Planetary waves

Planetary or Rossby waves, though probably unimportant in the fluid interior of the Earth, are of interest to earth scientists in general, because of their pervasive role in the general circulation of oceans and atmospheres. The present review does not presuppose any special knowledge of geophysical fluid dynamics. Following a recapitulation of some general wave concepts, it defines absolute vorticity and its role as a restoring force in rotatory motion. The quasi-geostrophic character, the westward propagation and the dispersion of planetary waves is then discussed, as is the difference between shear waves and waves with vertically uniform motion. A last section deals briefly with the influence of planetary wave dynamics on climatic patterns in the atmosphere and in the oceans.     

Interaction of low-frequency hydroacoustic waves with wind sea waves

On the basis of experimental data on hydrospheric pressure variations, obtained with the use of a laser hydrophone and laser gauge of hydrospheric pressure variations, while hydroacoustic radiators were running, generating hydroacoustic waves at frequencies of about 32, 245, and 421 Hz in water, it was established that there is no modulating action of wind sea waves on the propagating hydroacoustic signals along the “radiator-receiver” trace, within the limits of experimental error and the processing methods used.     

混合浪中长波对短波的位相调制

为研究长波对短波尤其是风浪高频成分的调制,在实验室风浪水槽中产生混合浪,分析风浪受规则长波的调制。采用本征模态方法分解出不同尺度的风浪模态,计算各模态位移平方关于长波位相的平均。结果表明,风浪主要波、小尺度波和介于二者之间的中等尺度波,其能量沿长波位相的分布具有不同特征:风浪主要波的能量随长波波陡增加而减少,其分布与长波同相且关于长波波谷对称;中等尺度波的能量则随长波波陡增加而增加,在长波波峰迎风面略高于背风面;小尺度风浪的能量随着风速和长波波陡的增加而增加,随着风区长度的增加而减少,在长波波峰迎风面明显高于背风面。     

Numerical hindcast of extreme waves

The cyclone wave parameters are predicted using Young’s parametric hurricane wave prediction model. The input cyclone tracks for this work are obtained from Fleet Naval Meteorology and Oceanography Center, USA. Extreme value analysis is carried out to obtain the wave heights and periods for 1 in 5, 10, 50 and 100 years return periods, respectively. The deep-water hindcast wave corresponding to 100 years from probable directions are allowed to propagate to Visakhapatnam coastal waters using nearshore spectral wind-wave mode. The offshore wave height for one in 100-year return period is 11.9 m, and the corresponding nearshore wave height at 10-m water depth varies between 4.6 and 5.6 m depending on the directional spreading. Weibull distribution is chosen to fit the 24 cyclonic data sets over a total period of 30 years (September 1972 to November 2002). This paper demonstrates usefulness of Young’s wave model for deep-water extreme wave hindcasting. Further, the results of the present study would be highly useful for assessing the design wave height for Visakhapatnam coast.     

瑞利波泄漏模式及其"之"字形频散研究

针对地基模型中可能出现泄漏模式的几种情况，对瑞利波勘探中泄漏模式波的求取进行了模拟研究。通过添加附加层的方法，使实频散方程求解瑞利波相速度的范围包含了所有的层速度区域，从而用导波来模拟计算泄漏模式波。通过对七个模型的模拟结果来看，附加层法不仅能模拟出原模型的实数导波，而且还能反映其泄露模式波的变化。同时，通过对Ⅴr-λ曲线的正演计算，说明泄漏模式波的存在也是产生“之”字形的原因之一。     

Nearshore propagation of cyclonic waves

Cyclone-generated surface waves are simulated using state-of-art SWAN (Simulating WAves Nearshore) model coupled with hydrodynamic model inputs. A severe cyclonic storm passed over the Arabian Sea during 4–9th November 1982 is selected from UNISYS track records. The cyclone lasted for nearly 6 days and subsided with a land fall at Gujarat coast, west coast of India. In this study, cyclonic wind fields are generated using a well-established relationship suggested by Jelesnianski and Taylor (1973). The associated water level variations due to storm surge and surge generated currents are simulated using POM (Princeton Ocean Model). The outputs are one-way coupled with the wave model SWAN for simulating wave parameters off Gujarat, north-east basin of Arabian Sea. An extensive literature review is carried out on the progress and methodology adopted for storm wave modelling and analysis. The results presented in this paper reveal the severity of the storm event and would be highly useful for assessing the extreme wave event/climate especially for the south coast of Gujarat.     

基于高阶有限差分纵横波分解的弹性波数值模拟

常规弹性波数值模拟方法得到的VSP波场信息中,P波和S波是相互耦合在一起的,波场信息复杂,在进行多波多分量地震波场特征分析时需要进行波场分离。这里采用纵波、横波解耦的弹性波波动方程高阶有限差分算法进行数值模拟,并采用PML边界条件处理人工边界条件,得到纵波、横波解耦的独立VSP纵波、横波记录,为进一步研究弹性波VSP波场特征奠定了基础。     

Near-polar starspots and polar dynamo waves

A possible mechanism for the formation of near-polar magnetic spots on some stars with convective envelopes is proposed. The mechanism is based on the idea that the maximum of the dynamo waves that are excited in thin convective shells by the dynamo mechanism is shifted appreciably from the maximum of the magnetic-field sources in the direction of motion of the dynamo wave. If there is no region of super-rotation near the equator for some reason (as a consequence of disruption due to tidal interaction with a companion in a binary system, for example) and the wave of stellar activity propagates toward the poles rather than toward the equator, this maximum will be in the near-polar regions.     

Stress waves in laterally loaded piles

The behaviour of single vertical piles subjected to lateral loading at the pile head was analysed. Based on the assumption of beam on elastic foundation, the analysis was made by using the method of direct analysis which is a numerical approach making direct use of governing physical laws without explicitly utilizing the differential equation of vibration. The analysis provides short-time pile response to pulse loadings. These results indicate, among others, that an interaction between the dilatation and shear waves results in a stress discontinuity of considerable magnitude which may deserve special attention in pile design.     

Seismic waves and correlation autoregressive processes

Stochastic models appropriate for seismic records of earthquakes and underground nuclear explosions are considered and a selective review of the existing models is presented. Special models of stationary processes, periodically correlated processes, and uniformly modulated stationary processes as well as a new class called correlation autoregressive processes are studied. Relevant properties of correlation autoregressive processes are presented. It is shown that the successful models presently used are all subclasses of the correlation autoregressive processes. Shortcomings of the existing nonstationary models and merits of the new class for seismic wave modeling are discussed and directions for the further research and development are suggested. It is hoped that the model and the ideas introduced in this article will provide a stimulation for further examination of correlation autoregressive processes and will promote statistical modeling of seismic records.     

Earthquake waves in a random medium

Measurements are conducted with small samples in the laboratory and thus for all practical purposes the medium is macroscopically homogeneous. On the other hand, the uncertainties and the irregular changes in situ are macroscopic inhomogeneities. This work is an attempt to account for these stochastic changes in the elastic properties and density in a rational manner. The method used is that of Karal and Keller which is based on the use of the Green's function and neglect of third-order correlations. The resulting integral equations are solved by Laplace transform. The analysis indicates that the energy decay in the mean motion through random mode coupling introduces damping into even a purley'elastic medium and enhances the damping in a significant manner in a hysteretic viscoelastic medium. This consideration is important in relating the damping and dispersion characteristics of wave in situ to those measured in the laboratory. The formulation is extended to multilayer systems through transfer matrices and to arbitrary inputs by Fourier transform. Sample calculations are presented for single and multilayer systems to obtain response spectra and for the response to Gaussian and actual earthquake input motions.     

Some kinematic features of refracted waves

The equation for the arrival time of a refracted wave is fully stated. This approximates as the arrival of the head wave minus the second and third terms of the equation. Time-distance curves are studied, and examples for carbonates, Precambrian, and crystalline specimens are given. Along with the linear velocity law, the parabolic law is also treated. Peculiarities of propagation of refracted waves in the medium are studied and depth of penetration is considered. Relations for refracted, diffracted, and reflected waves are examined and multiple refracted waves are considered as well. This seems to be a practical and general paper illuminating the refraction phenomenon. — Petroleum Abstracts.     

Coupling between internal and surface waves

In a fluid system in which two immiscible layers are separated by a sharp free interface, there can be strong coupling between large amplitude nonlinear waves on the interface and waves in the overlying free surface. We study the regime where long waves propagate in the interfacial mode, which are coupled to a modulational regime for the free-surface mode. This is a system of Boussinesq equations for the internal mode, coupled to the linear Schrödinger equations for wave propagation on the free surface, and respectively a version of the Korteweg-de Vries equation for the internal mode in case of unidirectional motions. The perturbation methods are based on the Hamiltonian formulation for the original system of irrotational Euler’s equations, as described in (Benjamin and Bridges, J Fluid Mech 333:301–325, 1997, Craig et al., Comm Pure Appl Math 58:1587–1641, 2005a, Zakharov, J Appl Mech Tech Phys 9:190–194, 1968), using the perturbation theory for the modulational regime that is given in (Craig et al. to appear). We focus in particular on the situation in which the internal wave gives rise to localized bound states for the Schrödinger equation, which are interpreted as surface wave patterns that give a characteristic signature of the presence of an internal wave soliton. We also comment on the discrepancies between the free interface-free surface cases and the approximation of the upper boundary condition by a rigid lid.     

About compact equations for water waves

A simple compact equation for gravity water waves, which includes a nonlinear wave term and advection term, is derived. Numerical simulations in the framework of this equation demonstrate an initial stage of freak wave breaking.