period range which might be generated by exceptionally intense meteorological activity in the troposphere. The results differ considerably from those previously obtained in North America. In the central part of the United States, infrasonic waves were frequently observed during convective storms. As a possible reason, we discuss different intensity and dynamics of weather systems in both regions.     

Simulation of the stratospheric gravity waves generated by the Typhoon Matsa in 2005

The generation of stratospheric gravity waves(GWs) due to typhoon is simulated by using a meso-scale model(WRF) with a typhoon case,the Matsa in 2005.An 8-day model run that covers the major stages of the Matsa’s development reproduces the key features of the typhoon.For example,good agreements in the typhoon’s track,the intensity,and the spiral clouds,as well as mean state of stratosphere,are seen between the simulation results and the observation.Simulation results clearly show that with typhoon propagates northwestward,pronounced stratospheric GWs are generated continuously in the vicinity of Matsa.The GWs exhibit the typical curve-like wave fronts away from the Typhoon Matsa,and propagate preferentially in the upstream of the background winds.These characteristics reflect that the stratospheric GWs are closely associated with the typhoon,and thus the GWs are referred to as Tropical Cyclone related Gravity Waves(TC-GWs).The results also show that these waves should have a rather large horizontal scale so that the outmost wave fronts can be seen at the distance of ～1000 km to the typhoon center in the horizontal plane of 20 km.This is consistent with the phenomenon of stratospheric TC-GWs with ～1000 km horizontal scale disclosed by the previous observational analysis results.     

Transformation and absorption of magnetosonic waves generated by solar wind in the magnetosphere

Resonant transformation of fast magnetosonic (FMS) wave flux into Alfven and slow magnetosonic (SMS) oscillations is investigated in the one-dimensionally inhomogeneous magnetosphere. Spatial distribution of energy absorption rate of FMS oscillations penetrating into the magnetosphere from the solar wind is studied. The FMS wave energy absorption rate caused by magnetosonic resonance excitation is shown to be several orders of magnitude greater than that caused by Alfven resonance excitation at the same surface. It is connected with the spectrum of incident FMS waves. The Kolmogorov spectrum is used in numerical calculations. Magnitude of the Fourier harmonics exciting resonant Alfven oscillations is much smaller than that of the harmonics driving lower-frequency magnetosonic resonance. It is shown that resonant transformation of FMS waves into SMS oscillations can be an effective mechanism of energy transfer from the solar wind to the magnetosphere.     

2.5D scattering of incident plane SV waves by a canyon in layered half-space

This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method (IBEM). A free field response analysis is performed to provide the displacements and stresses on the boundary of the canyon where fictitious uniform moving loads are applied to calculate the Green’s functions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The free field displacements are added to the fic...     

Analysis of runoff–storage relationships to evaluate the runoff-buffering potential of a sloping permeable domain

The runoff–storage relationship for a runoff system in a steady-state is analyzed as an indicator of the buffering potential of rainfall-runoff responses. In this relationship, a large storage increase in response to a given runoff increase indicates high buffering potential in the water balance equation. The evaluation method is applied to a sloping permeable domain. A two-dimensional form of the Richards equation is used to calculate runoff and storage. Macropore existence is represented by an enlargement effect of hydraulic conductivity near saturation. The runoff–storage relationship is controlled by the distribution of hydraulic quantities. The distribution of a pressure-head value is approximately classified into the following three zones: the I zone with vertical unsaturated flow, the U zone with unsaturated downslope flow, and the S zone with saturated downslope flow. The runoff-buffering potential is systematically evaluated by dependencies of the runoff–storage relationship on the classification of the pressure-head distribution. The potential is generally high for soil with a high permeability, but rather small in the range of low runoff rates where the S zone is not created. The macropore effect causes the range of high buffering potential to shift to high runoff rates through enlargement of the I zone. As a result, a moderate magnitude of the macropore effect gives the maximum increase in storage in response to a given increase in runoff.     

基于粘性-滑移界面接触模型半空间隧道衬砌对平面P波的散射

基于粘性-滑移模型模拟隧道衬砌和围岩之间的接触状态,采用间接边界积分方程法求解弹性半空间中隧道衬砌对平面P波的散射,着重考察了地表位移放大和衬砌动应力集中效应。结果表明:接触滑移边界的刚度系数和粘度系数对隧道衬砌的动应力分布影响较大,滑移刚度较小时,共振频率段动应力集中效果更加显著;随着粘度系数的增大,衬砌内部环向应力幅值逐渐减小。另外,界面刚度系数和粘度系数对隧道衬砌动力反应的影响程度也受控于入射频率和角度。     

Procedure of reduction of travel-time curves ofP andS waves at the focal surface

A method for the calculation of seismic waves velocities at focal depth is here proposed. A stratified earth model with spherical symmetry and the analytical relationship between the epicentral distance and the travel times of seismic waves are used.This method, applied to the southern Tyrrhenian region and to the Japanese islands, allows to reduce the observed travel times to the focal depth independently of a particular velocity model.     

Modeling of dam break wave propagation in a partially ice-covered channel

During the last four decades, several numerical formulations and specialized software have been developed in response to studies about dam break (DB) wave propagation and its hydraulic and environmental impacts on downstream hydraulic structures and valleys. These methods cannot, however, be used to predict wave propagation within partially covered channels or reservoirs located upstream of hydraulic structures. In fact, such problems require the modelling of the complex transition from a free surface flow into a pressurized one. Because rivers or channels partially covered with ice sheets are typical examples commonly met in winter in northern climates, it is vitally important to assess ice-cover effects on the DB wave propagation and develop appropriate tools to predict resulting hydrodynamic loads on hydraulic structures downstream. This paper proposes an original numerical formulation to model wave propagation and hydrodynamic pressure in partially covered channels. The proposed formulation uses one-dimensional St. Venant equations to simulate open-water flow and water hammer equations to simulate pressure flow within the partially covered channel. To illustrate the use of the hydrodynamic pressures obtained, a case study is presented where a channel cover and a dam located downstream are modelled using finite elements to investigate their dynamic structural response.     

Energy mode distribution: An analysis of the ratio of anti-Stokes to Stokes amplitudes generated by a pair of counterpropagating Langmuir waves

Results from plasma wave experiments in spacecrafts give support to nonlinear interactions involving Langmuir, electromagnetic, and ion-acoustic waves in association with type III solar radio bursts. Starting from a general form of Zakharov equation (Zakharov, V.E., 1985. Collapse and self-focusing of Langmuir waves. Hand-book of Plasma Physics Cap.2, 81–121) the equations for electric fields and density fluctuations (density gratings) induced by a pair of counterpropagating Langmuir waves are obtained. We consider the coupling of four triplets. Each two triplets have in common the Langmuir pump wave (forward or backward wave) and a pair of independent density gratings. We numerically solve the dispersion relation for the system, extending the work of (Alves, M.V., Chian, A.C.L., Moraes, M.A.E., Abalde, J.R., Rizzato, F.B., 2002. A theory of the fundamental plasma emission of type- III solar radio bursts. Astronomy and Astrophysics 390, 351–357). The ratio of anti-Stokes (AS) (ω₀+ω) to Stokes (S) (ω₀-ω^*) electromagnetic mode amplitudes is obtained as a function of the pump wave frequency, wave number, and energy. We notice that the simultaneous excitation of AS and S distinguishable modes, i.e., with Re{ω}=ω_r≠0, only occurs when the ratio between the pump wave amplitudes, r is ≠1 and the pump wave vector k₀ is , W₀ being the forward pump wave energy. We also observe that the S mode always receives more energy.     

Modifications of the dispersion relations for surface waves in a layer on a half-space

Summary Dispersion relations for Love and Rayleigh waves in a layer on a half-space are modified by introducing quadratic slownesses instead of velocities. The advantages of this approach are demonstrated on analytical formulae for computing the group velocity.     

含断层破碎带场地对平面SH波的放大作用

借助wolf的土层和半空间精确动力刚度矩阵和斜线荷载格林函数,采用间接边界元法在频域内求解了含断层破碎带场地对SH波的放大作用,着重分析了破碎带较窄断层两侧围岩动力响应的基本规律及场地动力特性对散射的影响.结果表明,断层破碎带对SH波有显著的影响,即使破碎带很窄,也可对SH波产生很大的放大作用;层状场地动力特性对放大作用有显著的影响.     

Scattering of waves by subterranean structures via the boundary element method

The boundary element method (BEM) is used to study the two-dimensional wave field generated when buried structures of arbitrary shape (i.e. inclusions) in an elastic medium are illuminated (or insonified) by dynamic line sources. Both steady-state responses and time-domain transients are presented. The problem is formulated in the frequency domain by means of appropriate Green's functions. The evaluation of the singular integrals is achieved (and to the best of the writers' knowledge, for the first time in the technical literature) in analytical form, which results in improvements in computational efficiency and accuracy. Closed-form solutions for regular geometries are then used to validate the method. The interaction of two cavities, the formation of shadow zones by inclusions and the complexity of the scattered field from bodies with irregular shapes are used as examples to demonstrate the versatility of the method. The responses computed in the time domain were invariably found to be causal, even for non-convex domains, which belies a recent assertion by some researchers that the application of boundary element methods to concave domains is associated with non-causal effects.     

Currents induced by vertical varied radiation stress in standing waves and evolution of the bed composed of fine sediments

This paper extends the conventional concept of radiation stress （Longuet-Higgins and Stewart, 1964） in progressive water waves to standing waves, so that its vertical profile could be defined and calculated in a new technical way. The hydrodynamic numerical model being coupled with the vertically varying radiation stress in standing waves is used to simulate the currents being induced by standing waves in the vertical section. Numerical modeling of suspended sediment transport is then carried out to simulate the evolution of the bed composed of fine sediments by the currents. The scour and deposition patterns simulated are in qualitative agreement with prior laboratory and field observations.