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1.
J. Vanneste 《Annales Geophysicae》1995,13(2):196-210
The instability of an internal gravity wave due to nonlinear wave-wave interaction is studied theoretically and numerically. Three different aspects of this phenomenon are examined. 1. The influence of dissipation on both the resonant and the nonresonant interactions is analysed using a normal mode expansion of the basic equations. In particular, the modifications induced in the interaction domain are calculated and as a result some modes are shown to be destabilised by dissipation. 2. The evolution of an initial unstable disturbance of finite vertical extent is described as the growth of two secondary wave packets travelling at the same group velocity. A quasi-linear correction to the basic primary wave is calculated, corresponding to a localised amplitude decrease due to the disturbance growth. 3. Numerical experiments are carried out to study the effect of a basic shear on wave instability. It appears that the growing secondary waves can have a frequency larger than that of the primary wave, provided that the shear is sufficient. The instability of waves with large amplitude and long period, such as tides or planetary waves, could therefore be invoked as a possible mechanism for the generation of gravity waves with shorter period in the middle atmosphere. 相似文献
2.
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. 相似文献
3.
应用三维交错网格应力-速度有限差分方法,数值模拟了含有倾斜裂缝孔隙介质地层中点声源所激发的井孔声场问题.为满足薄裂缝计算需求,开发了不均匀网格有限差分算法,提高了计算精度及计算速度.利用将孔隙介质方程参数取为流体极限的办法来处理裂缝中的流体,实现了流体-孔隙介质界面处的差分方程统一,使界面处的计算更加灵活方便.在验证了方法正确性的基础上,分别考察了单裂缝宽度、裂缝带宽度、裂缝倾斜角度以及孔隙介质渗透率等参数的变化对井轴上阵列波形的影响并进行了分析.结果表明,声波经过裂缝时可能产生反射横波及斯通利波,后者随裂缝宽度的减小而减小,而前者随裂缝宽度的改变,变化不大,在裂缝很小(20μm)时依然存在;裂缝带的宽度、密度越大,反射斯通利波越强;当裂缝(裂缝带)倾斜时,反射横波消失,但反射斯通利波受裂缝倾斜角度的影响较小;渗透率的改变对斯通利波的衰减影响较为明显. 相似文献
4.
Experiments were performed on the rotating platform 14 m in diameter equipped with a simple internal wave generator. Internal waves were generated for a wide range of Coriolis parameters. When the rotation is very weak, i.e., when the internal Rossby radius of deformation is much larger than the wavelength, then the stable nonlinear waves generated are solitary waves. These have a horizontal crest, as in the nonrotating case. When the rotation is strong, i.e., when the internal Rossby radius is at most comparable with the wavelength, then Sverdrup-like periodic waves can be generated, but no solitary wave can then propagate. For the intermediate case, Ostrovsky waves are generated. Their phase speed increases with increasing amplitude. Then, there are two characteristic wave lengths: one which varies with the inverse square root of the amplitude, as for the KdV wave, and the other, linked with the rotation, which varies as the square root of the amplitude. The experimental results are thus in agreement with most of the conclusions in recent analytical developments. 相似文献
5.
Abstract Inertial waves are excited in a fluid contained in a slightly tilted rotating cylindrical cavity while the fluid is spinning up from rest. The surface of the fluid is free. Since the perturbation frequency is equal to the rotation speed resonance occurs at a critical height to radius aspect ratio of the fluid. Detailed study of a particular inertial wave shows that in solid body rotation this “eigenratio” agrees with predictions from linear inviscid theory to within 0.5%. Measured time dependence of the eigenratio during spin-up from rest is a function of the tilt amplitude and agrees favorably with predictions from a numerical study. Mean flow associated with the inertial wave becomes unstable during spin-up and in the steady state. A boundary for the unstable region is found experimentally. 相似文献
6.
2004年8月3日近地TC-1卫星在磁尾XGSM~－12RE的等离子体片内,观测到了伴随着高速流的低于离子回旋频率的波,即超低频波(ULF,Ultra Low Frequency).该波垂直分量的振幅在高速流及其振荡减速期间大致相当;而平行分量振幅在高速流时明显大于其振荡减速时. 利用一个扰动双流模型对完全磁化离子横场漂移驱动的电磁不稳定性计算后,预测结果表明:(1)对于垂直分量来说,横场漂移速度与Alfvén速度的比值影响不稳定性增长率和激发波频率,随其比值增加,增长率变大,激发波频率从负值增加到正值.(2)对于平行分量来说,温度各向异性时等离子体热速度与Alfvén速度比值只影响不稳定性增长率和激发波频率,未改变不稳定性模类别;而温度各向同性时离子横场漂移速度与Alfvén速度比值既影响不稳定性模的种类及其分支,又影响激发波频率.进一步将卫星观测到的等离子体密度、温度、整体流速和磁场代入模型方程,进行数值计算与上述预测结果对比后发现:卫星观测中垂直分量的功率谱密度(PSD,Power Spectrum Density)增强时间和频段与理论模型中由β//、β⊥和v⊥/VA引起不稳定性激发的波一致;卫星观测中平行分量的功率谱密度增强时间与理论模型基本相符,但是前者的频率明显地低于后者.因此,除了需考虑平行磁场的离子整体流速对不稳定性激发波频率的可能影响,还需要统计上进一步核实伴随有高速流的ULF波与不稳定性的相关性. 相似文献
7.
Gui-jin Yao Ke-xie Wang Jun Ma Bao-jun Yang Hai-rong Zhang 《Geophysical Prospecting》2007,55(4):561-570
We focus on the theoretical analysis of the resonance phenomena and the geometric attenuation behaviour of critical refracted shear waves propagating along a fluid‐filled borehole. Using integration by parts, we asymptotically expand the vertical branch‐cut integral of shear waves in an infinite series related to each order of the derivative of the response function of the formation. It is proved that the vertical branch‐cut integral of shear waves at large offsets consists mainly of the contribution of the second asymptotic series, which is related to the first derivative of the response function of the formation at the shear branch point. Using the asymptotic expansion, we develop a simplified amplitude expression for shear waves, and the resonant frequency formula. The validity of the resonance frequencies obtained by the resonant frequency formula is verified numerically by comparison with the corresponding frequencies of the numerical integral results. We also give a rational explanation for the phenomenon of two peaks appearing within each resonant peak zone: i.e. that these are the contributions of the constructive interference of the shear waves and the mode poles. 相似文献
8.
The simplified macro‐equations of porous elastic media are presented based on Hickey's theory upon ignoring effects of thermomechanical coupling and fluctuations of porosity and density induced by passing waves. The macro‐equations with definite physical parameters predict two types of compressional waves (P wave) and two types of shear waves (S wave). The first types of P and S waves, similar to the fast P wave and S wave in Biot's theory, propagate with fast velocity and have relatively weak dispersion and attenuation, while the second types of waves behave as diffusive modes due to their distinct dispersion and strong attenuation. The second S wave resulting from the bulk and shear viscous loss within pore fluid is slower than the second P wave but with strong attenuation at lower frequencies. Based on the simplified porous elastic equations, the effects of petrophysical parameters (permeability, porosity, coupling density and fluid viscosity) on the velocity dispersion and attenuation of P and S waves are studied in brine‐saturated sandstone compared with the results of Biot's theory. The results show that the dispersion and attenuation of P waves in simplified theory are stronger than those of Biot's theory and appear at slightly lower frequencies because of the existence of bulk and shear viscous loss within pore fluid. The properties of the first S wave are almost consistent with the S wave in Biot's theory, while the second S wave not included in Biot's theory even dies off around its source due to its extremely strong attenuation. The permeability and porosity have an obvious impact on the velocity dispersion and attenuation of both P and S waves. Higher permeabilities make the peaks of attenuation shift towards lower frequencies. Higher porosities correspond to higher dispersion and attenuation. Moreover, the inertial coupling between fluid and solid induces weak velocity dispersion and attenuation of both P and S waves at higher frequencies, whereas the fluid viscosity dominates the dispersion and attenuation in a macroscopic porous medium. Besides, the heavy oil sand is used to investigate the influence of high viscous fluid on the dispersion and attenuation of both P and S waves. The dispersion and attenuation in heavy oil sand are stronger than those in brine‐saturated sandstone due to the considerable shear viscosity of heavy oil. Seismic properties are strongly influenced by the fluid viscosity; thus, viscosity should be included in fluid properties to explain solid–fluid combination behaviour properly. 相似文献
9.
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. 相似文献
10.
G. D. Aburdzhaniya O. A. Kharshiladze Kh. Z. Chargaziya 《Geomagnetism and Aeronomy》2013,53(4):471-478
The linear mechanism by which internal gravity waves (IGWs) are generated and subsequently intensified in a stably stratified dissipative ionosphere in the presence of an inhomogeneous zonal wind (shear flow) has been studied. In the case of shear flows, the operators of linear problems are nonself-adjoint and the corresponding eigenfunctions are nonorthogonal; a canonical approach can hardly be used to study such motions. It is more adequate to apply the so-called nonmodal calculation. Dynamic equations and equations of energy transfer of IGW disturbances in the ionosphere with a shear flow have been obtained based on a nonmodal approach. Exact analytical solutions for the constructed dynamic equations have been found. The growth rate of the IGW shear instability has been determined. It has been established that IGW disturbances are intensified in an algebraically power manner rather than exponentially in the course of time. The effectiveness of the linear mechanism by which IGWs are intensified when interacting with an inhomogeneous zonal wind is analyzed. It has been indicated that IGWs effectively obtain the shear flow energy during the linear evolution stage and substantially increase (by an order of magnitude) their amplitude and energy. The frequency and the wave vector of generated IGW modes depend on time; therefore, a wide spectrum of wavelike disturbances, depending on the linear, rather than nonlinear, turbulent effects, is formed in the ionosphere with a shear flow. Thereby, a new degree of freedom appears, and the turbulent state of atmospheric—ionospheric layers can be formed on IGW disturbances. 相似文献
11.
12.
Olga Podvigina 《地球物理与天体物理流体动力学》2013,107(3):299-326
We investigate instability of convective flows of simple structure (rolls, standing and travelling waves) in a rotating layer with stress-free horizontal boundaries near the onset of convection. We show that the flows are always unstable to perturbations, which are linear combinations of large-scale modes and short-scale modes, whose wave numbers are close to those of the perturbed flows. Depending on asymptotic relations of small parameters α (the difference between the wave number of perturbed flows and the critical wave number for the onset of convection) and ε (ε2 being the overcriticality and the perturbed flow amplitude being O(ε)), either small-angle or Eckhaus instability is prevailing. In the case of small-angle instability for rolls the largest growth rate scales as ε8/5, in agreement with results of Cox and Matthews (Cox, S.M. and Matthews, P.C., Instability of rotating convection. J. Fluid. Mech., 2000, 403, 153–172) obtained for rolls with k = k c . For waves, the largest growth rate is of the order ε4/3. In the case of Eckhaus instability the growth rate is of the order of α2. 相似文献
13.
Dynamic response of an eccentrically lined circular tunnel in poroelastic soil under seismic excitation 总被引：3，自引：0，他引：3
Seyyed M. Hasheminejad Siavash Kazemirad 《Soil Dynamics and Earthquake Engineering》2008,28(4):277-292
An exact analysis for two-dimensional dynamic interaction of monochromatic progressive plane compressional and shear seismic waves with a permeable circular tunnel lining of circumferentially varying wall thickness buried in a boundless porous elastic fluid-saturated formation is presented. The novel features of Biot dynamic theory of poroelasticity in conjunction with the translational addition theorems for cylindrical wave functions, along with the appropriate wave field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in form of infinite series. The analytical results are illustrated with numerical examples in which an air-filled and water-saturated permeable tunnel lining of variable wall thickness, embedded within water-saturated surrounding formations of distinct frame properties (soft, stiff, and stiff viscoelastic soil), is insonified by fast compressional or shear waves at selected angles of incidence. The effects of liner eccentricity, interface permeability, formation material type, incident wave frequency, and angle of incidence on the hoop stress amplitude are evaluated and discussed for representative values of the parameters characterizing the system. Limiting cases are considered and good agreements with the solutions available in the literature are obtained. 相似文献
14.
N. A. Zolotukhina 《Geomagnetism and Aeronomy》2009,49(4):438-449
It has been indicated that the magnetic field variations, registered by the geostationary satellites in the range 150–600 s after 14 SI/SC events, include transverse wave components that show the spectral—polarization properties of standing Alfvén waves. The amplitude of these waves increases with increasing pulse amplitude, the period increases with decreasing magnetic field magnitude, and the rotation direction and magnetic field vector orientation reverse their signs near the noon and midnight meridians. 相似文献
15.
Evolution of a large-scale river plume is studied numerically using the Massachusetts Institute of Technology general circulation model. The model parameters were set close to those observed in the area of the Columbia River mouth. The fine-resolution grid along with the non-hydrostatic dispersion included in the model allowed for the reproduction of detailed inner plume structure, as well as a system of internal waves radiated from the plume’s boundary. It was found that not only first-mode but also second- and third-mode internal waves are radiated from the plume at the latest stages of its relaxation when the velocity of the front propagation drops below an appropriate wave phase speed of internal baroclinic mode. The model output shows that the amplitude of these high-mode waves is of the same order as the leading first-mode waves, which in combination with the specific vertical structure (location of the maximum structure function beyond the pycnocline layer) creates favourable conditions for the generation of shear instabilities. High-resolution model output also reveals evidence of a fine internal structure of the plume characterized by the presence of secondary fronts inside the plume and secondary internal wave systems propagated radially from the lift-off area to the outer boundary. These structures intensify the mixing processes within the propagating plume with predominance of the entrainment mechanism developing on the lower boundary between the plume’s body and underlying waters. The scheme of horizontal circulation in the plume was reproduced by the methodology of Lagrange drifters released near the mouth at different depths.
相似文献16.
土是由一定尺寸大小颗粒所构成的多孔介质,具有明显的颗粒特性,当土颗粒间的孔隙被流体（如水或油）充满时则成为饱和土.利用微极理论和Biot波动理论的研究成果,把饱和土中多孔固体骨架部分近似地视为微极介质,孔隙中的流体部分视为质点介质,获得饱和多孔微极介质的弹性波动方程.借鉴Greetsma理论,建立了饱和多孔微极介质弹性本构方程力学参数与相应单相介质弹性参数的相互关系,使饱和多孔微极介质弹性波动方程中的物理参数具有明确的物理意义,易于在试验中确定.运用场论理论把饱和多孔微极介质的波动方程简化为势函数方程,建立了饱和多孔微极介质中五种弹性波的弥散方程,数值分析了五种简谐体波在无限饱和多孔微极介质中的传播特性. 结果表明,P1波、P2波和剪切S1波的波速弥散曲线与经典饱和多孔介质基本相同,当频率小于临界频率ω0时旋转纵波θ波和横波S2波不存在,当频率大于临界频率ω0时,θ波和S2波的传播速度随频率增加而减小. 相似文献
17.
通过对多分量地震资料的分析,我们发现随着频率的增加横波分裂时差减小.对于深部接收的VSP数据来说快横波的偏振方向保持不变，而对于浅层接收的VSP数据来说偏振方向却存在一个最大可以达到20°的旋转.尽管多尺度随机分布微裂隙岩石物理模型已经成功地模拟并解释了横波分裂时差随频率变化的现象，却不能解释与频率相关的横波分裂.据推测，如果微裂隙的排列方向和大裂隙的排列方向不同，利用低频信息获得的偏振方向将指示裂隙主方向，而利用高频信息获得的偏振方向则指示微裂隙方向.在背景多孔隙介质中存在多组裂隙的情况下，推导出垂直入射条件下横波偏振方向的解析式，给出了系统研究横波在介质中传播的方法.研究结果表明，横波偏振方向会随着频率的变化而变化，并且在入射方位、角度一定的条件下，是裂隙方位和密度的函数，这些认识可能有助于揭示观测到的、依赖频率变化的横波偏振现象. 相似文献
18.
Deep seismic sounding was performed along two profiles which cross at the Dinarides area right angles. One of the profiles goes far into the Adriatic Sea. Besides considerations on the lithophysical conditions, characteristics of the registered waves are analysed. The amplitude curves and curves of amplitude ratios are shown. Special attention was paid to the frequency of the registered waves. In order to obtain a better knowledge of the registered wave pattern three-component recordings of waves were carried out. The analysis of the records obtained is given, with particular regard to the possibility of creating converted waves. The Earth's crust structure along the profiles II and III is given. 相似文献
19.
Recently, mode converted shear waves (C‐waves) have been shown to enable overpressure prediction in media where primary wave acquisition is inhibited by gas and fluid effects – C‐wave moveout is analysed and a long standing relationship between differential stress and primary‐wave (P‐wave) velocity is modified and employed. Though pore‐pressure prediction based on C‐waves is supported by empirical evidence from laboratory and field experiments, a theoretical justification has yet to be developed. In this research note, we provide a supporting algebra for the original relationship between pore pressure and C‐wave velocity. 相似文献
20.
B. D. Dore 《Pure and Applied Geophysics》1970,83(1):87-97
Summary An expansion technique is used to investigate effects of finite amplitude on three-dimensional progressive internal waves in continuously stratified fluid of variable depth. The results are illustrated for the case of uniform density gradients. Reflection is neglected in the perturbation scheme. In two dimensions, damping of long progressive waves is considered through energy dissipation in the bottom boundary layer. 相似文献