Resonance induced by Rossby Lee waves

Abstract

The mutual interaction of fields induced by spatially separated potential vorticity sources in a quasi-geostrophic barotropic flow is investigated using the weakly nonlinear approach. It is found that a powerful nonlinear response can be triggered by Rossby lee waves. This resonance phenomenon which dominates all other nonlinear corrections depends on certain global resonance conditions and on the change in the phase of the Rossby lee wave across the distance separating the sources. The response is particularly strong for topographic forcing possessing δ-function characterisitics.     

垂直和倾斜断层围陷波的谱元法数值模拟及其波场特征对比

低速断层破碎带内传播的断层围陷波是断层内部信息的重要载体,研究其波场特征是反,演断层内部结构的关键。前人对围陷波的模拟主要针对垂直断层,但实际断层大部分是倾斜的。本文利用谱元法数值模拟地震波在垂直和倾斜断层区域的传播,并分别单独改变断层破碎带或断层两盘速度差异等参数,对比分析地震动在时域和频域发生的变化,研究这些参数对波场特征的影响。对比研究表明,当存在一定宽度的低速破碎带时,倾斜断层对近断层区域波场的影响和垂直断层相比在幅值分布上有比较显著的差异,尤其是当断层两盘同时还存在速度差异时;在倾斜和垂直断层破碎带上方,均能产生断层围陷波,其幅值特征差异不大,但在跨断层平面上的质点极化方式可能会存在差异:垂直断层围陷波质点极化方向表现为单一,而倾斜断层可能会出现多个方向。这些模拟结果有助于反演真实断层破碎带结构,也能够加深对近断层的强地面运动特征的认识。     

Trapped internal waves over undular topography in a partially mixed estuary

The flow of a stratified fluid over small-scale topographic features in an estuary may generate significant internal wave activity. Lee waves and upstream influence generated at isolated topographic features have received considerable attention during the past few decades. Field surveys of a partially mixed estuary, the Rotterdam Waterway, in 1987, also showed a plethora of internal wave activity generated by isolated topography, banks and groynes. Additionally it revealed a spectacular series of resonant internal waves trapped above low-amplitude bed waves. The internal waves reached amplitudes of 3–4 m in an estuary with a mean depth of 16 m. The waves were observed during the decreasing flood tide and are thought to make a significant contribution to turbulence production and mixing. However, while stationary linear and finite amplitude theories can be used to explain the presence of these waves, it is important to further investigate their time-dependent and non-linear behaviour. With the development of advanced non-hydrostatic models it now becomes possible to further investigate these waves through numerical experimentation. This is the focus of the work presented here. The non-hydrostatic finite element numerical model FINEL3D developed by Labeur was used in the experiments presented here. The model has been shown to work well in a number of stratified flow investigations. Here, we first show that the model reproduces the field data and for idealised stationary flow scenarios that the results are in agreement with the resonant response predicted by linear theory. Then we explore the effects of non-linearity and time dependence and consider the importance of resonant internal waves for turbulence production in stratified coastal environments.Responsible Editior: Hans Burchard     

谱元法数值模拟地表起伏对补偿线性矢量偶极源Rg波低谷点的影响

利用谱元算法数值模拟了不同地表起伏模型下的补偿线性矢量偶极(Compensated Linear Vector Dipole, CLVD)源Rg波低谷点的特征及相应的震源深度.结果表明,源区地表存在一定起伏情况下,Rg波低谷点依然存在,低谷点位置反映了源区地表起伏的信息,但与理论值仍有一定偏差.Rg波低谷点受远区地表起伏影响较小.     

Frictional effects on trapped shelf waves

This paper revisits models of coastal trapped waves and examines them with the inclusion of friction. In addition we use a numerical method which at least theoretically will have enhanced accuracy. The model has continuous stratification and variable depth. It is linear, quasigeostrophic and hydrostatic, and utilizes perturbation from this fundamental state. The model is applied with both idealized and realistic topography and stratification.Responsible Editior: Phil Dyke     

Geographically localised shelf waves on curved coasts

This paper presents a combined analytical and numerical extension to recent theoretical work on trapped continental shelf waves over smoothly curved coastlines. The geometry considered consists of an annular region joining two semi-infinite straight sections and, even though the isobaths remain evenly spaced, trapped modes appear in the annular region due entirely to the longitudinal curvature of the shelf there. Expanding in alongshore modes and requiring that the error is orthogonal to the transverse modes gives a linear algebraic system of equations for the frequency of trapping. Solutions for barotropic, non-divergent shelf waves show that trapped modes always exist if the coastline curves to form a headland.     

Traveling planetary waves in the stratosphere

This paper reviews the theory and observations of some traveling planetary waves in the stratosphere. Two categories of waves which appear prominently in the literature are discussed: westward propagating waves of periods in the range 3–7 days (the 5-day wave) and in the range 10–20 days (the 16-day wave). Although the observations seem to indicate that these waves are waves of the Rossby type (planetary waves), the evidence is less clear regarding (1) the question of whether these waves are forced internal waves or free (resonant) external waves, and (2) the identification of the observed waves with specific theoretical waves of the Rossby type. When recent observations are compared with theory, the evidence seems to favor the notion that the 5-day and 16-day waves of longitudinal wave number 1 may be identified, respectively, with the gravest and next gravest symmetric free Rossby modes. However, the observational evidence seems to be less clear regarding the nature of the 16-day wave than the 5-day wave.     

Resonant forcing of coastally trapped waves in a continuously stratified ocean

In a previous paper (Grimshaw, 1987) the resonant forcing of coastally trapped waves was discussed in the barotropic case. In order to extend that theory to more realistic situations, we have considered the analogous theory whereby a longshore current interacts with a longshore topographic feature, or the forcing is due to longshore wind stress, for the case of the continuously stratified ocean. As in the previous theory, near resonance, when a long-wave phase speed is close to zero (in the reference frame of the forcing), the wave motion is governed by a forced evolution equation of the KdV-type. The behaviour of the wave field is characterized by three parameters representing the bandwidth for resonance, the forcing amplitude and the dissipation. We have evaluated these parameters in various practical cases, and found that the bandwidths, which scale with ^1/2 when the forcing has dimensionless amplitude , can often be quite broad. Typically the second, third, or higher, modes may be resonant. Concurrently, the dissipation is also usually significant, leading to a steady state balance between the forcing, dissipation and nonlinear terms.     

Further evidence of normal mode Rossby waves

Further observational evidence of normal mode Rossby waves with higher meridional mode numbers is presented with the aid of global data from the troposphere to the stratosphere over the period November 1979 through April 1986.It is shown, without using ana priori assumption of meridional structure, that the third antisymmetric modes of zonal wavenumbers 1 and 2,i.e., (1,4) and (2,4) modes, substantially exist in the real atmosphere. These modes are, however, easily influenced by the nonuniform background field even in the equinoctial season; amplitude submaxima near the equator are apt to be dubious in the upper stratosphere so that the prototype meridional structure becomes obscure. The period of the (1,4) mode often falls into that of the (1,3) mode, about 16 days. Hence, these two modes cannot be classified simply by their periods, but the separation is made by their meridional structure.An appearance calendar of various modes is also presented for the analysis period. It is found that each mode appears irregularly throughout the year and that the year-to-year variation is fairly large.     

Motional modes of dilatational waves in elastic porous media containing two immiscible fluids

Numerical simulations of dilatational waves in an elastic porous medium containing two immiscible viscous compressible fluids indicate that three types of wave occur, but the modes of dilatory motion corresponding to the three waves remain uncharacterized as functions of relative saturation. In the present paper, we address this problem by deriving normal coordinates for the three dilatational waves based on the general poroelasticity equations of Lo et al. 2005 [13]. The normal coordinates provide a theoretical foundation with which to characterize the motional modes in terms of six connecting coefficients that depend in a well defined way on inertial drag, viscous drag, and elasticity properties. Using numerical calculations of the connecting coefficients in the seismic frequency range for an unconsolidated sand containing water and air as a representative example relevant to hydrologic applications, we confirm that the dilatational wave whose speed is greatest corresponds to the motional mode in which the solid framework and the two pore fluids always move in phase, regardless of water saturation, in agreement with the classic Biot theory of the fast compressional wave in a water-saturated porous medium. For the wave which propagates second fastest, we show, apparently for the first time, that the solid framework moves in phase with water, but out of phase with air [Mode (III)], if the water saturation is below about 0.8, whereas the solid framework moves out of phase with both pore fluids [Mode (IV)] above this water saturation. The transition from Mode (III) to Mode (IV) corresponds to that between the capillarity-dominated region of the water retention curve and the region reflecting air-entry conditions near full water saturation. The second of the two modes corresponds exactly to the slow compressional wave in classic Biot theory, whereas the first mode is possible only in a two-fluid system undergoing capillary pressure fluctuations. For the wave which has the smallest speed, the dilatational mode is dominated by the motions of the two pore fluids, which are always out of phase, a result that is consistent with the proposition that this wave is caused by capillary pressure fluctuations.     

Numerical model studies on the generation and dissipation of the diurnal coastal-trapped waves over the Sakhalin shelf in the Sea of Okhotsk

To clarify the generation and dissipation mechanisms of diurnal coastal-trapped waves (CTWs) over the Sakhalin shelf, a series of numerical experiments were conducted using a three-dimensional tidal model of the Okhotsk Sea with density stratification. The tidal model used has good reproduction owing to the careful fitting to the recent observations. The numerical experiments suggested that diurnal CTWs are primarily (~60%) generated by the conversion of tidal energy at the northern corner of the Sakhalin shelf, and further amplified by vorticity generation due to the water column oscillation from Sakhalin Bay and the influence of Kashevarov Bank. From the observations, it was found that diurnal CTWs are effectively dissipated by the strong spin-down due to bottom friction. The conventional turbulent closure model cannot reproduce the observed damping of diurnal CTWs, which raises a caution in modeling the tidal fields in high-latitude regions where diurnal CTWs exist. To resolve this underestimation of the damping, the vertical eddy viscosity was parameterized using its dependence on the observed major axis length of the diurnal tidal current ellipses, which improves the model reproduction on the damping of diurnal CTWs. The model also suggests that the spin-down effects due to friction associated with the sea-ice cover play an important role in the tidal current reduction in the region where diurnal CTWs exist, as the observations suggested.     

The formation of tidal sand waves: Fully three-dimensional versus shallow water approaches

Tidal sand waves, also named tidal dunes, are large scale bedforms generated by the growth of perturbations of the sea bottom driven by tidal currents. Indeed, the interaction of an oscillatory tidal current with a bottom waviness gives rise to steady recirculating cells which tend to drag the sediment from the troughs towards the crests of the bottom perturbation. The net motion of the sediment towards the crests is opposed by gravity force and the growth of the perturbation is controlled by a balance between these two effects. In the literature, to determine the conditions which lead to the formation of sand waves and to determine the characteristics of the bedforms generated by this instability mechanism, both fully three-dimensional and shallow water approaches are employed. The shallow water approach is computationally less expensive than the fully three-dimensional one but, in many cases, it might be less accurate. This paper compares the quantitative predictions obtained by means of the two approaches and quantifies the range of the parameters such that the shallow water approximation provides reliable predictions.     

昆仑山断裂带围陷波的有限差分数值模拟解释

利用交错网格有限差分方法对昆仑山断裂带人工爆破产生的围陷波进行了三维数值模拟解释.为提高断裂带最终模型的可信度,在围陷波模拟的同时考虑了人工爆破记录的三个分量.对昆仑山断裂带围陷波的模拟结果表明,影响围陷波特性的断裂带深度主要在1.0 km以内.S波速度和断裂带宽度对围陷波的到时、频率、振幅和相位影响较大.数值模拟解释获得的昆仑山断裂带的细结构参数是：浅部断裂带宽度为300 m,深部为250 m;深度在400 m以上断裂带内S波速度为0.98 km/s,外部围岩S波速度为1.70 km/s,Q值为13.8;S波速度和Q值随着深度的增加而增加;1000 m以下断裂带内S波速度为2.80 km/s,围岩S波速度为3.3 km/s.     

Study on rupture zone of the M=8.1 Kunlun Mountain earthquake using fault-zone trapped waves

Introduction The study on deep crustal faults has been one of the most vigorous subjects in seismology. In the past, 3-D deep seismic sounding and 3-D seismic tomography were usually used for this pur-pose. But it is difficult to obtain the fine structures of the faults in deep crust by these methods. Recently, seismologists in the world pay more attention to the fault zone trapped waves. Since the fault-zone trapped waves arise from coherent multiple reflections at two boundaries of the fau…     

Spectral methods for bulk and guided waves in weakly inhomogeneous media

Plane wave spectra localized around interference maxima provide the foundation for charting the propagation of source excited wavefields through weakly inhomogeneous bulk and layered environments. Attention is focused here on recent developments in spectral analysis, uniformization, restoration, and inversion, centered around the ‘bare bones’ spectral objects represented by ray fields in a bulk medium, by adiabatic modes in a layered medium, and by beams.     

Fault zone structures of northern and southern portions of the main central fault generated by the 2008 Wenchuan earthquake using fault zone trapped waves

The rupture process of the May 12,2008 MS8.0 Wenchuan earthquake was very complex. To study the rupture zones generated by this earthquake,four dense temporary seismic arrays across the two surface breaking traces of the main-shock were deployed in July and recorded a great amount of aftershocks. This paper focuses on the data interpretation of two arrays across the central main fault,the northern array line 1 and southern array line 3. The fault zone trapped waves recorded by the two arrays were used to st...     

汶川地震区断层围陷波探测

对汶川地震区开展震后科考和断层围陷波探测,本文主要介绍平通镇断层围陷波探测及初步结果。平通镇处在汶川8．0级地震断层带正上方,地表破坏十分严重。该断层围陷波测线横跨断层,以地震探槽为大致中点,沿NW—SE方向两端延伸,测线长约400m。这次观测结果表明,在汶川8．0级地震的新破裂带中可以观测到断层围陷波,反映了断层带内外的介质在物理性质上有较大的差异。该测线记录的断层围陷波优势频率大约为3—4Hz。探槽附近的台站断层围陷波较强,初步推测,该地段地壳内断层的宽度大约有200m。     

提高任意广角波动方程计算效率及压制倏逝波干扰方法

任意广角波动方程（Arbitrarily Wide-angle Wave Equation,AWWE）是一种高精度的时空域单程波动方程,与其他时空域单程波方程相比,具有更大的成像倾角,因此是偏移成像的有力工具之一.本文改进了现有的AWWE有限差分计算方案,避免了原计算方案中对矩阵反复求逆的过程,同时减少了矩阵相乘的次数,显著地提高了AWWE数值计算的效率.数值实验证实,采用改进之后的计算方案,其计算结果与原方案完全一致.此外,本文采用了一种方法,在有倏逝波干扰的情况下,能在频率-波数（f-k）域区分出倏逝波与非倏逝波,为设计f-k滤波器提供合理的视速度门槛信息.偏移实验证实,在深度延拓时仅仅进行数次f-k滤波就能很好地抑制倏逝波干扰,提高偏移成像质量.     

Spectral characteristics of waves and particles in the model of cyclotron wave-particle interactions near plasmapause

Further analysis of energetic electron precipitation at the evening sector of magnetosphere is performed. In the framework of the quantitative model of cyclotron wave-particle interactions developed in the previous Pasmanik et al. paper, the case of finite spread over energies of initial energetic electron distribution is studied. The solution for distribution function of energetic electron is found. The energetic spectrum of trapped and precipitating electrons and whistler wave spectrum are analysed.