On waves generated by a moving pressure field,II: Cnoidal wave effects

Summary In a recent paperHunt andTanner [3]²) investigated the waves generated by a steadily moving two-dimensional pressure distribution, which was zero ahead of the disturbance and a constantp ₀, tehind it, these regions being joined smoothly by a cubic function. Only those solutions with supercritical flow in both regions were considered, these were found to lead to an asymmetric solitary wave.This result is now extended to take account of the possibility of subcritical flow in either or both the regions, that is when there is a cnoidal wave train either behind and or ahead of the main solitary wave crest.The wave profiles are determined by the iterative method employed in the previous paper. This together with the wave drag associated with each system is computed for various values ofp ₀/U ², where is the fluid density andU a typical velocity.     

On the wave field generated by a variable wind

Abstract

By using an empirical expression relating the rate of increase in wave energy to the local wind speed, an equation for the phase speed at the peak of the wave spectrum is derived. The solution of the equation is determined for some simple wind fields. In particular, the wave field caused by a localised storm moving steadily over an unbounded ocean is considered. It is also shown that only a small fraction of the momentum transferred from the wind into the water propagates away from a local storm area in the form of wave momentum.     

Seismic waves generated by oscillating buildings: analysis of a release test

A three-stories, base-isolated building located in Rapolla (Potenza, Italy) was tested with a snap-back experiment. Free-field measures were performed using 3D seismometers, located at 10 and 50 m from the buildings in direction of motion and at 10 m from the building in direction transverse to the motion. At each measurement point it was possible to separate the soil amplification effects from two source terms, due to the base-isolated building and to the reaction block. The ground motion was noticeable: at 10 m in the longitudinal direction it was comparable with a small size, near-field earthquake.     

On pressure waves in the coastal region

Summary Several authors have tried to explain the different aspects of pressure waves in water including the phenomenon of «Singing» by assuming another fluid layer below the water column. In this note an attempt has been made to determine the thickness of such a layer.     

Properties of QBO and SAO generated by gravity waves

In this paper we present an extension for the 2D (zonal mean) version of our numerical spectral mode (NSM) that incorporates Hines’ Doppler spread parameterization (DSP) for small-scale gravity waves (GW). This model is applied to describe the seasonal variations and the semi-annual and quasi-biennial oscillations (SAO and QBO). Our earlier model reproduced the salient features of the mean zonal circulation in the middle atmosphere, including the QBO extension into the upper mesosphere inferred from UARS measurements. The model is extended to reproduce the upwelling at equatorial latitudes that is associated with the Brewer–Dobson circulation — which affects significantly the dynamics of the stratosphere as Dunkerton had pointed out. In the presence of GW, this upwelling is produced in our model with tropospheric heating, which generates also zonal jets outside the tropics similar to those observed. The resulting upward vertical winds increase the period of the QBO. To compensate for that, one needs to increase the eddy diffusivity and the GW momentum flux, bringing the latter closer to values recommended in the DSP. The QBO period in the model is 30 months (mo), which is conducive to synchronize this oscillation with the seasonal cycle of solar forcing. Associated with this QBO are interannual and interseasonal variations that become increasingly more important at higher altitudes — and this variability is interpreted in terms of GW filtering that effectively couples the dynamical components of the mesosphere. The computed temperature amplitudes for the SAO and QBO are in substantial agreement with observations at equatorial and extra-tropical latitudes. At high latitudes, however, the observed QBO amplitudes are significantly larger, which may be a signature of propagating planetary waves not included in the present model. The assumption of hydrostatic equilibrium not being imposed, we find that the effects from the vertical Coriolis force associated with the equatorial oscillations are large for the vertical winds and significant for the temperature variations even outside the tropics, but the effects are small for the zonal winds.     

Water waves generated by instantaneous disturbances at the bed of a sloping beach

The two-dimensional problem of the generation of water waves due to instantaneous disturbances prescribed at the bed of a beach sloping at an arbitrary angle is studied here. It is formulated in terms of an initial-boundary-value problem for the velocity potential describing the motion in the fluid region assuming the linear theory. Using the Laplace transform in time and the Mellin transform in distance, the problem is reduced to solving a difference equation whose method of solution is of considerable importance in the literature. The form of the free surface is obtained in terms of a multiple infinite integral that is evaluated by the method of steepest-descent. For some prescribed forms of the disturbance at the bed of the beach, the free surface is depicted in a number of figures for different beach angles. It is observed that as the beach angle decreases, the maximum wave height increases, which is plausible.     

Dynamic responses of a saturated poroelastic half-space generated by a moving truck on the uneven pavement

A truck–pavement–ground coupling model was established to study the dynamic responses of a saturated poroelastic half-space generated by a moving heavy truck on the uneven pavement. The ground was simulated as a fully saturated poroelastic half-space governed by Biot’s theory. The overlying pavement was simplified as a Kirchhoff thin plate. With the assumption of a sinusoidal pavement surface, the dynamic wheel–pavement force was obtained through a linear Hertizian contact model. The numerical results showed that this dynamic load could make considerable contributions to the stress and excess pore water pressure responses in the ground. Furthermore, the effective stress path of the soil unit beneath the pavement caused by the moving truck was firstly calculated and presented. It was found that the differences between the total stress path and the effective stress path became significant as the truck speed increased, thus the effective stress path was more suitable than total stress path to reflect the stress history of soil elements in the saturated ground during the passage of high-speed traffics.     

与日夜交替线移动相关的中尺度电离层扰动GPS网观测

本文选取由国际GPS服务中心(IGS)提供的北美中纬度地区GPS网TEC观测数据,通过多通道最大熵频谱分析方法研究了2005年（太阳活动低年）地磁活动平静期间日出和日落时由于日夜交替线的移动而激发的中尺度电离层扰动(MSTID),并统计分析其季节变化特性.结果表明：(1) 日出或日落期间,在中纬度地区经常观测到由日夜交替线移动激发的中尺度电离层扰动.扰动主要沿日夜交替线运动方向传播,平均持续时间约2～3 h;振幅在0.2～0.8 TECU之间,水平波长,水平相速度和周期分别为300±150 km,150±80 m/s和25±15 min;(2) 由日夜交替线移动激发的中尺度电离层扰动在春秋分出现率较少;在夏季,扰动在黄昏时出现率达最大值,在日出后少量出现;而冬季则日出后的扰动效应更为明显.分析表明,在中纬地区,这种扰动出现率随季节的变化与不同季节的日出日落时刻太阳EUV辐射通量变化过程的快慢,以及电离层中离子损失过程快慢有关.     

Elastic waves in visco-elastic half-space generated by various vehicle loads

In this paper, the response of a visco-elastic half-space subjected to moving loads with static and dynamic components is investigated. Four types of vehicle loads are considered, including the moving point load, uniformly distributed wheel load, elastically distributed wheel load, and a train load simulated as a sequence of elastically distributed wheel loads. In each case, the influence of the moving loads traveling in the subsonic, transonic and supersonic ranges on the dynamic responses of the half-space is studied. The parametric study conducted herein enables us to grasp insight into the mechanism of wave propagation for a visco-elastic half-space under moving loads.     

Numerical study on transient harbor oscillations induced by successive solitary waves

Tsunamis are traveling waves which are characterized by long wavelengths and large amplitudes close to the shore. Due to the transformation of tsunamis, undular bores have been frequently observed in the coastal zone and can be viewed as a sequence of solitary waves with different wave heights and different separation distances among them. In this article, transient harbor oscillations induced by incident successive solitary waves are first investigated. The transient oscillations are simulated by a fully nonlinear Boussinesq model, FUNWAVE-TVD. The incident successive solitary waves include double solitary waves and triple solitary waves. This paper mainly focuses on the effects of different waveform parameters of the incident successive solitary waves on the relative wave energy distribution inside the harbor. These wave parameters include the incident wave height, the relative separation distance between adjacent crests, and the number of elementary solitary waves in the incident wave train. The relative separation distance between adjacent crests is defined as the ratio of the distance between adjacent crests in the incident wave train to the effective wavelength of the single solitary wave. Maximum oscillations inside the harbor excited by various incident waves are also discussed. For comparison, the transient oscillation excited by the single solitary wave is also considered. The harbor used in this paper is assumed to be long and narrow and has constant depth; the free surface movement inside the harbor is essentially one-dimensional. This study reveals that, for the given harbor and for the variation ranges of all the waveform parameters of the incident successive solitary waves studied in this paper, the larger incident wave heights and the smaller number of elementary solitary waves in the incident tsunami lead to a more uniform relative wave energy distribution inside the harbor. For the successive solitary waves, the larger relative separation distance between adjacent crests can cause more obvious fluctuations of the relative wave energy distribution over different resonant modes. When the wave height of the elementary solitary wave in the successive solitary waves equals to that of the single solitary wave and the relative separation distance between adjacent crests is equal to or greater than 0.6, the maximum oscillation inside the harbor induced by the successive solitary waves is almost identical to that excited by the single solitary wave.     

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.     

On the propagation of plane waves in a porous visco-elastic material containing a fluid and deformed by a magnetic field

Summary In the present note, an attempt has been made to investigate the wave-motions in a poro-viscoelastic medium traversed by a static magnetic field, by using the equations ofMaxwell, and those ofBiot.     

Generation of waves by advected pressure fluctuations

Abstract

Because of the dispersion of surface gravity waves, the rate at which advected pressure fluctuations generate wave energy is independent of the coherence time of the pressure fluctuations provided that this time is long compared with the period of the waves. Phillips' (1957) analysis is correct insofar as it concerns wave components exactly “resonant” with the advected pressure fluctuations, but it does not deal adequately with the “bandwidth” of the resonance.     

A further investigation of wind generated waves

Summary Sixty-four wave records taken by the O. W. S. Weather Explorer are investigated and Fourier analysed. The relation between the wind speed and the equivalent heightH, and the frequency of maximum amplitude on the spectrum,f ₀, do not differ greatly from those previously obtained in 1955. The wave spectrum, however, can now be shown to be reducible to the same form for all wind speeds for large fetch,H _f ² /H ² being a function of (f-f ₀) only. The same function applies for shorter values of fetch, only, then, the relation is betweenH _f ² /yH ² andy (f-f ₀), wherey is the ratio of the values ofH and 1/f ₀ at the short fetch to those for the same wind speed at infinite fetch.Agreement can be found with a previous result by R. W. Burling [1955] under certain conditions. For a fetch of 4 miles, agreement to the same order is obtained with the values of mean square slope found by C. S. Cox and W. H. Munk [1954].It has not been possible to find agreement with the results of Project SWOP (J. Chase, L. J. Cote, W. Marks and others [1957]).

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Eine weitere Untersuchung windbedingter Wellen

Zusammenfassung Vierundsechzig Wellenregistrierungen wurden an Bord des O. W. S. Weather Explorer aufgezeichnet und nach der Fourier-Methode analysiert. An dem Verhältnis zwischen der Windgeschwindigkeit und der äquivalenten HöheH sowie der Frequenz der maximalen Amplitude auf dem Wellenspektrumf ₀ wurde im Vergleich zu dem im Jahre 1955 festgestellten Verhältnis nur sehr wenig geändert. Bei großem Fetch kann jedoch das Wellenspektrum als auf die gleiche Form für alle Windgeschwin-digkeiten zurückführbar dargestellt werden, daH _f ² /H ² nur eine Funktion von (f-f ₀) ist. Die gleiche Funktion gilt auch für geringere Fetchlängen, nur ist dann die Beziehung zwischenH _f ² /yH ² undy(f-f ₀), wobeiy das Verhältnis der WerteH und 1/f ₀ bei kurzem Fetch zu den Werten gleicher Windgeschwindigkeit bei unendlichem Fetch darstellt.Unter bestimmten Bedingungen kann eine Übereinstimmung mit einem früheren Ergebnis von R. W. Burling [1955] erreicht werden. Bei einem Fetch von 4 sm erhält man mit dem Quadrat des mittleren Gefälles nach C. S. Cox und W. H. Munk [1954] eine Übereinstimmung gleicher Größenordnung.Eine Übereinstimmung mit den Ergebnissen des Projektes SWOP (J. Chase, L. J. Cote, W. Marks u. a. [1957]) ließ sich nicht erzielen.

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Une autre étude des vagues engendrées par le vent

Résumé Soixante-quatre enregistrements de vagues obtenus par le navire météorologique «Weather Explorer» seront analysés d'après la méthode de Fourier. Le rapport entre la vitesse de vent, la hauteur équivalenteH et la fréquence de l'amplitude maximale sur le spectre d'onde n'a pas beaucoup changé lorsqu'on le compare au rapport constaté en 1955.H _f ² /H ² n'étant qu'une fonction de (f-f ₀), on peut représenter le spectre d'ondes comme d'être réductible à la même forme, à laquelle toutes les vitesses de vent peuvent être référées en présence d'un grand «fetch». La même fonction s'applique à une longueur inférieure de fetch, mais dans ce cas la relation se fait entreH _f ² /yH ² ety(f-f ₀);y étant le rapport des valeursH et 1/f ₀ en présence d'un court fetch à des valeurs d'égale vitesse de vent en présence d'un fetch infini.Dans certaines conditions, l'accord se laisse atteindre avec des résultats récents de R. W. Burling [1955]. Lorsque le fetch a 4 milles marins de longueur, l'accord se fait dans le même ordre de grandeur à l'aide des valeurs du carré de la pente moyenne d'après C. S. Cox et W. H. Munk [1954].Il n'était pas possible d'obtenir un accord avec les résultats du projet SWOP (J. Chase, L. J. Cote, W. Marks et d'autres [1957]).

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Short-period VLF emissions as solitary envelope waves in a magnetospheric plasma maser

Space and ground-based experiments have shown evidence of natural short-period VLF emissions in which separate spectral elements are repeated with a periodicity of 2–7 s. Their basic morphological properties are found on the basis of original experimental data. In our opinion, excitation of such emissions is the result of quasi-linear relaxation effects that compensate for natural spectral dispersion. The quasi-linear relaxation of the energetic electron distribution function incrementally changes wave cyclotron instability and hence the VLF emission spectral forms. Some properties of the quasi-linear interaction of whistler waves with magnetospheric radiation belt electrons are studied. It is shown that quasi-linear relaxation can increase the cyclotron instability at the leading edge of an electromagnetic pulse. This effective saturation of absorption facilitates the division of VLF hiss-like emission into separate electromagnetic pulses without spectral modification from one pulse to the next. Some features and manifestations of this effective saturation of absorption are discussed. The results are important for a better understanding of temporal and spatial structures of VLF whistler-mode emissions and energetic electron fluxes.