Large Scale Perturbations in Extratropical Atmosphere-Part Ⅰ: On Rossby Waves

This study reexamines the propagation mechanism and geostrophic property of the classical two-dimensional Rossby waves in a non-divergent barotropic atmosphere. It will be found that propagation of large scale atmospheric waves depends crucially on horizontal divergence. A small Rossby number in Rossby waves is not sufficient for the waves to have a small ageostrophic component, because the two-dimensional classical Rossby waves do not manifest the geostrophic balance as good as observed in the atmosphere.     

A NUMERICAL METHOD FOR SOLVING THE EVOLUTION EQUATION OF SOLITARY ROSSBY WAVES ON A WEAK SHEAR

In this paper an evoluion equation in integral-differential form for finite amplitude Rossby waves on a weak shear is presented and an efficient method for its numerical solution is set up. It is shown that a propagation of solitary wave is possible whenever a proper weak shear in basic flows acts with the nonlinear effects and dispersion of the media, both in the atmosphere and in the ocean. To test the numerical method for solving the evolution equation, a series of experiments are carried out. The results indicate that the solitary solutions, do exist and interact with each other in quite a succinct, manner. Therefore the method is successful and efficient for solving initial value problems of the above equation. The time decoupling problem arising in the numerical scheme and the related filtering technique are discussed. A variety of interesting phenomena such as the interaction of solitary Rossby waves, damping, dispersion and the development of nonlinear wave train are numerically studied.     

CISK-related Rossby Waves in the Tropical Atmosphere

In terms of a baroclinic quasi-geostrophic wave-filtering technique in connection with a dimensionless paramet-er, η(z), of condensation-released latent heat that indicates the CISK mechanism, a model is established for des-cribing tropical atmosphere CISK-Rossby waves alongside its analytical solution. Theoretical study shows that there exists pronounced difference between Rossby waves, CISK-involving and classic, and the former can be used to in-terpret some aspects of the low-frequency oscillation in the tropical atmosphere     

A Simple Quasi-Geostrophic Coupled Ocean-Atmosphere Model

The quasi-geostrophic atmospheric and oceanic equations of momentum and thermodynamics with dissipation factors are used to create a simple coupled ocean-atmosphere model describing the large-scale shallow-water motion. We discuss the ocean-atmosphere coupling effect in mid-high and low latitudes separately and analyze characteristics of which the oscillatory periods of coupled low-frequency modes (ocean mode) vary with the coupling frequency and latitudinal number. This can interpret the correlation between low-frequency oscillation and ocean-atmosphere interaction. Then from the dispersion curves of atmosphere and ocean, we reveal effect of the coupling strength on the propagation of Rossby waves. The convection mechanism between the two modes is also discussed in view of the slowly varying wave train.The results show that Newtonian cooling and Rayleigh friction play a stable rule in oceanic Rossby waves, the period of coupled low-frequency mode grows with the increment of the coupling frequency. The     

Planetary Stationary Waves in the Atmosphere Part I: Orographic Stationary Waves

It is proposed that the orographic stationary waves are required by long-term balance of momentum in the atmosphere with zonally asymmetric orographic forcing. This hypothesis may be confirmed successfully with the theoretical model of geostrophic waves. In the Part I, we will explain the observed phase distributions of orographic stationary waves at middle and high latitudes of the Northern Hemisphere, according to the long-term balance of zonal momentum over the stationary orographic forcing. It is revealed that the geographic distribution of stationary waves depends not only on local topgraphy but also on mean circulation fields and angular momentum flux in the atmosphere. So these waves cannot be simulated by the models in a restricted area.     

EQUATORIAL SOLITARY WAVES OF TROPICAL ATMOSPHERIC MOTION IN SHEAR FLOW

Starting from the primary equations, the author derives the KdV equation which describes solitary Rossby waves in the tropical atmosphere, and indicates that, because these waves are ageostrophic, they differ from the quasigeostrophic solitary Rossby waves studied by Redekopp et al. Owing to nonlinear action, these waves are also different from traditional linear waves of the tropical atmosphere. The author believes that the stationary tropical atmospheric waves reflect the characteristics of solitary waves in that the energy does not disperse.     

The Phenomena of Bifurcation and Catastrophe of Large-Scale Horizontal Motion in the Atmosphere under the Effect of Rossby Parameter

The stability question of large-scale horizontal motion in the atmosphere under the effect of Rossby parameter is discussed in this paper by using the qualitative analysis theory of ordinary differential equations. The following aspects are reviewed: The stability of large-scale horizontal motion in the atmosphere accords with the common inertial stability criterion when the effect of Rossby parameter is not considered (Yang, 1983), and that, on the other hand, the motion will bifurcate two times with the variation of absolute vorticity of basic Zephyr flow at the initial position under the effect of Rossby parameter. Furthermore, in the inertial stable region, if the effect of geostrophic deviation at the initial position is considered, the motion will not only bifurcate but also generate a catastrophe.     

NONLINEAR SCHRÖDINGER EQUATION IN THE ROTATIONAL BAROTROPIC ATMOSPHERE AND ATMOSPHERIC BLOCKING

In this paper,the WKB method is used to obtain the nonlinear Schrödinger equation satisfied by nonlinear Rossby wave in the rotational barotropic atmosphere.It is found that the nonlinear Schrödinger equation has an envelope solitary wave solution under the condition 1≤m≤2(m the zonal wavenumber),and the phase speed of envelope solitary Rossby wave in the atmosphere is related to the square of its amplitude linearly,that is,the larger the amplitude of envelope solitary Rossby wave,the smaller its propagation speed.Farthermore,the blocking high and cut-off low pressures which are consistent with the observations of blocking in the atmosphere are obtained by calculating envelope solitary Rossby wave,and the blocking structures persist more than five days,the results demonstrate that the envelope solitary Rossby wave is a possible mechanism about the formation,maintenance and breakout of blocking in the atmosphere.     

Unstable Tropical Air-Sea Interaction Waves and Their Physical Mechanisms

In this paper, the tropical air-sea interaction is discussed by using a simple air-sea coupled model, in which the inertia-gravity waves are filtered off and only the equatorial Rossby waves are reserved in both the atmosphere and the ocean. There exist two kinds of air-sea interaction waves in the coupled model, that is, the high-frequency fast waves and the low-frequency slow waves. The phase speed of the fast waves is westward and the frequencies are close to those of the equatorial Rossby waves in the atmosphere. The slow waves propagate westward in the part of short wavelengths and eastward in that of long wavelengths. There exist instabilities for both the westward and eastward propagating slow waves. If the fast waves are filtered off, there is little effect on the slow waves which have great influence on the long range process in the tropical air-sea coupled system. According to the tropical air-sea interaction waves we obtain here, a possible explanation to the propagating process of ENSO event     

The Propagation of Inertia-Gravity Waves and Their Influence on Mean Zonal Flow, Part One: the Propagation of Inertia-Gravity Waves

Inertia-gravity waves play an increasingly important role in the middle atmosphere dynamics. As a result, more attention has been paid to the study of inertia-gravity waves, especially to the middle atmosphere gravity waves. This paper presents some aspects of inertia-gravity waves with emphasis on the propagation. Two methods are used here, namely, geometric optical method and physical optical method. We can see from the study that inertia-gravity waves are similar to planetary waves in some respects and they are different from planetary waves in others.     

PROPAGATION OF INTERNAL INERTIO-GRAVITY WAVE SPECTRA IN VERTICAL WIND SHEAR ENVIRONMENTS*

The variation of the spectral structure of the internal inertio-gravity waves (ⅡGWs) propagating in the atmospheric wind shear environments is discussed in this paper.From the hydrodynamic equation set in Boussinesq approximation,a spectral propagation equation ⅡGWs satisfy is derived,then the spectral correspondence in the upper atmosphere is numerically calculated,after a forced spectrum is given as a Van-Zandt one at the lower boundary.The results show that if ⅡGWs do not encounter the critical-layer absorption,then their spectral structure may be not changed significantly; otherwise it may be changed greatly,and a few of spectral components are filtered.Also the isotropy of the assumed VanZandt spectrum is distorted in upward-propagating process.That is the directional filtering effect of the atmospheric wind on the gravity wave spectrum.     

Theories on Formation of an Anomalous Anticyclone in Western North Pacific during El Ni?o: A Review

The western North Pacific anomalous anticyclone(WNPAC) is an important atmospheric circulation system that conveys El Ni?o impact on East Asian climate. In this review paper, various theories on the formation and maintenance of the WNPAC, including warm pool atmosphere–ocean interaction, Indian Ocean capacitor, a combination mode that emphasizes nonlinear interaction between ENSO and annual cycle, moist enthalpy advection/Rossby wave modulation, and central Pacific SST forcing, are discussed. It is concluded that local atmosphere–ocean interaction and moist enthalpy advection/Rossby wave modulation mechanisms are essential for the initial development and maintenance of the WNPAC during El Ni?o mature winter and subsequent spring. The Indian Ocean capacitor mechanism does not contribute to the earlier development but helps maintain the WNPAC in El Ni?o decaying summer.The cold SST anomaly in the western North Pacific, although damped in the summer, also plays a role. An interbasin atmosphere–ocean interaction across the Indo-Pacific warm pool emerges as a new mechanism in summer. In addition, the central Pacific cold SST anomaly may induce the WNPAC during rapid El Ni?o decaying/La Ni?a developing or La Ni?a persisting summer. The near-annual periods predicted by the combination mode theory are hardly detected from observations and thus do not contribute to the formation of the WNPAC. The tropical Atlantic may have a capacitor effect similar to the tropical Indian Ocean.     

FURTHER STUDIES ON EVAPORATION-WIND FEEDBACK

The results from simple dynamic studies on the evaporation-wind feedback show that the effect cannot change the nature of tropical atmospheric waves (by retarding the speed), so that the evaporation-wind feedback alone cannot be an exciting mechanism of intraseasonal oscillation in the tropical atmosphere. This is different from that of the wave-CISK mechanism. With combined effect of the cumulus convection heating and evaporation-wind feedback, the CISK-Kelvin waves and CISK-Rossby waves will develop unstably, explaining the dynamic mechanism of tropical intraseasonal oscillation in a more complete and reasonable way than the convection heating alone. Therefore, the evaporation-wind feedback is also important to the intraseasonal oscillation in the tropical atmosphere.     

Some Effects of Rotation Rate on Planetary-Scale Wave Flows

A series of experiments were performed in a rotating annulus of fluid to study effects of rotation rate on planeta-ry-scale baroclinic wave flows. The experiments reveal that change in rotation rate of fluid container causes variation in Rossby number and Taylor number in flows and leads to change in flow patterns and in phase and amplitude of quasi-stationary waves. For instance, with increasing rotation rate, amplitude of quasi-stationary waves increases and phase shifts upstream. On the contrary, with decreasing rotation rate, amplitude of quasi-stationary waves decreases and phase shifts downstream. In the case of the earth’s atmosphere, although magnitude of variation in earth’s rotation rate is very small, yet it causes a very big change in zonal velocity component of wind in the atmosphere and of currents in the ocean, and therefore causes a remarkable change in Rossby number and Taylor number deter-mining regimes in planetary-scale geophysical flows. The observation reveals that intensity and geographic location of subtropic anticyclones in both of the Northern and Southern Hemispheres change consistently with the variation in earth’s rotation rale. The results of fluid experiments are consistent, qualitatively, with observed phenomena in the atmospheric circulation.     

NONLINEAR WAVES IN BAROTROPIC MODEL

In this paper, from the system of equation describing a barotropic atmosphere using the method of Taylor expansion for the nonlinear terms, the periodic solutions of the nonlinear inertio-surface gravity waves and Rossby waves have been obtained.The finite-amplitude nonlinear inertio-surface gravity waves and Rossby waves with horizontal divergence satisfy all the KdV equation. The solutions are all the cnoidal function, i, e., the cnoidal waves which include the linear waves and form the solitary waves under certain conditions. For the finite-amplitude Rossby waves with horizontal divergence, we find the new dispersive relation including both the wave number and the amplitude parameter. In case of small amplitude it is reduced to the Yeh formula. It is shown that the larger the amplitude and width, the faster the finite-amplitude inertio-surface gravity waves and the slower the finite-amplitude Rossby waves with horizontal divergence propagate. The blocking or cut-off system in which the amplitude and width are large may be considered as Rossby solitary waves.     

THE EFFECTS OF THE PLATEAU'S TOPOGRAPHIC GRADIENT ON ROSSBY WAVES AND ITS NUMERICAL SIMULATION

By using barotropic model equations, this article analyzed the characteristics of Rossby waves, the propagation features of wave energy and the influence of dynamic and thermal effects of the Tibetan Plateau on Rossby waves, and the focus is on discussing the plateau's topographic gradient effects on atmospheric Rossby waves. Then based on the WRF3.2 and the NCEP/NCAR FNL reanalysis data, we devised comparative tests of changing the plateau's topographic gradient and simulated a process of persistent heavy rain that happened in May 2010 in South China. The results are shown as follows. The Tibetan Plateau’s topography is conducive to the formation of atmospheric Rossby waves. while the plateau's terrain, its friction and heating effects can all make the atmospheric Rossby waves develop into the planetary waves; The effects of plateau's north and south slopes on the Rossby wave’ phase velocity is opposite, and when the slope reached a certain value can the quasi-steady normal fluctuations be generated; Simultaneously, due to the plateau's topographic gradient, descending motion appears at the west side of the plateau while ascending motion appears at the east side, and the vertical movement increased with the amplification of topographic gradients. The plateau's topographic gradient also obviously amplified the precipitation in South China, and the rainfall area increased with the amplification of topographic gradients and gradually moved from south to north and from west to east, which is conducive to the occurrence and development of convective activities in the downstream areas of the Tibetan Plateau; Moreover, for the plateau’s dynamic and thermal effects, the Rossby wave’ propagation shows upstream effects of energy dispersion, so the plateau can then affect the weather in downstream areas. Moreover, the wave group velocity increased with the degree of topographic slope.     

Planetary Stationary Waves in the Atmosphere Part II: Thermal Stationary Waves

The contribution of thermal forcing to the planetary stationary waves will be studied also by assuming that heat balance in stationary waves over zonally asymmetric thermal forcing must be maintained over a long time period. Using the same model of geostrophic waves introduced in Part I, we may explain successfully the observed and simulated responses to the thermal forcing in the atmosphere, such as the wave 1 structure at high levels of middle latitudes, the seasonal changes of the stationary waves in the Northern Hemisphere, the opposite phase distributions of stationary waves at high and low levels of the subtropical regions in both hemispheres and so on.     

The Relationship Between Abnormal Meiyu and Medium-Term Scale Wave Perturbation Energy Propagation Along the East Asian Subtropical Westerly Jet

The East Asian subtropical westerly jet(EASWJ) is one of the most important factors modulating the Meiyu rainfall in the Yangtze-Huaihe River Basin, China. This article analyzed periods of the medium-term EASWJ variation,wave packet distribution and energy propagation of Rossby waves along the EASWJ during Meiyu season, and investigated their possible influence on abnormal Meiyu rain. The results showed that during the medium-term scale atmospheric dynamic process, the evolution of the EASWJ in Meiyu season was mainly characterized by the changes of3-8 d synoptic-scale and 10-15 d low-frequency Rossby waves. The strong perturbation wave packet and energy propagation of the 3-8 d synoptic-scale and 10-15 d low-frequency Rossby waves are mostly concentrated in the East Asian region of 90°-150°E, where the two wave trains of perturbation wave packets and wave-activity flux divergence coexist in zonal and meridional directions, and converge on the EASWJ. Besides, the wave trains of perturbation wave packet and wave-activity flux divergence in wet Meiyu years are more systematically westward than those in dry Meiyu years, and they are shown in the inverse phases between each other. In wet(dry) Meiyu year, the perturbation wave packet high-value area of the 10-15 d low-frequency variability is located between the Aral Sea and the Lake Balkhash(in the northeastern part of China), while over eastern China the wave-activity flux is convergent and strong(divergent and weak), and the high-level jets are strong and southward(weak and northward). Because of the coupling of high and low level atmosphere and high-level strong(weak) divergence on the south side of the jet over the Yangtze-Huaihe River Basin, the low-level southwest wind and vertically ascending motion are strengthened(weakened), which is(is not)conducive to precipitation increase in the Yangtze-Huaihe River Basin. These findings would help to better understand the impact mechanisms of the EASWJ activities on abnormal Meiyu from the perspective of medium-term scale Rossby wave energy propagation.     

THE SEMI-GEOSTROPHIC ADAPTATION PROCESS WITH TWO-LAYER BAROCLINIC MODEL IN LOW LATITUDE ATMOSPHERE

In this paper, the adaptation process in low latitude atmosphere is discussed by means of a two-layer baroclinic model on the equator β plane, showing that the adaptation process in low latitude is mainly dominated by the internal inertial gravity waves. The initial ageostrophic energy is dispersed by the internal inertial gravity waves, and as a result, the geostrophic motion is obtained in zonal direction while the ageostro-phic motion maintains in meridional direction, which can be called semi-geostrophic balance in barotropic model as well as semi-thermal-wind balance in baroclinic model. The vertical motion is determined both by the distribution of the initial vertical motion and that of the initial vertical motion tendency, but it is unrelated to the initial potential vorticity. Finally, the motion tends to be horizontal. The discussion of the physical mechanism of the semi-thermal-wind balance in low latitude atmosphere shows that the achievement of the semi-thermal-wind balance is due to the adjustment between the stream field and the temperature field through the horizontal convergence and divergence which is related to the vertical motion excited by the internal inertial gravity waves. The terminal adaptation state obtained shows that the adaptation direction between the mean temperature field and the shear flow field is determined by the ratio of the scale of the initial ageostrophic disturbance to the scale of one character scale related to the baroclinic Rossby radius of deformation. The shear stream field adapts to the mean temperature field when the ratio is greater than 1, and the mean temperature field adapts to the shear stream field when the ratio is smaller than 1.     

SOME CATASTROPHE PROPERTIES OF TWO-LAYER SHEAR FLOW

In this paper a simple current system which consists of two stratified incompressible layers is examined. For the basic equations of the motion of fluid a lower order spectrum model is established by means of Galerkin method. Adopting the difference of wind velocity between the upper and lower layers, As =as a control parameter, the bifurcation and stability of the solution of the dynamical systemare discussed. It is found that the flow states in the lower layer will have a catastrophe, when where Cg is the phase velocity of the internal inertio-gravitational wave in a geostrophic current.These results may give a reasonable explanation for the mechanism of the catastrophe phenomena, including the "pressure-jump" in the atmosphere.