A critical analysis of the concept of planetary wave breaking

The concept of planetary wave breaking (McIntyre andPalmer, 1983; 1984) is critically reviewed. It is concluded that the wave breaking signature is not unique to any particular dynamic event in the stratosphere. Therefore, the classification of stratospheric transport events, such as wave breaking, groups fundamentally different events together. Better qualification of the wave breaking signature and a more solid theoretical basis of planetary wave breaking must be presented if the concept is to be of significant utility in describing stratospheric tracer transport.     

Nonlinear wave propagation on a sphere: Interaction between Rossby waves and gravity waves; stability of the Rossby waves

Abstract

An analytical spectral model of the barotropic divergent equations on a sphere is developed using the potential-stream function formulation and the normal modes as basic functions. Explicit expressions of the coefficients of nonlinear interaction are obtained in the asymptotic case of a slowly rotating sphere, i.e. when the normal modes can be expressed as single spherical harmonics.     

On the seasonal cycle of stratospheric planetary waves

Quasi-stationary planetary waves exhibit different seasonal behaviour in the two winter stratospheres. Whereas, in a climatological sense, wave amplitudes are large throughout northern winter, in the Southern Hemisphere there is a climatological minimum in midwinter. It is suggested here that the southern hemisphere behaviour is basically linear, the midwinter minimum arising from the opacity of the strong westerlies of southern midwinter to stationary wave propagation. On the other hand, it is further suggested that, in the northern hemisphere winter, the westerlies are prevented from becoming so strong (in a climatological sense) by the action of the waves themselves on the means state and that the penetration of large-scale waves into the midwinter northern stratosphere thus depends on a nonlinear feedback process. Preliminary tests of this hypothesis are conducted, using a highly truncated beta-plane model of the stratospheric flow.     

An evaluation of the classical and extended Rossby wave theories in explaining spectral estimates of the first few baroclinic modes in the South Pacific Ocean

Previous literature has suggested that multiple peaks in sea level anomalies (SLA) detected by two-dimensional Fourier Transform (2D-FT) analysis are spectral components of multiple propagating signals, which may correspond to different baroclinic Rossby wave modes. We test this hypothesis in the South Pacific Ocean by applying a 2D-FT analysis to the long Rossby wave signal determined from filtered TOPEX/Poseidon and European Remote Sensing-1/2 satellite altimeter derived SLA. The first four baroclinic mode dispersion curves for the classical linear wave theory and the Killworth and Blundell extended theory are used to determine the spectral signature and energy contributions of each mode. South of 17°S, the first two extended theory modes explain up to 60% more of the variance in the observed power spectral energy than their classical linear theory counterparts. We find that Rossby wave modes 2–3 contribute to the total Rossby wave energy in the SLA data. The second mode contributes significantly over most of the basin. The third mode is also evident in some localized regions of the South Pacific but may be ignored at the large scale. Examination of a selection of case study sites suggests that bathymetric effects may dominate at longer wavelengths or permit higher order mode solutions, but mean flow tends to be the more influential factor in the extended theory. We discuss the regional variations in frequency and wave number characteristics of the extended theory modes across the South Pacific basin.     

雅可比椭圆函数在大气和海洋动力学中的应用:二维非线性Rossby波研究

提出了扩展雅可比椭圆函数方法,来求得Petviashvili方程的精确解析解.Petviashvili方程被视为正压准地转位涡度方程的非地转扩展,应用该方法可以得到很多二维非线性Rossby波的周期波解,在取极限情况下,也可以得到二维Rossby孤立子解.     

Statistical model on the surface elevation of waves with breaking

In the surface wind drift layer with constant momentum flux, two sets of the consistent surface eleva- tion expressions with breaking and occurrence conditions for breaking are deduced from the first in- tegrals of the energy and vortex variations and the kinetic and mathematic breaking criterions, then the expression of the surface elevation with wave breaking is established by using the Heaviside function. On the basis of the form of the sea surface elevation with wave breaking and the understanding of small slope sea waves, a triple composite function of real sea waves is presented including the func- tions for the breaking, weak-nonlinear and basic waves. The expression of the triple composite func- tion and the normal distribution of basic waves are the expected theoretical model for surface elevation statistics.     

A numerical experiment on the general circulation of the middle atmosphere with a three-dimensional model explicitly representing internal gravity waves and their breaking

The general circulation of the middle atmosphere is simulated by means of a three-dimensional primitive equation model which covers from the south pole to the north pole but is limited to a ten-degree sector in the latitudinal direction; cyclic conditions are imposed at the east—west lateral boundaries. The model is capable of explicitly representing internal gravity waves of zonal wavelength greater than a few hundred kilometers with the use of a one-degree mesh, but planetary-scale waves were excluded. No parameterization is employed for subgrid-scale eddy viscosity (or diffusivity).With the assumption of a simple external-heating function corresponding to solstice conditions, a time integration was performed for about thirty days from the motionless state. During the whole period, random forcings were imposed on each grid of the lowest level in order to generate small-scale upwardly propagating internal gravity waves.The experiment has shown that small-scale waves were indeed excited, propagated upward, broke up near the mesopause, and greatly changed the thermally induced zonal mean motion and temperature fields in the upper mesosphere and lower thermosphere. As a result, important features of the general circulation at those levels, such as reversals of the zonal motion and the latitudinal gradient of zonal mean temperature were reproduced.     

A theory of enhanced saturation of the gravity wave spectrum due to increases in atmospheric stability

In this paper we consider a vertical wavenumber spectrum of vertically propagating gravity waves impinging on a rapid increase in atmospheric stability. If the high-wavenumber range is saturated below the increase, as is usually observed, then the compression of vertical scales as the waves enter a region of higher stability results in that range becoming supersaturated, that is, the spectral amplitude becomes larger than the saturation limit. The supersaturated wave energy must then dissipate in a vertical distance of the order of a wavelength, resulting in an enhanced turbulent energy dissipation rate. If the wave spectrum is azimuthally anisotropic, the dissipation also results in an enhanced vertical divergence of the vertical flux of horizontal momentum and enhanced wave drag in the same region. Estimates of the enhanced dissipation rates and radar reflectivities appear to be consistent with the enhancements observed near the high-latitude summer mesopause. Estimates of the enhanced mean flow acceleration appear to be consistent with the wave drag that is needed near the tropopause and the high-latitude summer mesopause in large-scale models of the atmosphere. Thus, this process may play a significant role in determining the global effects of gravity waves on the large-scale circulation.     

A practical method for analysis of river waves and for kinematic wave routing in natural channel networks

The behaviour of river waves is described using a simplified dimensionless form of the momentum equation in conjunction with the continuity equation. Three dimensionless parameters were derived based on a quantitative linear analysis. These parameters, which depend on the Froude number of the steady uniform flow and the geometric characteristics of the river, permit quantification of the influence of inertia and pressure in the momentum equation. It was found that dynamic and diffusion waves occur mainly on gentle channel slopes and the transition between them is characterized by the Froude number. On the other hand, the kinematic wave has a wide range of applications. If the channel slope is greater than 1%, the kinematic wave is particularly suitable for describing the hydraulics of flow. Since slopes in natural channel networks are often greater than 1%, an analytical solution of the linearized kinematic wave equation with lateral inflow uniformly distributed along the channel is desirable and was therefore derived. The analytical solution was then implemented in a channel routing module of an existing simple rainfall–runoff model. The results obtained using the analytical solution compared well with those obtained from a non‐linear kinematic wave model. Copyright © 2000 John Wiley & Sons, Ltd.     

A note on the equivalence of three major propagator algorithms for computational stability and efficiency

It is shown in this note that the three methods, the orthonormalization method, the minor matrix method and the recursive reflection-transmission matrix method are closely related and solve the numerical instability in the original Thomson-Haskell propagator matrix method equally well. Another stable and efficient method based on the orthonormalization and the Langer block-diagonal decomposition is presented to calculate the response of a horizontal stratified model to a plane, spectral wave. It is a numerically robust Thomson-Haskell matrix method for high frequencies, large layer thicknesses and horizontal slownesses. The technique is applied to calculate reflection-transmission coefficients, body wave receiver functions and Rayleigh wave dispersion.     

A note on specific variability of long surface gravity waves and drag coefficient in coastal upwelling zone

In this paper we solve analytically wave kinematic equations and the wave energy transport equation, for basic long surface gravity wave in the coastal upwelling zone. UsingGent andTaylor's (1978) parameterization of drag coefficient (which includes interaction between long surface waves and the air flow) we find variability of this coefficient due to wave amplification and refraction caused by specific surface water current in the region. The drag coefficient grows towards the shore. The growth is faster for stronger current. When the angle between waves and the current is less than 90° the growth is mainly connected with the waves steepness, but when the angle is larger, it is caused by relative growth of the wave phase velocity.     

The discrete wave number formulation of boundary integral equations and boundary element methods: A review with applications to the simulation of seismic wave propagation in complex geological structures

We review the application of the discrete wave number method to problems of scattering of seismic waves formulated in terms of boundary integral equation and boundary element methods. The approach is based on the representation of the diffracting surfaces and interfaces of the medium by surface distributions of sources or by boundary source elements, the radiation from which is equivalent to the scattered wave field produced by the diffracting boundaries. The Green's functions are evaluated by the discrete wave number method, and the boundary conditions yield a linear system of equations. The inversion of this system allows the calculation of the full wave field in the medium. We investigate the accuracy of the method and we present applications to the simulation of surface seismic surveys, to the diffraction of elastic waves by fractures, to regional crustal wave propagation and to topographic scattering.     

Analytical partial derivatives of the phase- and group velocities for Rayleigh waves propagating in a layer on a half-space

The dispersion relation for Rayleigh waves in a layer on a half-space is modified by introducing the quadratic wave number instead of the phase velocity. The implicit function theorem is then used to derive analytical formulae for the group velocity and for the phase- and group velocity partial derivatives with respect to the parameters of the medium. As two examples, the method is applied to the interpretation of dispersion curves for short-period Rayleigh waves observed in a sedimentary basin of the West Carpathians, and in the Moravo-Silesian region, Czech Republic.     

张衡一号卫星记录的空间电磁波传播特征分析方法及算法实现

本研究主要利用张衡一号电磁卫星（CSES）记录的电磁场波形数据,研发了电磁波波矢量分析工具,该工具包提供电磁波形频谱变换、奇异值分解（SVD）方法以及坡印廷能流计算功能.选取了张衡一号卫星在ULF/ELF/VLF频段观测到的哨声波、准周期辐射、电离层嘶声波等典型波动事件,开展了频谱分析和波矢量分析.通过与DEMETER卫星的对比观测研究,验证了算法的正确性,并且初步探讨了这些波动的传播特征,其结果也验证了张衡一号卫星在电磁场观测方面具有良好的性能.本研究研发的波矢量分析工具包可直接运用到张衡一号卫星的常规数据处理和科学分析应用中.

     

A discussion on the amplitude ratios of PP and P waves for earthquakes with different focal mechanisms

Using the WKBJ approximation method we calculate the synthetic teleseismograms of P and PP waves to match the observed ones of six large Chinese earthquakes with known focal mechanisms: Tibet earthquake of July 14, 1973; Haicheng earthquake of February 4, 1975; Songpan earthquakes of August 16, 1976, August 21, 1976 and August 23, 1976 and Nignhe earthquake of November 15, 1976. The focal mechanism of the Tibet earthquake is discussed to examine the technique used in the calculation. We note that the amplitude ratios of PP and P waves (A _PP/A _P) have different characteristics for dip—slip events and strike—slip events within certain epicentral distances. We calculate the synthetic teleseismograms of P and PP waves for the strike—slip and dip—slip events with fault angles of 330°, 240° and 0°, focal depths of 8 km, 17 km and 24 km, at the assumed station with an azimuth of 310° and epicentral distances from 40°; to 80°. The diagrams of maximum amplitude ratios of PP and P waves (A _PP/A _P) versus distances are given. The possibility to use the (A _PP/A _P) values to give an approximate estimation for the focal mechanism type is discussed. This work may be useful for determining the focal mechanism type for those earthquakes which have only few records such as the Chinese earthquakes from the 1930s to 1960s. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 150–160, 1991.