Long edge waves over a continental shelf

Summary The existence of long edge waves over a continental shelf is examined for a representative collection of shelf profiles. The frequencies of both trapped and leaky modes are found, when they exist, in terms of the shelf parameters. Certain theoretical trapped waves over a semi-infinite shelf are shown not to exist in the real ocean.A typical shelf profile on the east coast of Australia is modelled in four different ways from the above collection. The amplification of the leaky mode at the shoreline is found in terms of frequency for each model. Comparison of the results illustrates the severe errors introduced by crude approximations to the profile both at the shoreline and at the shelf cut-off region.

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Lange Randwellen über einem Festlandsockel

Zusammenfassung Die Existenz von langen Randwellen über einem Festlandsockel wird untersucht für eine repräsentative Sammlung von Schelfprofilen. Die Frequenzen sowohl der trapped (geführten) als auch der leaky (energieoder impulsabgebenden) Eigenfunktionsformen werden — wenn sie existieren — ermittelt, ausgedrückt in Schelf-Parametern. Es wird gezeigt, daß gewisse, trapped waves (geführte Wellen) über einem semi-unendlichen Schelf im wirklichen Ozean nicht existieren.Mit Hilfe der obigen Sammlung hat man ein typisches Schelfprofil von der Ostküste Australiens in vier verschiedenen Arten modelliert. Die Verstärkung des leaky mode an der Küstenlinie wird für jedes Modell gefunden in Termen der Frequenz. Der Vergleich der Ergebnisse verdeutlicht die schweren Fehler, die durch grobe Näherungen an das Profil entstehen, sowohl an der Küstenlinie als auch in dem Gebiet des Übergangs vom Schelf in die Tiefsee.

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Ondes transversales à longues crêtes au-dessus d'un plateua continental

Résumé On examine l'existence d'ondes transversales à longues crêtes au-dessus d'un plateau continental, afin de constituer une collection représentative des profils du plateau. On a trouvé les fréquences du «trapped mode» (mode captif) et du «leaky mode» (mode de transfert d'énergie et du moment) — quand ils existent — et cela en fonction des paramètres du plateau. On montre qu'il n'y a pas, dans l'océan réel, certaines ondes captées théoriques qui existeraient au-dessus d'un plateau semi-infini.Grâce à la collection dont il est parlé ci-dessus, on a modelé de quatre façons différentes un profil typique de la côte Est de l'Australie. Pour chaque modèle on a trouvé l'amplification du «leaky mode» sur la ligne de côte en fonction de la fréquence. La comparaison des résultats montre les erreurs importantes introduites par des approximations sommaires du profil, à la fois près de la ligne de côte et dans la région de transition du plateau continental en mer abyssale.

     

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     

Low frequency waves in plasmas with spatially varying electron temperature

Low frequency electrostatic waves are studied in magnetized plasmas with an electron temperature which varies with position in a direction perpendicular to the magnetic field. For wave frequencies below the ion cyclotron frequency, the waves need not follow any definite dispersion relation. Instead a band of phase velocities is allowed, with a range of variation depending on the maximum and minimum values of the electron temperature. Simple model equations are obtained for the general case which can be solved to give the spatial variation of a harmonically time varying potential. A simple analytical model for the phenomenon is presented and the results are supported by numerical simulations carried out in a 2.5-dimensional particle-in-cell numerical simulation. We find that when the electron temperature is striated along B₀ and low frequency waves (_ci) are excited in this environment, then the intensity of these low frequency waves will be striated in a manner following the electron temperature striations. High frequency ion acoustic waves (_ci) will on the other hand have a spatially more uniform intensity distribution.     

On steady and travelling waves over bottom topography in the model of homogeneous flow in a beta-plane channel

Abstract

A spectral low-order model is proposed in order to investigate some effects of bottom corrugation on the dynamics of forced and free Rossby waves. The analysis of the interaction between the waves and the topographic modes in the linear version of the model shows that the natural frequencies lie between the corresponding Rossby wave frequencies for a flat bottom and those applying in the “topographic limit” when the beta-effect is zero. There is a possibility of standing or eastward-travelling free waves when the integrated topograhic effect exceeds the planetary beta-effect.

The nonlinear interactions between forced waves in the presence of topography and the beta-effect give rise to a steady dynamical mode correlated to the topographic mode. The periodic solution that includes this steady wave is stable when the forcing field moves to the West with relatively large phase speed. The energy of this solution may be transferred to the steady zonal shear flow if the spatial scale of this zonal mode exceeds the scale of the directly forced large-scale dynamical mode.     

A note on edge waves on a flat shelf

Abstract

A variational approximation to the dispersion relation for trapped waves on a flat shelf of depth h ₁, bounded internally by a vertical coast and externally by a semi-infinite ocean of depth h ₂>h ₁, is obtained through an integral-equation formulation that accounts for all of the non-propagated modes that are excited at the discontinuity in depth (the conventional formulation of the edge-wave problem allows only for the propagated mode on the shelf and the dominant, non-propagated mode in the deep water). Coriolis effects are neglected. The exact result in the limit ω² h ₂/g↓0 (ω = angular frequency) is obtained by conformal mapping and compared with the variational approximation, which proves to be quite accurate over the entire range 1>h ₂/h ₁>x. The effects of the higher-order, non-propagated modes are found to be small for the long waves observed over the Southern California shelf by Snodgrass, Munk and Miller (1962).     

Geoelectromagnetic variations over a sloping ocean floor up to and including the coastline

Summary The electric and magnetic field variations over an arbitrarily sloping ocean floor are represented in series of Bessel functions forH-polarized uniform plane wave excitation. Calculation of the spatial variations of electric eurrents and apparent resistivity near a coastline will determine the usefulness of the magnetotelluric method in this application.The work presented herein was conducted at the Institute for Applied Mathematics of the University of Oslo, Oslo, Norway.     

Quasigeostrophic planetary waves in a two-layer ocean with one-dimensional periodic bottom topography

Although the study of topographic effects on the Rossby waves in a stratified ocean has a long history, the wave property over a periodic bottom topography whose lateral scale is comparable to the wavelength is still not clear. The present paper treats this problem in a two-layer ocean with one-dimensional periodic bottom topography by a simple numerical method, in which no restriction on the wavelength and/or the horizontal scale of the topography is required. The dispersion diagram is obtained for a wavenumber range of [?π/L _b , π/L _b ], where L _b is the periodic length of the topography. When the topographic?β?is not negligible compared to the planetary β, the Rossby wave solutions around the wavenumbers which satisfy the resonant condition among the waves and topography disappear and separate into an infinite number of discrete modes. For convenience, each mode is numbered in order of frequency. As topographic height is increased, the high frequency barotropic Rossby wave (mode 1) becomes a topographic mode which can exist even on the f plane, and the highfrequency baroclinic mode (mode 2) becomes a surface intensified mode. Behaviors of low frequency modes are somewhat complicated. When the topographic amplitude is small, the low frequency baroclinic modes tend to be bottom trapped and the low frequency barotropic modes tend to be surface intensified. As topographic amplitude further increases, the relation between the mode number and vertical structure changes. This change can be attributed to the increase of the frequency of the topographic mode with the topographic amplitude.     

Sediments and water fluxes in a muddy coastline: interplay between waves and tidal channel hydrodynamics

Tidal channels are ubiquitous in muddy coastlines and play a critical role in the redistribution of sediments, thus dictating the general evolution of intertidal landforms. In muddy coastlines, the morphology of tidal channels and adjacent marshes strongly depends on the supply of fine sediments from the shelf and on the resuspension of sediments by wind waves. To investigate the processes that regulate sediment fluxes in muddy coastlines, we measured tidal velocity and sediment concentration in Little Constance Bayou, a tidal channel in the Rockefeller State Wildlife Refuge, Louisiana, USA. The tidal measurements were integrated with measurements of wave activity in the bay at the mouth of the channel, thus allowing the quantification of feedbacks between waves and sediment fluxes. Results indicate that the sediment concentration in the channel is directly related to the wave height in the adjacent bay during flood and high slack water, whereas the concentration during ebb depends on local channel velocity. Moreover, the sediment flux during ebb is of the same order of magnitude as the sediment flux during the previous flood, indicating that only a small fraction of transported sediments are stored in the marsh during a tidal cycle. Finally, very low tides, characterized by high ebb velocities, export large volumes of sediment to the ocean. Copyright © 2010 John Wiley & Sons, Ltd.     

Propagation of seismic waves in a viscoelastic medium and the effect of topography

In this paper we have simulated the propagation of seismic waves in viscoelastic medium and calculated the effect of irregular surface topography by using finite element method. Several types of elastic and viscoelastic medium models, such as block structure, vidges and/or valley with and without a soft layer underneath have been studied. The distribution of maximum amplitude of displacement and acceleration on surface has been calculated in the case of vertically incident SH and P waves from the basement. The possible application in earthquake engineering is also discussed. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 442–449, 1991.     

正压大气模式下具有β效应与地形效应的Rossby孤立波

正压大气模式下,采用摄动方法和时空伸长变换推导了具有β效应、地形效应和耗散的mKdV-Burgers方程,得到Rossby孤立波振幅的演变满足带有β效应,地形与耗散的mKdV-Burgersm方程的结论.说明β效应、地形效应是诱导Rossby孤立波的重要因素.     

Seismic energy release over a broad frequency band

There remains much uncertainty on the absolute elastic wave energy released by fault rupture. Few direct estimates of the partition of seismic wave energy in ground shaking have been made. In this work, ground particle velocities from integrated accelerograms are used to compute the kinetic energy crossing unit area per unit time. Simplified theory for the near-field strong-motion case would appear to give a valid lower energy bound; the wave attenuation does not present a major problem. The partition of energy in predominantly P, S, and surface wave portions, for given frequency windows, is tabulated using strong-motion accelerograms recorded at different azimuths to the fault-sources of six California earthquakes (5.5<M _L<7.2). Checks against earlier magnitudeM _L and momentM ₀ correlations indicate significantly higher overall wave energy outputs than expected, but further calibration is needed.The study demonstrates that stable estimates of frequency-dependent seismic wave energies in the nearfield can be obtained from strong-motion records. Hence, energy flux may have a wider application to risk mapping than previously thought. In particular, a shift from peak acceleration scaling to (kinetic) energy inputs for engineering design appears to involve only routine processing.     

流体饱和半空间二维地形三分量弹性波散射间接边界元模拟

无限长局部地形地震波斜入射响应问题称为二维三分量问题,在计算量远小于三维的情况下,一定程度上反映了近地表场地的三维动力响应特征.基于天然土体的成层性及固液两相耦合特性,以层状多孔介质内部移动线荷载(孔隙水压)动力格林函数作为基本解,开展流体饱和半空间二维地形三分量弹性波散射的2.5维间接边界元模拟研究.总场响应由自由波...     

Transmission of Rayleigh waves over the surface of a heterogeneous medium

Summary The frequency equation of Rayleigh waves propagating over the free surface of an isotropic, perfectly elastic, heterogeneous semi-infinite medium with material properties varying as = ₀ e ^az , = ₀ e ^az , = ₀ e ^az (a>0) has been obtained. Solution of the frequency equation in closed form is obtained in two cases (i) =0, (ii) =, and the Rayleigh wave dispersion curves for phase and group velocities drawn. In both the cases the medium yields single Rayleigh modes which cannot propagate below certain cut-off frequencies. It is found that in case (i), <c<c ₀ and 0.87500 <c _g <c ₀, and in case (ii), 1.03082 <c<c ₁ and 0.90850 <c _g <c ₁, wherec andc _g denote phase nad group velocities respectively, is the constant shear wave velocity of the mediumc ₀ andc ₁ are the corresponding Rayleigh wave velocities of the homogeneous medium of the same Poisson's ratio. The motion of the surface particles is found to be retrograde elliptical as in the homogeneous case, but the ratic of the major and minor axes now becomes frequency dependent and is plotted against frequency. In both the cases (i) and (ii), the ratio starts at a lower value at the cut-off frequency and approaches the corresponding value of the homogeneous medium at high frequencies.     

Love waves in the fiber-reinforced layer over a gravitating porous half-space

This paper aims to study the propagation of Love waves in fiber-reinforced layer lying over a gravitating anisotropic porous half-space. The closed form of dispersion equation has been derived for the Love waves in terms of Whittaker function and its derivative, which are further expanded asymptotically, retaining the terms up to second degree. The frequency equation shows that the transverse and longitudinal rigidity of reinforced material, as well as gravity and porosity of the porous halfspace have significant effect on the propagation of Love waves. The study reveals that the increment in width of reinforced layer decreases the phase velocity. For a particular width of the reinforced layer, it is also observed that the phase velocity increases with increasing porosity of the half-space, but it decreases with increasing gravity.     

Ground motions around a deep semielliptic canyon with a horizontal edge subjected to incident plane SH waves

We study scattering of antiplane shear waves induced by a deep semielliptic canyon with a horizontal edge. We employ the region-point-matching technique to cope with the problem considered. Through an auxiliary boundary, a part of the circumference of a semiellipse, the whole analyzed region is divided into two subregions. We express the displacement fields in terms of Mathieu functions. We unify two distinct elliptic coordinates via a simple coordinate transformation relation. Integration of the coordinate transformation relation into the region-point-matching technique simplifies the procedure for constructing simultaneous equations. Imposing the continuity conditions and traction-free ones, we obtain the expansion coefficients. Frequency-domain results demonstrate ground motion variability based on several key factors. Ground surface responses under seismic shaking are also simulated in the time domain.     

Propagation of Rayleigh waves in a layer lying over a heterogeneous half space

Summary Propagation of Rayleigh waves in a layer lying over a heterogeneous incompressible half space has been studied. The dispersion equations have been derived and displacements due to an infinite line source have also been investigated.     

ST radar observations of atmospheric waves over mountainous areas: a review

Lee and mountain waves are dominant dynamic processes in the atmosphere above mountain areas. ST VHF radars had been intensively used to investigate these wave processes. These studies are summarized in this work. After discussing features of long-period quasi-stationary lee waves, attention is drawn to the frequent occurrence of freely propagating waves of shorter periods, which seem to be more common and characteristic for wave processes generated over mountainous areas. Characteristics of these waves such as their relation to the topography and background winds, the possibility of trapping by and breaking in the tropopause region and their propagation into the stratosphere is investigated. These orographically produced waves transport energy and momentum into the troposphere and stratosphere, which is considered an important contribution to the kinetic energy of the lower atmosphere. The occurrence of inertia-gravity waves in the stratosphere had been confused with lee waves, which is discussed in conclusion. Finally further questions on mountain and lee waves are drawn up, which remain to be solved and where investigations with ST radars could play a fundamental role.