Topographic effects on solitary Rossby waves

The model for baroclinic solitary waves previously described by Flierl is developed to include effects of bottom variations.Topographic disturbances are shown to act, through their first and second derivatives, on both the phase speed correction and the maximum horizontal amplitude.The combined effects of mean shear flow steepening and bottom variations are considered; an equation is derived, showing the relative importance of each effect.     

大气Rossby波动力学的研究进展

Rossby波是旋转大气和海洋中的一类重要波动,在天气和气候演变中起有重要的作用。该文介绍了北半球中纬度地区的两类重要Rossby波——斜压不稳定波和准定常行星波,在最近20余年来取得的一些重要研究进展。文中涉及的主要研究领域有：斜压不稳定波包动力学、湿斜压过程对斜压不稳定波的作用、北半球风暴轴动力学、斜压波包与高影响天气的预报、准定常行星波的形成机理、准定常行星波的水平传播与能量频散、准定常行星波的垂直传播与能量频散、三维准定常行星波的传播与能量频散。     

On the contribution of Rossby waves driven by surface buoyancy fluxes to low-frequency North Atlantic steric sea surface height variations

Previous studies have shown that wind-forced baroclinic Rossby waves can capture a large portion of low-frequency steric sea surface height (SSH) variations in the North Atlantic. In this paper, the classical wind-driven Rossby wave model derived in a 1.5-layer ocean is extended to include surface buoyancy forcing, and the new model is then used to assess the contribution from buoyancy-forced Rossby waves to low-frequency North Atlantic steric SSH variations. Buoyancy forcing is determined from surface heating as freshwater fluxes are negligible. It is found that buoyancy-forced Rossby waves are important in only a few regions belonging to the subtropical-to-midlatitude and eastern subpolar North Atlantic. In these regions, the new Rossby wave model accounts for 25%–70% of low-frequency steric SSH variations. Furthermore, as part of the analysis it is also shown that a simple static model driven by local surface heat fluxes captures 60%–75% of low-frequency steric SSH variations in the Labrador Sea, which is a region where Rossby waves are found to have no influence on the steric SSH.     

线性和非线性地形罗斯贝波

本文在半地转概念下,讨论了线性和非线性地形罗斯贝波的稳定性及其解。指出:线性和非线性稳定性判据形式一致。在线性时,地形东西向及南北向坡度对稳定波动的周期和传播速度有明显影响,其解为周期函数;在不稳定时,解为非周期函数。二级近似时其解为孤立波形式——不稳定时,在地形不同位置可形成东移或西移的孤立波槽或孤立波脊;而在稳定时只形成孤立波槽。三级近似时解出现间断点。     

Oscillatory Rossby Solitary Waves in the Atmosphere

The linear Rossby wave frequency expression is expanded at higher accuracy based on the scale difference char?acteristics of atmospheric long waves in the and directions. That the nature of the waves represented by the expan?sion is identical to that of the original ones is demonstrated both in phase velocity and wave energy dispersion speed , followed by the derivation of the nonlinear expression describing atmospheric long wave behaviors with the associated approximate analytic solution obtained. Then, for the first time atmospheric’ oscillatory Rossby solitary wave’ with its dispersion relation is obtained by numerical calculation with the aid of physical parameters of the real atmosphere. The solitary wave is found to be very close to such longwave systems as blocking highs and cut-off de?pressions in the actual atmosphere.     

Cross-equatorial structures of equatorially trapped nonlinear Rossby waves

Analysis of the Sea Surface Height (SSH) from satellite altimeters has shown that equatorially trapped Rossby waves exhibit asymmetric cross-equatorial structures; their northern extrema are much larger in magnitude than their southern counterparts. Such asymmetry is inconsistent with the classical theory for the first baroclinic, first meridional equatorially trapped Rossby mode, which predicts that SSH and zonal velocity are symmetric in latitude and the meridional velocity is latitudinally antisymmetric (Matsuno, 1966). Chelton et al. (2003) attributed the observed asymmetry to the mean-shear-induced modifications of first meridional mode Rossby waves. The present paper examines nonlinear rectification of cross-equatorial wave structures in the presence of different zonal mean currents. Nonlinear traveling Rossby waves embedded in shears are calculated numerically in a 1.5-layer model. Nonlinearity is shown to increase the cross-equatorial asymmetry substantially making the northern extrema even more pronounced. However, nonlinearity only slightly increases the magnitude of the westward phase speed.     

N层模式大气中的斜压孤立Rossby波

文中导得了N层模式的KdV方程,作为例子计算了三层模式的孤立Rossby波流型。基本气流的垂直切变、水平切变和Froude数对孤波流型都有重要影响;不同模态的孤波具有不同流型,不同高度位面上的孤波流型一般是不同的。     

Rossby waves in a rotating fluid of spheroidal configuration

The ray method is used to study quasi-geostrophic waves in a thin layer of incompressible, inviscid fluid of constant density both in a rotating spheroidal shell and on a rotating spheroid bounded above by a free surface. Asymptotic approximations to solutions of both the time-dependent and time-reduced problems are found; the dispersion relation obtained has the form of the Rossby-Haurwitz formula when the shell is spherical, and is asymptotically equivalent to that found by Longuet-Higgins (1965) for the free surface problem on a sphere. The approximation is first applied to free oscillations in a rotating spherical shell and Longuet-Higgins' (1964) results are rederived. Spheroidal shells in which the shell thickness depends only upon the latitude are studied next and a necessary and sufficient condition for oscillations to occur is obtained.     

The effects of zonal flow on nonlinear Rossby waves

In this paper, we using phase plane method have derived the stability criteria of linear and nonlinear Rossby waves under the conditions of semi-geostrophic approximation and have gotten the solutions and geostrophic vorticity of corresponding solitary Rossby waves. It is pointed out that the wave stability is connected with the distri-bution of zonal flow and when the zonal flow is different the solitary wave trough or ridge is formed.     

Mechanism of Kelvin and Rossby waves during ENSO events

Summary ?The fields of sea-level height anomaly (SLHA) and surface zonal wind anomaly (SZWA) have been analyzed to investigate the typical evolution of spatial patterns during El Ni?o-Southern Oscillation (ENSO) events. Sea surface temperature (SST) changes during ENSO events are represented as an irregular interplay of two dominant modes, low-frequency mode and biennial mode. Cyclostationary principal component (PC) time series of the former variables are regressed onto the PC time series of the two dominant SSTA modes to find the spatial patterns of SLHA and SZWA consistent with the two SSTA modes. The two regressed patterns of SLHA explain a large portion of SLHA total variability. The reconstruction of SLHA using only the two components reasonably depicts major ENSO events. Although the low-frequency component of SST variability is much larger than the biennial component, the former does not induce strong Kelvin and Rossby waves. The biennial mode induces much stronger dynamical ocean response than the low-frequency mode. Further decomposition of the SLHA modes into Kelvin and Rossby components shows how these two types of equatorial waves evolve during typical ENSO events. The propagation and reflection of these waves are clearly portrayed in the regressed patterns leading to a better understanding of the wave mechanism in the tropical Pacific associated with ENSO. A close examination suggests that the delayed action oscillator hypothesis is generally consistent with the analysis results reported here. Rossby wave development in the central Pacific in the initiation stage of ENSO and the subsequent reflection of Kelvin waves at the western boundary seems to be an important mechanism for further development of ENSO. The development of Kelvin waves forced by the surface wind in the far-western Pacific cannot be ruled out as a possible mechanism for the growth of ENSO. While Kelvin waves in the far-western Pacific serve as an intiation mechanism of ENSO, they also cause the termination of existing ENSO condition in the central and eastern Pacific, thereby leading to a biennial oscillation over the tropical Pacific. The Kelvin waves from the western Pacific erode the thermocline structure in the central Pacific preventing further devlopment of ENSO and ultimately terminating it. It should be emphasized that this wave mechanism is clear and active only in the biennial mode. Received August 15, 2001; revised March 6, 2002     

Propagation of the Rossby waves on two dimensional rectangular grids

Summary A simple two-dimensional quasi-geostrophic linearized model of the atmosphere is used to investigate the behaviour of the quasi-geostrophic modes for five horizontal rectangular grids. Numerical expressions for frequencies of Rossby waves for all grids are evaluated. It was found that the B and C grids produce only negative frequencies as well as the continuous case. The D grid has negative and zero frequencies. Finally, it was found that the A and E grids produce positive frequencies and eastward moving Rossby waves.With 2 Figures     

Weakly non-linear Rossby waves in a rotating fluid of spheriodal configuration

A modified ray method is used to study weakly non-linear Rossby waves in a thin layer of incompressible inviscid fluid of constant density both in a rotating spheroidal shell and on a rotating spheroid bounded above by a free surface. This method yields the same dispersion relation and conservation law as in the linear case (London) but gives an equation for a new, second order mean term. This mean term is shown to be unstable for all free oscillations on any axisymmetric bottom topography in the free surface problem. This contrasts with the analogous problem on the Beta-plane where the corresponding mean term is stable.     

Anemobaric low-frequency waves in the Chukchi Sea

The characteristics of currents and sea level wave perturbations of synoptic scale in the Chukchi Sea are compared with well-known dispersion relations of low-frequency waves of different types. This comparison allowed identifying the currents and sea level wave perturbations as internal Kelvin waves and barotropic and baroclinic topographic waves. Assessments of statistical relations between wave perturbations of currents and different meteorological characteristics showed that the energy supply of low-frequency waves is provided sporadically by various components of anemobaric (wind-induced) forces in the local areas of the Chukchi Sea and the Bering Strait.     

The algebraic decay of equatorial Rossby waves in a shear flow

Through numerical integration, we show that equatorial Rossby waves, like their midlatitude counterparts, decay algebraically in the limit t → ∞ in a linear shear flow. For small times, the growth expected for some components does not translate into any growth of the wave disturbance as a whole when the initial conditions has a broad Fourier spectrum. The conclusion is that Rossby waves will amplify with time only when the mean flow has an inflection point or when the initial eddy field is strongly concentrated in long waves tilted against the shear.     

Vortex Rossby waves on smooth circular vortices: Part I. Theory

A complete theory of the linear initial-value problem for Rossby waves on a class of smooth circular vortices in both f-plane and polar-region geometries is presented in the limit of small and large Rossby deformation radius. Although restricted to the interior region of barotropically stable circular vortices possessing a single extrema in tangential wind, the theory covers all azimuthal wavenumbers. The non-dimensional evolution equation for perturbation potential vorticity is shown to depend on only one parameter, G, involving the azimuthal wavenumber, the basic state radial potential vorticity gradient, the interior deformation radius, and the interior Rossby number.In Hankel transform space the problem admits a Schrödinger’s equation formulation which permits a qualitative and quantitative discussion of the interaction between vortex Rossby wave disturbances and the mean vortex. New conservation laws are developed which give exact time-evolving bounds for disturbance kinetic energy. Using results from the theory of Lie groups a nontrivial separation of variables can be achieved to obtain an exact solution for asymmetric balanced disturbances covering a wide range of geophysical vortex applications including tropical cyclone, polar vortex, and cyclone/anticyclone interiors in barotropic dynamics. The expansion for square summable potential vorticity comprises a discrete basis of radially propagating sheared vortex Rossby wave packets with nontrivial transient behavior. The solution representation is new, and for this class of swirling flows gives deeper physical insight into the dynamics of perturbed vortex interiors than the more traditional approach of Laplace transform or continuous-spectrum normal-mode representations. In general, initial disturbances are shown to excite two regions of wave activity. At the extrema of these barotropically stable vortices and for a certain range of wavenumbers, the Rossby wave dynamics are shown to become nonlinear for all initial conditions. Extensions of the theory are proposed.     

大地形对切变基流上罗斯贝波稳定性的影响

利用WKB近似讨论大地形对切变基流上Rossby波稳定性的影响.北半球东西走向地形有利导式长波槽辐合能量于地形北坡附近,对曳式长波槽有使能量从地形南坡区域辐散的趋势.南半球地形的影响正好相反.散度顶有利于导式长波槽在东西风带过渡区域的能量辐射,有利于曳式长波槽能量在这里辐合.     

Refraction of Rossby waves on a multiple β-plane

A multiple β-plane is introduced to explore the relation between plane and spherical Rossby waves. The fundamental problem, the refraction of a plane Rossby wave across a discontinuity in β, is solved. It is shown that refraction on the multiple β-plane agrees in the limit with refraction on the full sphere only if a suitable correction is made for the geometric distortion of the β-plane. The full spherical modes of Rossby waves trapped in a band about the equator (Longuet-Higgins, 1964) have their counterpart in a simple model consisting of an “equatorial” β-plane bounded above and below by “polar” β-planes.     

Activities of low-frequency waves in the tropical atmosphere and enso

ENSO, particularly the occurrence of ENSO is still an important research object in climatic variation. Using the ECMWF data, the relationship between ENSO and the activities of low-frequency waves in the tropical atmosphere is analyzed in this paper. It is shown that the occurrence of ENSO is closely related to the intraseasonal oscillation and the quasi-stationary waves (the period > 90 days) in the tropical atmosphere. Associated with the occurrence of El Nino event, the kinetic energy of low-frequency waves has obvious variation: the kinetic energy of atmospheric intraseasonal (30–60 days) oscillation (ISO) decreases abruptly and the kinetic energy of quasi-stationary waves increases abruptly. Moreover, the ISO and quasi-stationary waves propagate eastward clearly corresponding to El Nino; but they clearly propagate westward in La Nina cases.