Acceleration of mean zonal flows by planetary waves

The mechanism of acceleration of the mean zonal flow by a planetary wave is explained intuitively by considering the wave drag which a corrugated bottom feels when it excites the wave. The explanation is justified by solving the problem of vertical propagation of a planetary wave packet and the second order mean motion induced around it. The discussion is slightly extended to the case of small damping, to illustrate in a compact form the fact that the mean zonal acceleration is determined by a forcing due to wave transience plus that due to wave dissipation.The mean flow induced by a steady, dissipating planetary wave is discussed, and it is shown that it depends largely on the dissipation scale-height of the wave whether the northern region is heated or cooled. For example, if the wave velocity-amplitude increases upward in spite of dissipation, the induced easterly flow increases with height and the temperature of the northern region increases relative to that in the southern region. A similar point has been made byDunkerton (1979) in connection with westerly flows induced by Kelvin waves.The Lagrangian-mean motion induced by a planetary wave is briefly discussed in connection with the mechanism of acceleration of the mean zonal flow, in the case of a slowly varying wave packet. Further, in order el elucidate the effects of wave dissipation and time dependence of wave amplitude, the results obtained for a steady, dissipating wave and for a growing baroclinic wave are mentioned.     

Stochastic model of seismic torsional ground motion: Application to Lotung soft site

The purpose of this paper is to present a stochastical approach, which analyse the torsional ground motion, induced by the spatial variability of seismic motions. For this purpose, a torsional ground motion analytical model is proposed and a normalised differential motion parameter is introduced. The approach regards the seismic motion as the combination of a travelling wave on the site (coherent component) and a zero mean randomizing factor that introduces a loss of correlation effect. The soil parameters as fundamental frequency and damping coefficient are integrating by modeling the coherent component with the commonly used Kanai-Tajimi power spectral density. The parametric analysis of the model shows an increase of the induced torsion with both the soil frequency and the motion scattering parameter, and a decrease with the separation distance, the apparent wave velocity and the correlation length. Finally, in order to test the proposed torsional ground motion model prediction, it is compared to the experimental results recorded by the EPRI LSST array in Lotung, Taiwan (Laouami and Labbé, 2002). The comparison leads to the identification of the model parameters for the Lotung soft site.     

透射边界高频失稳机理及稳定实现——P-SV波动

波动数值模拟的稳定性是获得可靠结果的前提.透射边界是一类具有高阶、高效等特点的人工边界,其引发的高频失稳是由内域格式和透射边界的不当耦合所致.本文针对P-SV波动有限元模拟中透射边界引发的失稳问题,基于GKS定理的群速度解释,通过对有限元和透射边界的频散分析揭示了数值失稳机理为透射边界和相邻内域格式支持了群速度指向内域的高频P波或SV波,波动能量将从边界进入内域引发数值失稳.同时,对比连续模型频散指出引发失稳的谐波是由有限元离散引入.本文采用修改的数值积分方法调整有限元刚度,以消除有限元中引发边界失稳的高频波动成分,从而稳定实现透射边界.理论分析和数值实验均表明本文稳定措施的有效性.

     

Wide-angle linear forward modelling of synthetic seismograms

We address the issue of linearity and scale dependence in forward modelling of seismic data from well logs, for large ray parameters, wide angles or large offsets. We present a forward model, within the context of seismic‐to‐well matching, that is linearized in the elastic properties of the earth. This model preserves linearity at large ray parameters and can handle fine‐layering effects such as induced anisotropy. Starting from a low‐contrast small‐ray‐parameter model, we extend it to a large‐ray‐parameter model by fully linearizing the elastic‐property contrasts. Overall linearity of the forward model is extended by partitioning the compressional‐wave and shear‐wave velocity fields into two fundamental scales: a kinematic scale that governs wavefield propagation effects and a dynamic scale that governs wavefield scattering effects. This analysis reveals that the standard practice in forward modelling of strongly filtering the ratio of compressional‐wave velocity to shear‐wave velocity is well founded in the underlying physics. The partitioning of the velocity fields also leads naturally to forward modelling that accounts fully for stretch effects, to resolution of the angle‐of‐incidence versus ray‐parameter dichotomy in seismic‐amplitude analysis, and to full accounting for induced anisotropy and dispersion effects due to fine‐layering of isotropic media. With the onset of routine long‐offset acquisition and the compelling need to optimize asset management in order to maximize reserve recovery, this forward model recognizes the physics of seismic wave propagation and enables a more complete exploitation of amplitude information in pre‐critical seismic data.     

介观尺度孔隙流体流动作用对纵波传播特征的影响研究——以周期性层状孔隙介质为例

介观尺度孔隙流体流动是地震频段岩石表现出较强速度频散与衰减的主要作用.利用周期性层状孔隙介质模型,基于准静态孔弹性理论给出了模型中孔隙压力、孔隙流体相对运动速度以及固体骨架位移等物理量的数学解析表达式,同时利用Biot理论将其扩展至全频段条件下,克服了传统White模型中介质分界面处流体压力不连续的假设. 在此基础上对准静态与全频段下模型介质中孔隙压力、孔隙流体相对运动速度变化形式及其对弹性波传播特征的影响进行了讨论,为更有效理解介观尺度下流体流动耗散和频散机制提供物理依据.研究结果表明,低频条件下快纵波孔压在介质层内近于定值,慢纵波通过流体扩散改变总孔隙压力, 随频率的增加慢波所形成的流体扩散作用逐渐减弱致使介质中总孔压逐渐接近于快纵波孔压,在较高频率下孔压与应力的二次耦合作用使总孔压超过快纵波孔压.介质中孔隙流体相对运动速度与慢纵波形成的流体相对运动速度变化形式一致;随频率的增加孔隙流体逐渐从排水的弛豫状态过渡到非弛豫状态,其纵波速度-含水饱和度变化形式也从符合孔隙流体均匀分布模式过渡到斑块分布模式,同时介质在不同含水饱和度下的衰减峰值与慢纵波所形成的孔隙流体相对流动速度具有明显的相关性.     

介观尺度孔隙流体流动作用对纵波传播特征的影响研究——以周期性层状孔隙介质为例

介观尺度孔隙流体流动是地震频段岩石表现出较强速度频散与衰减的主要作用.利用周期性层状孔隙介质模型,基于准静态孔弹性理论给出了模型中孔隙压力、孔隙流体相对运动速度以及固体骨架位移等物理量的数学解析表达式,同时利用Biot理论将其扩展至全频段条件下,克服了传统White模型中介质分界面处流体压力不连续的假设. 在此基础上对准静态与全频段下模型介质中孔隙压力、孔隙流体相对运动速度变化形式及其对弹性波传播特征的影响进行了讨论,为更有效理解介观尺度下流体流动耗散和频散机制提供物理依据.研究结果表明,低频条件下快纵波孔压在介质层内近于定值,慢纵波通过流体扩散改变总孔隙压力, 随频率的增加慢波所形成的流体扩散作用逐渐减弱致使介质中总孔压逐渐接近于快纵波孔压,在较高频率下孔压与应力的二次耦合作用使总孔压超过快纵波孔压.介质中孔隙流体相对运动速度与慢纵波形成的流体相对运动速度变化形式一致;随频率的增加孔隙流体逐渐从排水的弛豫状态过渡到非弛豫状态,其纵波速度-含水饱和度变化形式也从符合孔隙流体均匀分布模式过渡到斑块分布模式,同时介质在不同含水饱和度下的衰减峰值与慢纵波所形成的孔隙流体相对流动速度具有明显的相关性.     

网格剖分及其精度和计算量分析

网格剖分程度直接影响着地震波正演数值模拟的计算精度及其计算量.以均匀介质模型为例,分析不同网格大小对波场模拟精度和计算量的影响,得出精细化网格剖分是实现高精度地震波正演模拟的有效方法,然而其计算量较大.以均匀倾斜介质模型为例,探讨倾斜地层网格剖分问题,数值实例分析不同震源频率对不同网格剖分方案引起的波场传播精度的影响,...     

On the steady mass transport induced by wave motions in a viscous rotating fluid

Abstract

The steady second-order motion induced by a first-order wave motion in a homogeneous, viscous and rotating fluid is examined. If the wave motion produces a steady Ekman layer suction by non-linear interactions, this suction must induce a steady component of interior, relative vorticity parallel to the axis of rotation in order to conserve mass. A boundary value problem for the determination of the induced, steady interior mass transport velocity is presented. The mass transport induced by a Kelvin wave is examined as an illustration and possible application of the theory.     

Wave dispersion and optimal mass modelling for one-dimensional periodic structures

Discrete analysis methods are frequently used for the study of the structure and soil. However, the assumption of the displacement interpolation function makes the waves dispersive, which means the numerical dispersion. The wave dispersion induced by the discretization depends on the mass modelling. Also, the existence of added lumped masses makes waves dispersive even for the continuum modelling. In order to examine these wave dispersions, a one-dimensional periodic structure is adopted as an analysis model and the dynamic transfer matrix method is applied. A wave solution and a finite element solution are used for the evaluation of the transfer matrix. The phase and group velocities in the structure are explicitly represented. These values are compared among the continuum modelling and the discretization modelling in which several consistent mass ratios are adopted. The optimal consistent mass ratio, which makes the wave velocity of the discrete model the same as that of the continuum model, is newly developed here. The validity of this mass modelling technique is presented by examining the frequency response function and impulse response function.     

P-wave dispersion and attenuation in fractured and porous reservoirs – poroelasticity approach

Natural fractures in hydrocarbon reservoirs can cause significant seismic attenuation and dispersion due to wave induced fluid flow between pores and fractures. We present two theoretical models explicitly based on the solution of Biot's equations of poroelasticity. The first model considers fractures as planes of weakness (or highly compliant and very thin layers) of infinite extent. In the second model fractures are modelled as thin penny-shaped voids of finite radius. In both models attenuation is a result of conversion of the incident compressional wave energy into the diffusive Biot slow wave at the fracture surface and exhibits a typical relaxation peak around a normalized frequency of about 1. This corresponds to a frequency where the fluid diffusion length is of the order of crack spacing for the first model and the crack diameter for the second. This is consistent with an intuitive understanding of the nature of attenuation: when fractures are closely and regularly spaced, the Biot's slow waves produced by cracks interfere with each other, with the interference pattern controlled by the fracture spacing. Conversely, if fractures are of finite length, which is smaller than spacing, then fractures act as independent scatterers and the attenuation resembles the pattern of scattering by isolated cracks. An approximate mathematical approach based on the use of a branching function gives a unified analytical framework for both models.     

A local time-domain transmitting boundary for simulating cylindrical elastic wave propagation in infinite media

Finite element simulation of the time-dependent wave propagation in infinite media requires enforcing the transmitting boundary to replace the truncated far-field infinite domain so as to model the effect of the wave radiation towards infinity. This paper proposed a novel local time-domain transmitting boundary for simulating the cylindrical elastic wave radiation problem. This boundary is a mechanical model consisting of the spring, dashpot and mass elements, with the auxiliary degrees of freedom introduced, which is dynamically stable and easily implemented into the commercial finite element codes. Numerical analysis of the cylindrical elastic wave radiation problem indicates that the proposed transmitting boundaries with the order N=3 for cylindrical P and SV waves and with the order N=4 for cylindrical SH wave have very high accuracy, even when the artificial boundary at wave source. The proposed transmitting boundary with order N=0 can be applied approximately to the general two-dimensional infinite elastic wave problems that contain the more complex outgoing wave fields at artificial boundary than the cylindrical waves. The plane-strain Lamb problem is analyzed with the acceptable engineering accuracy achieved. On the other hand, the proposed transmitting boundary with higher order can be a tool to localize the temporal convolution that appears in an exact time-domain transmitting boundary for the general infinite wave problems. This potential applicability is mentioned.     

A steady nonlinear and singular vortex Rossby wave within a rapidly rotating vortex. Part II: Application to geophysical vortices

In a previous paper, Caillol [Geophys. Astrophys. Fluid Dyn., 2014, 108] investigated the steady nonlinear vortical structure of a singular vortex Rossby mode that has survived to a strong critical-layer-like interaction with a linearly stable, columnar, axisymmetric and dry vortex. We presented a general theory for this wave/mean flow interaction through the nonlinear critical layer theory and calculated the mean azimuthal and axial winds induced at the critical radius at the end of this interaction in the final stage. We here apply that theory to rapidly rotating geophysical vortices: tropical cyclones, cold-air mesocyclones and tornadoes. We find that the numerous assumptions invoked in that paper agree well with the reality of those intense vortices. We also find that in spite of a lack of moist-convection modelling, this dry vortex is fairly well accelerated at the critical radius by such a shear wave with a magnitude of order the square root of the damped-wave amplitude. The intensification level strongly depends on the aspect ratio, height of the system: rapid vortex and parent vortex, over core radius. The thinner the vortex is, the sharper the intensification is. This result is in sharp contrast to the numerous numerical simulations on VR wave/vortex interactions that yield a much smaller intensification of order the square of the wave amplitude. This weakly nonlinear approach nevertheless fails to model small vertical wavelength VR wave/vortex interactions for their related asymptotic expansions are divergent and for they yield strongly nonlinear VR waves coupled with evolving critical layers whose extent can no longer be considered as thin.     

An analysis of wave dissipation at the Hendijan mud coast, the Persian Gulf

Effects of non-rigid muddy bed on the wave climate at the Hendijan coast along the northwestern part of the Persian Gulf have been examined through field measurements and numerical wave transformation modeling. The field survey included measurements of wave characteristics at an offshore and a nearshore station, and mud sampling to obtain the thickness of the fluid mud layer and its rheological properties. Comparisons of wave spectra at the two stations show energy dissipation along the wave trajectory with higher dissipation in the wave period band around 6?s, because depending on the site a given frequency band tends to be more effective in wave–mud interaction. Dissipation induced by the non-rigid bed is introduced into the REF/DIF wave transformation model through the application of viscoelastic constitutive equations for fluid mud. Numerical outputs of the nearshore wave height, for which the viscoelastic parameters included in the model were obtained independently from oscillatory frequency-sweep tests, are found to be comparable with measured values at the nearshore station. This implies that the model is useful for estimating the design wave conditions in the study area.     

雷达波有限元仿真模拟

为了突出雷达波自身的动力学特点,本文首先用Ｇａｌｅｒｋｉｎ’ｓ方法推导了含衰减项的雷达波有限元方程,用有限元方法实现了管状体、弯曲界面等复杂形体的雷达波场的仿真模拟．通过对比同一模型合衰减和不含衰减两种情况的波场,明显地展示了考虑雷达波自身特点后的波场仿真性较好．     

雷达波有限元仿真模拟

为了突出雷达波自身的动力学特点,本文首先用Ｇａｌｅｒｋｉｎ’ｓ方法推导了含衰减项的雷达波有限元方程,用有限元方法实现了管状体、弯曲界面等复杂形体的雷达波场的仿真模拟．通过对比同一模型合衰减和不含衰减两种情况的波场,明显地展示了考虑雷达波自身特点后的波场仿真性较好．     

A 3-D phase-averaged model for shallow-water flow with waves in vegetated water

A 3-D shallow-water flow model has been developed to simulate the flow in coastal vegetated waters with short waves. The model adopts the 3-D phase-averaged shallow-water flow equations with radiation stresses induced by short waves. It solves the governing equations using an implicit finite volume method based on quadtree rectangular mesh in the horizontal plane and stretching mesh in the vertical direction. The flow model is coupled with a spectral wave deformation model called CMS-Wave. The wave model solves the spectral wave-action balance equation and provides wave characteristics to the flow model. The model considers the effects of vegetation on currents and waves by including the drag and inertia forces of vegetation in the momentum equations and the wave energy loss due to vegetation resistance in the wave-action balance equation. The model has been tested using several sets of laboratory experiments, including steady flows in a straight channel with submerged vegetation and in a compound channel with vegetated floodplain and random waves through a vegetated channel and on a vegetated beach slope. The calculated water levels, current velocities, and wave heights are in general good agreement with the measured data.     

3-D acoustic wave equation forward modeling with topography

In order to model the seismic wave field with surface topography, we present a method of transforming curved grids into rectangular grids in two different coordinate systems. Then the 3D wave equation in the transformed coordinate system is derived. The wave field is modeled using the finite-difference method in the transformed coordinate system. The model calculation shows that this method is able to model the seismic wave field with fluctuating surface topography and achieve good results. Finally, the energy curves of the direct and reflected waves are analyzed to show that surface topography has a great influence on the seismic wave＇s dynamic properties.     

A numerical study on the effects of wave–current–surge interactions on the height and propagation of sea surface waves in Charleston Harbor during Hurricane Hugo 1989

The effects of wave–current interactions on ocean surface waves induced by Hurricane Hugo in and around the Charleston Harbor and its adjacent coastal waters are examined by using a three-dimensional (3D) wave–current coupled modeling system. The 3D storm surge modeling component of the coupled system is based on the Princeton Ocean Model (POM), the wave modeling component is based on the third generation wave model, Simulating WAves Nearshore (SWAN), and the inundation model is adopted from [Xie, L., Pietrafesa, L. J., Peng, M., 2004. Incorporation of a mass-conserving inundation scheme into a three-dimensional storm surge model. J. Coastal Res., 20, 1209–1223]. The results indicate that the change of water level associated with the storm surge is the primary cause for wave height changes due to wave–surge interaction. Meanwhile, waves propagating on top of surge cause a feedback effect on the surge height by modulating the surface wind stress and bottom stress. This effect is significant in shallow coastal waters, but relatively small in offshore deep waters. The influence of wave–current interaction on wave propagation is relatively insignificant, since waves generally propagate in the direction of the surface currents driven by winds. Wave–current interactions also affect the surface waves as a result of inundation and drying induced by the storm. Waves break as waters retreat in regions of drying, whereas waves are generated in flooded regions where no waves would have occurred without the flood water.     

Wave-induced steady streaming,mass transport and net sediment transport in rough turbulent ocean bottom boundary layers

The interaction between two important mechanisms which causes streaming has been investigated by numerical simulations of the seabed boundary layer beneath both sinusoidal waves and Stokes second order waves, as well as horizontally uniform bottom boundary layers with asymmetric forcing. These two mechanisms are streaming caused by turbulence asymmetry in successive wave half-cycles (beneath asymmetric forcing), and streaming caused by the presence of a vertical wave velocity within the seabed boundary layer as earlier explained by Longuet-Higgins. The effect of wave asymmetry, wave length to water depth ratio, and bottom roughness have been investigated for realistic physical situations. The streaming induced sediment dynamics near the ocean bottom has been investigated; both the resulting suspended load and bedload are presented. Finally, the mass transport (wave-averaged Lagrangian velocity) has been studied for a range of wave conditions. The streaming velocities beneath sinusoidal waves (Longuet-Higgins streaming) is always in the direction of wave propagation, while the streaming velocities in horizontally uniform boundary layers with asymmetric forcing are always negative. Thus the effect of asymmetry in second order Stokes waves is either to reduce the streaming velocity in the direction of wave propagation, or, for long waves relative to the water depth, to induce a streaming velocity against the direction of wave propagation. It appears that the Longuet-Higgins streaming decreases as the wave length increases for a given water depth, and the effect of wave asymmetry can dominate, leading to a steady streaming against the wave propagation. Furthermore, the asymmetry of second order Stokes waves reduces the mass transport (wave-averaged Lagrangian velocity) as compared with sinusoidal waves. The boundary layer streaming leads to a wave-averaged transport of suspended sediments and bedload in the direction of wave propagation.     

Towards a data assimilation system for morphodynamic modeling: bathymetric data assimilation for wave property estimation

Data assimilation is mainly concerned with the proper management of uncertainties. The main objective of the present work is to implement and analyze a data assimilation technique capable of assimilating bathymetric data into a coupled flow, wave, and morphodynamic model. For the case presented here, wave significant height, wave direction of incidence, and wave peak period are being optimized based on bathymetric data taken from a twin experiment. An adjoint-free variational scheme is used. In this approach, a linear reduced order model (ROM) is constructed as an approximation of the full model. The ROM is an autoregressive model of order 1 (AR1) that preserves the parametrization. Since the ROM is linear, the construction of its adjoint is straightforward, making the implementation of 4D variational data assimilation effortless. The scheme is able to update the morphodynamic model satisfactorily despite the fact that the model shows nonlinear behavior even for very small perturbations of all three parameters. The size and direction of the perturbations necessary for constructing the ROM have a significant impact on the performance of the technique.