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.

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.

DECAY ESTIMATES OF PLANAR STATIONARY WAVES FOR DAMED WAVE EQUATIONS WITH NONLINEAR CONVECTION IN MULTI-DIMENSIONAL HALF SPACE

This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space R n ＋ ： u tt u ＋ u t ＋ divf （u） = 0, t 〉 0, x = （x 1 , x ′ ） ∈ R n ＋ ：= R ＋ × R n 1 , u（0, x） = u 0 （x） → u ＋ , as x 1 → ＋ ∞ , u t （0, x） = u 1 （x）, u（t, 0, x ′ ） = u b , x ′ = （x 2 , x 3 , ··· , x n ） ∈ R n 1 . （I） For the non-degenerate case f ′ 1 （u ＋ ） 〈 0, it was shown in [10] that the above initialboundary value problem （I） admits a unique global solution u（t, x） which converges to the corresponding planar stationary wave φ（x 1 ） uniformly in x 1 ∈ R ＋ as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. And in [10] Ueda, Nakamura, and Kawashima proved the algebraic decay estimates of the tangential derivatives of the solution u（t, x） for t → ＋ ∞ by using the space-time weighted energy method initiated by Kawashima and Matsumura [5] and improved by Nishihkawa [7]. Moreover, by using the same weighted energy method, an additional algebraic convergence rate in the normal direction was obtained by assuming that the initial perturbation decays algebraically. We note, however, that the analysis in [10] relies heavily on the assumption that f ′ （u） 〈 0. The main purpose of this paper isdevoted to discussing the case of f ′ 1 （u b ） ≥ 0 and we show that similar results still hold for such a case. Our analysis is based on some delicate energy estimates.

ANALYSES OF THE DYNAMIC EFFECTS ON WINTER CIRCULATION OF THE TWO MAIN MOUNTAINS IN THE NORTHERN HEMISPHERE——Ⅰ.RELATIONSHIP AMONG GENERAL CIRCULATION,TELECONNECTION AND STATIONARY WAVES

The distribution of troughs and ridges of geopotential height,the teleconnection patterns and the propagation pat- terns of stationary waves are the main features of the January mean geopotential height field at 500hPa.Data analyses and numerical experiments indicate that these three characteristics are associated to one another and closely related to the mechanical forcing of the Rocky Mountains and Tibetan Plateau.There exists a prominent negative correlation in the intensity variation between the American trough and the Asian trough at high and middle latitudes.Such negative correlation,in connection with the interannual variation of the intensity of the jets in front of the two troughs,leads to the existence of similar teleconnection patterns in North America and East Asia.On the other hand,the different propa- gation behaviour of quasi-stationary waves downstream of the two main mountains results in a fundamental difference in the distribution of correlation chains in North America and East Asia.

THE FORCING OF ANOMALOUS DIVERGENT WIND AND TRANSIENT VORTICITY FLUXES TO THE ANOMALY OF STATIONARY WAVES

The forcing of anomalous divergent wind and transient vorticity fluxes to the anomaly of stationary waves of DJF (December—January—February) 1982/1983 is studied.The results show that the anomaly of the transient vorticity flux convergence tends to cancel or dissipate the anomaly of the vorticity sources generated by divergent wind.The stationary wave anomalies are maintained by both of these forcings.It is also found that,for the DJF 1982/1983 case,both of the vorticity source anomaly over the tropical and equatorial eastern Pacific and that over the midlatitude North Pacific are important to maintain the atmospheric circulation anomaly over the Pacific/North America region.

SPATIAL AND TEMPORAL VARIATIONS OF THE KINEMATIC CHARACTERISTICS IN THE PROPAGATION OF ATMOSPHERIC STATIONARY WAVES

Time-mean global general circulation data are employed to analyze the temporal and spatial variations of the meridional gradient of zonal mean potential vorticity,the critical wavenumber n_s for horizontal wave- propagation,and the critical wavenumber K_c for vertical wave-propagation.Thereby the kinematic charac- teristics in the propagation of atmospheric stationary waves and their annual variations are studied.Results show that in the troposphere n_s and K_c usually decrease with the increase of either latitude or altitude. Synoptic and near-resonant Rossby waves could be trapped during their upward and meridional propagations. These characteristics possess prominent annual variations,especially in the Northern Hemisphere.It is found that the spatial and temporal variations of these kinematic characteristics are in good agreement with those of the atmospheric wave patterns.

THE ROLE OF THE MERIDIONAL CIRCULATION IN STATIONARY WAVE PROPAGATION

In a general baroclinic atmosphere,when the basic state includes meridional circulation,the sta- tionary waves might not only pass through the equatorial easterlies,but also strengthen significantly. The orographic forcing in the Northern Hemisphere mid-latitude might cause marked responses in the low latitude atmosphere.This suggests that the meridional circulation plays an important role in the connection of stationary responses in mid and low latitudes,and so does the heating forcing in the Northern Hemisphere mid-latitude.Forced by the heating forcing in the Northern Hemisphere mid- latitude,the features similar to the Northern Hemisphere summer monsoon circulation can be ob- tained.It appears that the meridional circulation plays certain role in the formation of summer mon- soon circulation.The heating anomaly forcing located at the eastern equatorial Pacific makes the sta- tionary waves present PNA(Pacific-North America)pattern in the winter hemisphere,but it does not in the summer hemisphere.It suggests that the meridional circulation has a marked influence on the route of stationary wave propagation both in the winter and summer hemispheres.

The Structure and Propagation of Stationary Planetary Wave Packet in the Barotropic Atmosphere

Monthly or seasonally mean anomalies of large-scale atmospheric circulation are better represented by wave packets or their combination. Both qualitative and quantitative analyses of equations of wave packet dynamics, which are obtained by the use of WKB approximation, are very helpful for the understanding of structure, formation and propagation of stationary and quasi-stationary planetary wave packet patterns in the atmosphere. Indeed, these equations of wave packet dynamics can be directly solved by the method of characteristic lines, and the results can be simply and clearly interpreted by physical laws. In this paper, a quasi-geostrophic barotropic model is taken for simplicity, and the wave packets superimposed on several ideal profiles of the basic current and excited by some ideal forcings are investigated in order to make comparison of the accuracy of calculation with the analytical solution. It is revealed that (a) the rays of stationary planetary wave packet do not coincide with but go away from the great circle with significant difference if the shear of the basic zonal flow is not too small; (b) being superimposed on a westerly jet flow with positive shear (Uλ/y>0), the stationary wave packets excited by low-latitudinal forcing are first intensified during their northeastward propagation in the Northern Hemisphere, then reach their maximum of amplitude at some critical latitude, and after that weaken again; (c) the connected line of extremes (the positive and negative centres) of wave packet does not coincide with but crosses the ray by an angle, the larger the scale of external forcing, the larger the angle; and (d) the whole pattern of a trapped stationary wave packet is complicated by the interference between the incident and reflected waves.

The East Pacific Wavetrain:Its Variability and Impact on the Atmospheric Circulation in the Boreal Winter

The East Pacific wavetrain （EPW） refers to here the intense stationary wave activity detected in the troposphere over the East Pacific and North America in 45 northern winters from 1958 to 2002. The EPW is generated in the lower troposphere over the East Pacific, propagating predominantly eastward into North America and slightly upward then eventually into the stratosphere. The intensity of the EPW varies from year to year and exhibits apparent decadal variability. For the period 1958-1964, the EPW was in its second maximum, and it was weakest for the period 1965-1975, then it was strongest for the period 1976-1987. After 1987, the EPW weakened again. The intensity and position of the members （i.e., the Aleutian low, the North American trough, and the North American ridge） of the EPW oscillate from time to time. For an active EPW versus a weak EPW, the Aleutian low deepens abnormally and shifts its center from the west to the east of the date line, in the middle and upper troposphere the East Asian trough extends eastward, and the Canadian ridge intensifies at the same time. The opposite is true for a weak EPW. Even in the lower stratosphere, significant changes in the stationary wave pattern are also observed. Interestingly the spatial variability of the EPW assumes a Pacific-North American （PNA）-like telecon- nection pattern. It is likely that the PNA low-frequency oscillation is a reflection of the oscillations of intensity and position of the members of the EPW in horizontal direction.

Interannual Variability of the Winter Stratospheric Polar Vortex in the Northern Hemisphere and Their Relations to QBO and ENSO

We investigated the interannual variations of the winter stratospheric polar vortex in this paper. EOF analysis shows that two modes of variability dominate the stratospheric polar vortex on interannual timescales The leading mode （EOF1） reflects the intensity variation of the polar vortex and is characterized by a geopotential height seesaw between the polar region and the mid-latitudes. The second one （EOF2） exhibits variation in the zonal asymmetric part of the polar vortex, which mainly describes the stationary planetary wave activity. As the strongest interannual variation signal in the atmosphere, the QBO has been shown to influence mainly the strength of the polar vortex. On the other hand, the ENSO cycle, as the strongest interannual variation signal in the ocean, has been shown to be mainly associated with the variation of stationary planetary wave activity in the stratosphere. Possible influences of the stratospheric polar vortex on the tropospheric circulation are also discussed in this paper.

A Comparison of Polar Vortex Response to Pacific and Indian Ocean Warming

During recent decades, the tropical Indo-Pacific Ocean has become increasingly warmer. Meanwhile, both the northern and southern hemispheric polar vortices （NPV and SPV） have exhibited a deepening trend in boreal winter. Although previous studies have revealed that the tropical Indian Ocean warming （IOW） favors an intensifying NPV and a weakening SPV, how the tropical Pacific Ocean warming （POW） influences the NPV and SPV remains unclear. In this study, a comparative analysis has been conducted through ensemble atmospheric general circulation model （AGCM） experiments. The results show that, for the Northern Hemisphere, the two warmings exerted opposite impacts in boreal winter, in that the IOW intensified the NPV while the POW weakened the NPV. For the Southern Hemisphere, both the IOW and POW warmed the southern polar atmosphere and weakened the SPV. A diagnostic analysis based on the vorticity budget revealed that such an interhemispheric difference in influences from the IOW and POW in boreal winter was associated with different roles of transient eddy momentum flux convergence between the hemispheres. Furthermore, this difference may have been linked to different strengths of stationary wave activity between the hemispheres in boreal winter.

The Characteristics of the Shear-Vibrating Quartz Crystal Resonator

<正>According to the piezoelectric equation and the vibration theory of the quartz crystal,the relations between the vibrating frequency and structural parameters under the thickness-shear-vibration of AT-cut quartz crystal have been studied. The frequency conditions under which quartz crystal resonator formed stationary wave inside the electrode district and the transmission characteristics of wave outside the electrode district have also been discussed.A quartz crystal resonator was developed based on this analysis.The experiment showed that the force-sensing characteristics were independent of the fixation of the crystal edge.The detecting distinguish ability was up to 0.001°,and the short-term frequency stability was up to 1.38×10~ (-10)/min.

On the Blocking Flow Patterns in the Euro–Atlantic Sector:A Simple Model Study

The flow patterns of Euro-Atlantic blocking events in winter are investigated by dividing the sector into three sub- regions： 60°-30°W （Greenland region）; 20°W-30°E [eastern Atlantic-Europe （EAE） region]; and 50°-90°E （Ural region）. It is shown that blocking events in winter are extremely frequent in the three sub-regions. Composite 500-mb geopotential height fields for intense and long-lived blocking events demonstrate that the blocking fields over Greenland and Ural regions exhibit southwest-northeast （SW-NE） and southeast-northwest （SE-NW） oriented dipole-type patterns, respectively, while the composite field over the EAE region exhibits an Ω-type pattern. The type of composite blocking pattern seems to be related to the position of the blocking region relative to the positive center of the climatological stationary wave （CSW） anomaly existing near 10°W. The physical cause of why there are different composite blocking types in the three sub-regions is identified using a nonlinear multiscale interaction model. It is found that when the blocking event is in almost the same position as the positive CSW anomaly, the planetary-scale field can exhibit an Ω-type pattern due to the enhanced positive CSW anomaly. Neverthe- less, a SW-NE （SE-NW） oriented dipole-type block can occur due to the reduced positive CSW anomaly as it is farther in the west （east） of the positive CSW anomaly. The total fields of blocking in the three regions may exhibit a meandering flow comprised of several isolated anticyclonic and cyclonic vortices, which resembles the Berggren-Bolin-Rossby meandering jet type.

Analysis of Stationary-Wave Nonstationarity in the Northern Hemisphere 500-hPa Height Field

In this paper,the concept of stationary-wave nonstationarity is presented and elucidated in the framework of the Lorenz circulation decomposition.This concept indicates the relative magnitude of the zonal nonuniform abnormity to the intensity of stationary waves on the monthly mean scale.Based on the Lorenz circulation decomposition,the nonstationarity degree I_（us）（I_（us）~1） of the global（local） stationary waves is defined,and then used to analyze the stationary-wave nonstationarity at 30°-60°N,where the intensity of stationary waves at 500 hPa in the Northern Hemisphere,as is well known,is very high.The following findings are obtained：（1） There exist seasonal southward and northward movements in the position of the nonstationarity zones of the global stationary waves.The steady stationary waves occur in midlatitudes （35°-55°N） in winter and in the subtropical region（south of 35°N） in summer,associated with the major troughs over East Asia and North America and the weak European trough in winter,and with the relatively steady subtropical high system in summer.A high value center of I_（us） is at 35°N in spring and 50°N in summer,which might be caused by the seasonal variation of stationary-wave intensity,particularly in association with the interannual variability of trough/ridge positions of stationary waves on the monthly mean maps.（2） There exists obvious asymmetry in I_（us）~1,with the steady zones always located in the areas controlled by strong troughs/ridges and the unsteady ones in the areas where the stationary-wave intensity is low.The I_（us）~1 in the subtropics（south of 35°N） is larger in winter than in summer,and vice versa in the midlatitude region（north of 35°N）.The summertime distribution of I_（us）~1 on the whole shows a rather complicated structure.However,North Europe is the most unsteady area for local stationary waves,as represented by high values of I_（us）~1 in both summer and winter,while over the North American continent （about 120°E-60°W）,the I_（us）~1 is slightly less than 1 in summer,indicating that the stationary waves in this region are more steady than those over other mid and high latitude regions.（3） From North China to Northwest Pacific,there is a high value zone of I_（us）~1 in summer,with its center（45°N,130°E） located in the east of Heilongjiang Province.This influences the summer climate of northern China,including Northeast, North,and Northwest China.It is obvious that the nonstationarity is an intrinsic attribute of stationary waves,and can be regarded as being of the same importance as the intensity and energy-spectrum structure of stationary waves in the studies of the general circulation system.

冯诺依曼代数中的广义波算子

Let M⊆B(H)be a countable decomposable properly infinite von Neumann algebra with a faithful normal semifinite tracial weightτwhere B(H)is the set of all bounded linear operators on Hilbert space H.The main purpose of this article is to introduce generalized weak wave operators Wf_(±),generalized weak abelian wave operators ■ and generalized stationary wave operators U_(±) in M and then to explore the relation among W_(±),■,U_(±) and generalized wave operators W_(±).

INFLUENCE OF THE BASIC FLOW IN THE TROPICS ON THE STATIONARY PLANETARY WAVES AT MIDDLE AND HIGH LATITUDES DURING THE NORTHERN HEMISPHERE WINTER

The relationship between the quasi-stationary planetary waves forced by topography and heat source during the Northern Hemisphere winter is investigated by means of a quasi-geostrophic,34-level,spherical coordinate model with the Rayleigh friction,the Newtonian cooling and the horizontal eddy thermal diffu- sion. The calculated results show that when the basic flow is the westerly in the tropical stratosphere,the amplitude of quasi-stationary planetary wave for zonal wavenumber 2 at middle and high latitudes is larger during the Northern Hemispheric winter;while when the basic flow is the easterly,it is smaller.This is in agreement with the observed results. The calculated results also show that influence of the basic flow in the tropical troposphere on the quasi- stationary planetary waves is larger than that of the basic flow in the tropical stratosphere on the quasi- stationary planetary waves.

Stationary phase and practical numerical evaluation of ship waves in shallow water

A simple and highly-efficient method for numerically evaluating the waves created by a ship that travels at a constant speed in calm water, of large depth or of uniform depth, is given. The method, inspired by Kelvin＇s classical stationary-phase analysis, is suited for evaluating far-field as well as near-field waves. More generally, the method can be applied to a broad class of integrals with integrands that contain a rapidly oscillatory trigonometric function with a phase function whose first derivative（and possibly also higher derivatives） vanishes at one or several points, commonly called points of stationary phase, with the range of integration.

The East Asian Upper-Tropospheric Jet Streams and Associated Transient Eddy Activities Simulated by a Climate System Model BCC_CSM1.1

In this paper, major features of the upper-tropospheric jet streams simulated by a coupled Climate System Model BCC_ CSMI.1 are evaluated through comparison with the NCEP/NCAR reanalysis. The jet streams consist of the East Asian subtropical jet （EASJ） and the East Asian polar-front jet （EAPJ）. Associated stationary wave and synoptic-scale transient eddy activities （STEA） are also examined. The results show that the climatological positions of the westerly jet streams are well captured by BCC_CSMI.1, but with slight intensity biases. Statistics from the 6-h model outputs reveal that the jet core number （JCN） of ESPJ is significantly underestimated. Examination of the simulated seasonal evolution of the westerly jet stream indicates that the model has produced a westward movement of the EASJ core in May, one month earlier than that in the reanalysis. Analysis of stationary wave activities shows that the overestimated meridional wind component may have caused considerable enhancement of meridional momentum and heat transport. The stationary Rossby wave represented by the wave activity flux at the southern flank of the Tibetan Plateau is favorable to the growth of asymmetric zonal wind and the multiple-center pattern of JCN. Unlike the stationary wave heat flux transport, the model tends to systematically generate weaker transient heat flux over East Asia. Further analysis of STEA exhibits a general consistent pattern between the simulation and the reanalysis, while the intensity of the northern STEA branch associated with the EAPJ is greatly reduced. The deficiencies of eddy momentum and heat flux transport and accompanied eddy forcing may contribute to the biases of the simulated upper-tropospheric jet streams, suggesting the potential importance of midlatitude internal atmospheric dynamics in shaping the tropospheric general circulation, which is not yet fully and accurately resolved in the current BCC-CSMI.1.

Diagnostic Study of Global Energy Cycle of the GRAPES Global Model in the Mixed Space-Time Domain

Some important diagnostic characteristics for a model’s physical background are reflected in the model’s energy transport, conversion, and cycle. Diagnosing the atmospheric energy cycle is a suitable way towards understanding and improving numerical models. In this study, formulations of the “Mixed Space-Time Domain”energy cycle are calculated and the roles of stationary and transient waves within the atmospheric energy cycle of the Global-Regional Assimilation and Prediction System （GRAPES） model are diagnosed and compared with the NCEP analysis data for July 2011. Contributions of the zonal-mean components of the energy cycle are investigated to explain the performance of numerical models. The results show that the GRAPES model has the capability to reproduce the main features of the global energy cycle as compared with the NCEP analysis. Zonal available potential energy （AZ） is converted into stationary eddy available potential energy （ASE） and transient eddy available potential energy （ATE）, and ASE and ATE have similar values. The nonlinear conversion between the two eddy energy terms is directed from the stationary to the transient. AZ becomes larger with increased forecast lead time, reflecting an enhancement of the meridional temperature gradient, which strengthens the zonal baroclinic processes and makes the conversion from AZ to eddy potential energy larger, especially for CAT （conversion from AZ to ATE）. The zonal kinetic energy （KZ） has a similar value to the sum of the stationary and transient eddy kinetic energy. Barotropic conversions are directed from eddy to zonal kinetic energy. The zonal conversion from AZ to KZ in GRAPES is around 1.5 times larger than in the NCEP analysis. The contributions of zonal energy cycle components show that transient eddy kinetic energy （KTE） is associated with the Southern Hemisphere subtropical jet and the conversion from KZ to KTE reduces in the upper tropopause near 30？S. The nonlinear barotropic conversion between stationary and transient kinetic energy terms （CKTE） is reduced predominantly by the weaker KTE.

The Riemann Problem for Chaplygin Gas Flow in a Duct with Discontinuous Cross-Section

The fluid flows in a variable cross-section duct are nonconservative because of the source term.Recently,the Riemann problem and the interactions of the elementary waves for the compressible isentropic gas in a variable cross-section duct were studied.In this paper,the Riemann problem for Chaplygin gas flow in a duct with discontinuous cross-section is studied.The elementary waves include rarefaction waves,shock waves,delta waves and stationary waves.